Lars Magnus Hvattum

• Alteren, Johanne; Hvattum, Lars Magnus; Oskars, Trond Roger; Straume, Solveig & Teryokhin, Sergei (2026). Tidens mangfold. In Alteren, Johanne; Hvattum, Lars Magnus; Oskars, Trond Roger; Straume, Solveig & Teryokhin, Sergei (Ed.), Tid. Fjordantologien 2026. Scandinavian University Press (SCUP). ISSN 9788294167364. p. 13–19. doi: 10.18261/9788294167371-26-01. Full text in Research Archive
• Konovalenko, Anna; Hvattum, Lars Magnus & Iversen, Kim Aleksander Hammer (2026). Data describing planned routes and driven routes from a last-mile delivery vehicle routing problem. Data in Brief. 66(June). doi: 10.1016/j.dib.2026.112744. Full text in Research Archive Show summary

  This dataset provides real-world last-mile delivery routes from a logistics company, offering valuable resources for research in route optimization and logistics. The dataset addresses a substantial gap between theoretical route planning and routing performed by drivers who often do not follow the proposed routes. The dataset comprises 19,497 pairs of routes, including both planned routes, generated by human dispatchers employing heuristic optimization tools, and the routes that the drivers eventually followed in practice. The routes were completed by 400 unique drivers, covering 10,864 unique locations. In the dataset, the routes are presented as sequences of stops, where each stop is a separate row in the presented datafile. The dataset includes detailed information on routes, stops and drivers’ identifiers, timing, and distance measurements. It allows for a deeper analysis of driver behavior patterns, factors of route deviations, and their impact on delivery performance.

• Konovalenko, Anna; Hvattum, Lars Magnus & Urrutia, Sebastián (2026). Two paradigms for combining optimization and satisfiability : Maximum satisfiability and optimum satisfiability problems. Journal of Information and Optimization Sciences. ISSN 0252-2667. 47(2), p. 399–427. doi: 10.47974/jios-1392. Full text in Research Archive Show summary

  Maximum satisfiability (MaxSAT) and optimum satisfiability (OptSAT) problems are two optimization versions of the NP-complete Boolean satisfiability problem. In the literature, these versions have been described and tackled separately by using specialized solvers for each problem. This paper investigates a connection between MaxSAT and OptSAT where each problem can be reduced to the other. We consider several heuristic solvers and different sets of benchmark instances for each problem and investigate whether one class of solvers can tackle instances of the other problem with competitive results. Through computational experiments, we conclude that specialized solvers for one of the problems cannot compete with specialized solvers for the other problem and point out potential improvements of the solvers that are needed to successfully address a wider range of problem instances.

• Algendi, Abdalrahman; Urrutia, Sebastián & Hvattum, Lars Magnus (2025). A matheuristic for the home healthcare routing and scheduling problem with ferry-dependent travel times. Computers & Operations Research. ISSN 0305-0548. 188(2026)(April ). doi: 10.1016/j.cor.2025.107372. Full text in Research Archive Show summary

  Home healthcare in coastal regions of Norway presents unique operational challenges, as caregivers must combine road driving with scheduled ferry trips to reach certain patients. Unlike conventional time-dependent travel, fixed ferry timetables impose strict synchronization requirements, where a missed departure may lead to prolonged idle times, cascading delays, or even unserved patients. Despite its practical significance, this integration of driving and ferry transportation has not been examined in the home healthcare routing and scheduling literature, leaving a gap between research and practice. To address this gap, we formulate a mixed-integer linear programming model that incorporates patient and caregiver time windows, skill matching requirements, and synchronization constraints, including those induced by ferry-dependent travel. Given the complexity of the problem, we propose a two-phase matheuristic. Phase I constructs a feasible solution through a sequential graph expansion strategy that employs either classical or weighted proximity search, while Phase II refines this solution using the same search method. Computational tests on 20 realistic instances derived from two Norwegian healthcare centers demonstrate that the proposed method with weighted proximity search outperforms direct model solving and the classical proximity search in terms of feasibility, optimality, and solution quality. In particular, the method solves instances with up to 30 patients (50 visits) to proven optimality and identifies high-quality feasible solutions for instances with up to 80 patients (135 visits) within a 3600-second time limit. [Available online 18 December 2025]

• Sgall, Jiří; Balogh, János; Békési, József; Dósa, György; Hvattum, Lars Magnus & Tuza, Zsolt (2025). No tiling of the 70x70 square with consecutive squares. Theoretical Computer Science. ISSN 0304-3975. 1060(2026)(January ). doi: 10.1016/j.tcs.2025.115607. Full text in Research Archive Show summary

  The total area of the 24 squares 1 × 1, 2 × 2, …, 24 × 24 is equal to the area of the 70 × 70 square. Can this equation be demonstrated by a tiling of the 70 × 70 square with the 24 squares 1 × 1, 2 × 2, …, 24 × 24? The answer is “NO”, no such tiling exists. This has been demonstrated by computer search. However, until now, no proof without use of computer was given. We fill this gap and give a complete combinatorial proof.

• Konovalenko, Anna; Hvattum, Lars Magnus & Iversen, Kim Aleksander Hammer (2025). Predicting last-mile delivery route deviations using machine learning. Expert Systems With Applications. ISSN 0957-4174. 298(2026)(Part D). doi: 10.1016/j.eswa.2025.129921. Full text in Research Archive Show summary

  Route planning in last-mile delivery is a complex task with many challenges, directly impacting delivery efficiency and costs. Drivers often deviate from optimized planned routes based on their knowledge. Using the properties of machine learning, this study aims to determine whether machine learning techniques can effectively predict deviations by drivers from planned routes and quantify the extent of such deviations. We propose to predict route deviations by analyzing a logistics company’s historical data of planned and actual routes using deep neural networks, with the dataset made publicly available. Our methodology incorporates both regression and classification models. The regression model estimates the degree of deviation, while the classification model aims to predict whether the deviation from a planned route will exceed a given threshold, based on different deviation metrics. As the input, we leverage the sequential structure of the route with route properties and drivers information. The computational experiments explore extending the given input to the models and testing various state-of-art neural network architectures. Our results demonstrate strong performance on both tasks, with our models achieving 9 - 19% improvements in regression metrics and 3 - 15% improvements in classification metrics compared to specified benchmarks, with statistical tests confirming the significance of these improvements.

• Algendi, Abdalrahman; Urrutia, Sebastián; Hvattum, Lars Magnus & Melo, Rafael A. (2025). Nested logic-based Benders decomposition for an integrated home healthcare problem. European Journal of Operational Research. ISSN 0377-2217. 328(2026)(1), p. 32–48. doi: 10.1016/j.ejor.2025.06.006. Full text in Research Archive Show summary

  In this study, we apply nested logic-based Benders decomposition to solve an integrated home healthcare staffing, assignment, routing, and scheduling problem with application in Norway. The proposed method operates at two decomposition levels. Consequently, the entire problem is decomposed into three hierarchical sub-problems: the staffing problem, the assignment problem, and the routing and scheduling problem. These sub-problems are interrelated through two levels of logic-based Benders cuts. Computational experiments on 40 test instances demonstrate the superior performance of nested logic-based Benders decomposition compared to directly solving a mixed-integer linear programming model available in the literature. Specifically, the proposed solution method achieved proven optimality in 28 instances and provided feasible solutions for the remaining 12 instances. In contrast, directly solving the mixed-integer linear programming model yielded proven optimality in 16 instances, provided feasible solutions for 20 instances, and failed to find feasible solutions for 4 instances within the same computational time limit.

• Danielsen, Ketil & Hvattum, Lars Magnus (2025). Solution-based versus attribute-based tabu search for binary integer programming. International Transactions in Operational Research. ISSN 0969-6016. 32(6), p. 3780–3800. doi: 10.1111/itor.70011. Full text in Research Archive
• Konovalenko, Anna; Hvattum, Lars Magnus & Msakni, Mohamed Kais (2025). Using machine learning to identify hidden constraints in vehicle routing problems. Computers & Operations Research. ISSN 0305-0548. 179(July). doi: 10.1016/j.cor.2025.107029. Full text in Research Archive Show summary

  Last-mile delivery involves a series of complex tasks in an unpredictable environment. Decision support tools based on optimization algorithms construct efficient routes for drivers, optimizing the cost of making deliveries. However, drivers often deviate from these routes due to factors not considered in the decision-making process. This discrepancy raises the question of how to identify routes that are useable in real-world scenarios. Our research proposes using modern machine learning techniques to classify routes based on their practical usability. In a controlled environment, we demonstrate that machine learning can learn hidden factors influencing route viability by focusing on variants of the vehicle routing problem with additional constraints like time window, capacity and precedence. For each underlying constraint, we show that a machine learning model can be trained to classify routes based on whether or not they violate the constraint. Using datasets generated from well-known benchmark instances, we present computational experiments to evaluate model performance. We discuss which types of constraints are more challenging to recognize and how large a dataset must be to allow for accurate classification. This research has the potential to improve existing decision tools, enabling them to generate routes that better account for real-world complexities.

• Konovalenko, Anna & Hvattum, Lars Magnus (2025). Exploring tabu tenure policies with machine learning. Electronics (Basel). 14(13). doi: 10.3390/electronics14132642. Full text in Research Archive Show summary

  Tabu search is a well-known local search-based metaheuristic, widely used for tackling complex combinatorial optimization problems. As with other metaheuristics, its performance is sensitive to parameter configurations, requiring careful tuning. Among the critical parameters of tabu search is the tabu tenure. This study aims to identify key search attributes and instance characteristics that can help establish comprehensive guidelines for a robust tabu tenure policy. First, a review different tabu tenure policies is provided. Next, critical baselines to understand the fundamental relationship between tabu tenure settings and solution quality are established. We verified that generalizable parameter selection rules provide value when implementing metaheuristic frameworks, specifically showing that a more robust tabu tenure policy can be achieved by considering whether a move is improving or non-improving. Finally, we explore the integration of machine learning techniques that exploits both dynamic search attributes and static instance characteristics to obtain effective and robust tabu tenure policies. A statistical analysis confirms that the integration of machine learning yields statistically significant performance gains, achieving a mean improvement of 12.23 (standard deviation 137.25, 𝑛= 10,000 observations) when compared to a standard randomized tabu tenure selection (p-value < 0.001). While the integration of machine learning introduces additional computational overhead, it may be justified in scenarios where heuristics are repeatedly applied to structurally similar problem instances, and even small improvements in solution quality can accumulate to large overall gains. Nonetheless, our methods have limitations. The influence of the tabu tenure parameter is difficult to detect in real time during the search process, complicating the reliable identification of when and how tenure adjustments impact search performance. Additionally, the proposed policies exhibit similar performance on the chosen instances, further complicating the evaluation and differentiation of policy effectiveness.

• Hvattum, Lars Magnus (2025). Where to Split in Hybrid Genetic Search for the Capacitated Vehicle Routing Problem. Algorithms. 18(3). doi: 10.3390/a18030165. Full text in Research Archive Show summary

  One of the best heuristic algorithms for solving the capacitated vehicle routing problem is a hybrid genetic search. A critical component of the search is a splitting procedure, where a solution encoded as a giant tour of nodes is optimally split into vehicle routes using dynamic programming. However, the current state-of-the-art implementation of the splitting procedure assumes that the start of the giant tour is fixed as a part of the encoded solution. This paper examines whether the fixed starting point is a significant drawback. Results indicate that simple adjustments of the starting point for the splitting procedure can improve the performance of the genetic search, as measured by the average primal gaps of the final solutions obtained, by 3.9%.

• Balogh, Janos; Dosa, Gyorgy; Hvattum, Lars Magnus; Olaj, Tomas Attila Paulsen; Szalkai, Istvan & Tuza, Zsolt (2025). Covering a square with consecutive squares. Annals of Operations Research. ISSN 0254-5330. 350(3), p. 911–926. doi: 10.1007/s10479-025-06633-5. Full text in Research Archive
• Bentsen, Håkon; Reznik, Alexandr & Hvattum, Lars Magnus (2024). Testing initial solutions in a variable neighbourhood search for binary integer programming problems. International Journal of Metaheuristics (IJMHeur). ISSN 1755-2176. doi: 10.1504/IJMHEUR.2024.10066097. Full text in Research Archive
• Sgall, Jiří; Balogh, János; Békési, József; Dósa, György; Hvattum, Lars Magnus & Tuza, Zsolt (2024). No tiling of the 70×70 square with consecutive squares. In Broder, Andrei Z. & Tamir, Tami (Ed.), 12th International Conference on Fun with Algorithms (FUN 2024). Schloss Dagstuhl Leibniz - Zentrum für Informatik. ISSN 9783959773140. p. 1–16. doi: 10.4230/LIPIcs.FUN.2024.28. Full text in Research Archive Show summary

  The total area of the 24 squares of sizes 1, 2, . . . , 24 is equal to the area of the 70 × 70 square. Can this equation be demonstrated by a tiling of the 70 × 70 square with the 24 squares of sizes 1, 2, . . . , 24? The answer is “NO”, no such tiling exists. This has been demonstrated by computer search. However, until now, no proof without use of computer was given. We fill this gap and give a complete combinatorial proof. Keywords and phrases: Square packing; Gardner’s problem; Combinatorial proof.

• Algendi, Abdalrahman; Urrutia, Sebastián; Hvattum, Lars Magnus & Helgheim, Berit (2024). Home healthcare staffing, routing, and scheduling problem with multiple shifts and emergency considerations. Networks: An International Journal. ISSN 0028-3045. 85(2), p. 223–242. doi: 10.1002/net.22260. Full text in Research Archive Show summary

  Effective planning of human resources is critical in designing an efficient home healthcare system. In this study, we present a novel home healthcare staffing, routing, and scheduling problem inspired by a real-world application. The proposed problem addresses a set of patients, with varying daily visit requirements, being served by a set of caregivers with different qualification levels over a multi-day multi-shift planning horizon. The problem aims to minimize the number of extra shifts for caregivers, maximize the allocation of caregivers to emergencies, and minimize the sum of route durations over the planning horizon. These objectives are optimized hierarchically while considering a set of restrictions, including time windows, skill matching, synchronization, care continuity, and labor regulations. To tackle the problem, we introduce a mixed-integer linear programming model. The model is then extended and two sets of valid inequalities are incorporated to enhance its tightness. Computational experiments are conducted on a set of 20 instances. The results highlight the efficiency of the proposed extension in increasing both the number of instances that can be solved to optimality and the number of instances for which a feasible solution is found.

• Konovalenko, Anna & Hvattum, Lars Magnus (2024). Optimizing a Dynamic Vehicle Routing Problem with Deep Reinforcement Learning: Analyzing State-Space Components. Logistics. 8(4), p. 1–18. doi: 10.3390/logistics8040096. Full text in Research Archive Show summary

  Background: The dynamic vehicle routing problem (DVRP) is a complex optimization problem that is crucial for applications such as last-mile delivery. Our goal is to develop an application that can make real-time decisions to maximize total performance while adapting to the dynamic nature of incoming orders. We formulate the DVRP as a vehicle routing problem where new customer requests arrive dynamically, requiring immediate acceptance or rejection decisions. Methods: This study leverages reinforcement learning (RL), a machine learning paradigm that operates via feedback-driven decisions, to tackle the DVRP. We present a detailed RL formulation and systematically investigate the impacts of various state-space components on algorithm performance. Our approach involves incrementally modifying the state space, including analyzing the impacts of individual components, applying data transformation methods, and incorporating derived features. Results: Our findings demonstrate that a carefully designed state space in the formulation of the DVRP significantly improves RL performance. Notably, incorporating derived features and selectively applying feature transformation enhanced the model’s decision-making capabilities. The combination of all enhancements led to a statistically significant improvement in the results compared with the basic state formulation. Conclusions: This research provides insights into RL modeling for DVRPs, highlighting the importance of state-space design. The proposed approach offers a flexible framework that is applicable to various variants of the DVRP, with potential for validation using real-world data.

• Knudseth, Sunniva Haukvik; Molland, Even; Hoff, Arild; Hvattum, Lars Magnus & Oppen, Johan (2024). Decision support for allocating farmed fish to customer orders using a bi-objective optimization model. Decision Making in Manufacturing and Services. ISSN 1896-8325. 16, p. 67–90. doi: 10.7494/dmms.2022.16.5019. Full text in Research Archive Show summary

  Aquaculture is an important industry in certain coastal areas. Focusing on farming of salmon and trout, an operational planning problem arises with the goal of allocating supply of fish to demand expressed through customer orders. This paper provides a conceptual model of such a planning problem, defines a corresponding bi-objective mathematical programming model. The problem is novel with respect to the structure of the transportation of fish, and the rules for satisfying customer orders with respect to fish size, quality, certification, and health status. Computational experiments are conducted to gain further insights into the use of the provided model to provide support for planners involved in the operational decision making. Results indicate that the bi-objective optimization model can be useful in situations where supply is insufficient to cover all the demand within a given planning horizon.

• Shaabani, Homayoun; Hvattum, Lars Magnus; Laporte, Gilbert & Hoff, Arild (2024). Stability metrics for a maritime inventory routing problem under sailing time uncertainty. EURO Journal on Transportation and Logistics. ISSN 2192-4376. 13. doi: 10.1016/j.ejtl.2024.100146. Full text in Research Archive Show summary

  We study a multi-product maritime inventory routing problem (MIRP) with sailing time uncertainty. We explicitly consider the replanning that happens after uncertainty is revealed. The objective is to determine the stability of the adjusted plans after the occurrence of an uncertain event and to evaluate the effect of incorporating different stability metrics in the rescheduling process. Five stability metrics are introduced, and mathematical formulations of the MIRP incorporating each metric are presented. A reoptimization framework is then used to analyze the impact of each stability metric. Calculations are performed using 360 instances. The main result is that adjustments to the original plan occur at no additional cost almost 50% of the time. If decision makers want a more stable plan, they should accept a 5% cost deterioration, resulting in 20% more stable solutions.

• Bisadi, Arameh; Zare, Amir & Hvattum, Lars Magnus (2024). Optimizing spare part management for vessels in liner shipping. In Bányai, Tamás (Eds.), Recent topics in maintenance management. IntechOpen. ISSN 9780854669165. doi: 10.5772/intechopen.1005036. Full text in Research Archive Show summary

  Seagoing vessels require regular maintenance. Preventive maintenance can be planned ahead of time, and can be executed either at sea or while visiting a port. The spare parts used when performing maintenance can come from warehouses that store the parts until needed at a port, but they can also come from on-vessel storages. Some spare parts must be available on a vessel at all times, in the case that corrective maintenance is required. This chapter considers liner shipping, where each vessel follows a pre-planned itinerary and a number of preventive maintenance tasks have been scheduled over time. A mathematical model is proposed that can be used to decide where to store spare parts, how many spare parts to keep in inventory, when to order spare parts from suppliers, and when and where to perform the scheduled maintenance tasks. Numerical experiments show that the model can be solved very quickly. The model can thus be used as a tool to support making decisions related to inventory management for spare parts.

• Fagerholt, Kjetil; Hvattum, Lars Magnus; Papageorgiou, Dimitri J. & Urrutia, Sebastián (2023). Maritime inventory routing : recent trends and future directions. International Transactions in Operational Research. ISSN 0969-6016. 30(6), p. 3013–3056. doi: 10.1111/itor.13313. Full text in Research Archive Show summary

  We review recent literature pertaining to the maritime inventory routing problem (MIRP), a stimulating, albeit niche, subclass of vendor-managed inventory problems. MIRPs deal with optimally distributing products with a (typically heterogeneous) vessel fleet between production and consumption ports with inventory tracking and inventory limits. We present two mixed-integer linear programming models for the MIRP—one based on discrete time, the other based on continuous time—and we discuss the advantages and disadvantages of each of the two modeling approaches. In surveying more than 50 papers spanning the decade 2013–2023, we investigate MIRP variants from many different applications and discuss how these have been modeled and solved. Our purpose is to provide a comprehensive overview of state-of-the-art MIRP research published in this period, collated along multiple dimensions. In addition to providing information about available test instances, we highlight recent trends and interesting avenues for future research. As such, we believe this survey will be useful to students, researchers, and practitioners in this domain.

• Skålnes, Jørgen; Ahmed, Mohamed Ben; Hvattum, Lars Magnus & Stålhane, Magnus (2023). New benchmark instances for the inventory routing problem. European Journal of Operational Research. ISSN 0377-2217. 313(3), p. 992–1014. doi: 10.1016/j.ejor.2023.08.010. Full text in Research Archive Show summary

  The existing sets of benchmark instances for the inventory routing problem (IRP) have been beneficial for investigating and illustrating the properties of the problem. However, they possess certain features and design choices that are not necessarily representative of all real-world IRPs. Therefore, we propose a new collection of 270 real-world-like instances ranging from 10 to 200 customers. These instances vary in terms of the number of vehicles and their capacity, the length of the planning horizon, the demand structure, and the geographical distribution of customers. Transportation and inventory holding costs resemble costs found in practice. We present an instance space analysis showing that the new instances nicely complement the original instances. To derive lower and upper bounds for each instance, we present computational experiments with two high-quality solution methods: a matheuristic and an exact branch-and-cut method. The results confirm that the new set of instances is hard to solve with the proposed methods, and they demonstrate the need for developing new solution methods. Keywords: distribution, test instance, branch-and-cut, matheuristic, vendor-managed inventory

• Shaabani, Homayoun; Hvattum, Lars Magnus; Laporte, Gilbert & Hoff, Arild (2023). A goal programming model for the stability analysis of a maritime inventory routing replanning problem. Maritime Transport Research. 5(December). doi: 10.1016/j.martra.2023.100101. Full text in Research Archive
• Shaabani, Homayoun; Hoff, Arild; Hvattum, Lars Magnus & Laporte, Gilbert (2023). A matheuristic for the multi-product maritime inventory routing problem. Computers & Operations Research. ISSN 0305-0548. 154(June), p. 1–19. doi: 10.1016/j.cor.2023.106214. Full text in Research Archive Show summary

  This paper considers a multi-product maritime inventory routing problem in which the routes of the vessels are determined while inventories in the ports must remain within given bounds. Since there is more than one product, each port can be a consumption port for one product and a production port for another product. We propose a matheuristic to deal with large-size instances with a planning horizon of 60 days. The first phase of the heuristic identifies a subset of the arcs in order to use them as input parameters for the second phase. In the second phase, a mathematical model is solved with the selected arcs fixed. These two phases are iterated until a stopping criterion is satisfied. The solutions produced by the matheuristic are compared with those obtained by CPLEX. Comparing the single-product version of the problem with the multi-product version revealed that instances with multiple products require significantly more run time compared with the single-product instances.

• Ahmed, Mohamed Ben; Hvattum, Lars Magnus & Agra, Agostinho (2023). The effect of different mathematical formulations on a matheuristic algorithm for the production routing problem. Computers & Operations Research. ISSN 0305-0548. 155(July), p. 1–19. doi: 10.1016/j.cor.2023.106232. Full text in Research Archive Show summary

  We perform an experimental study to evaluate the performance of a matheuristic for the production routing problem (PRP). First, we develop a basic matheuristic that prescribes starting from a partial initial solution, completing it using a sequence of constructive heuristics, and improving it using a general-purpose mixed-integer programming heuristic. Next, we investigate the effect of three state-of-the-art mathematical formulations on the proposed matheuristic convergence. The formulations are implemented and tested with and without the use of valid inequalities. In addition, by suggesting different techniques to generate a feasible starting solution for our matheuristic, we assess the contribution of an initial solution to the matheuristic’s overall performance. We conduct extensive computational experiments on benchmark data instances for the PRP. The results show that a proper choice of an embedded mathematical formulation depends on the data instances’ features, such as the number of customers and the length of the planning horizon. The comparisons undertaken in this study indicate that having a better initial solution does not necessarily lead to finding a better final solution. Keywords: lot sizing, inventory routing, mixed integer formulation, valid inequality, proximity search, experimental analysis

• Hvattum, Lars Magnus; Kriegl, Marc-André & Čulík, Miroslav (2023). Identifying talent in association football through plus-minus ratings. In Dominicy, Yves & Ley, Christophe (Ed.), Statistics meets sports : what we can learn from sports data. Cambridge Scholars Publishing. ISSN 9781527592735. p. 175–200. Full text in Research Archive Show summary

  This book inscribes itself in the growing context of sports analytics and the combination of data science with sports medicine, which deeply impact the world of sports. Today, ever-more data are being collected and lead to ground-breaking and game-changing new insights. This book provides a solid understanding of these new trends in sports and offers the interested reader with a starting point from which to dive into this blossoming field.

• Moazzeni, Sahar; Darmian, Sobhan Mostafayi & Hvattum, Lars Magnus (2023). Multiple criteria decision making and robust optimization to design a development plan for small and medium-sized enterprises in the east of Iran. Operational Research. ISSN 1109-2858. 23. doi: 10.1007/s12351-023-00761-1. Full text in Research Archive Show summary

  This paper is based on a project of developing small and medium-sized enterprises in South Khorasan, Iran. A combination of multiple criteria decision making and robust multi-objective optimization is used for prioritizing industrial clusters and optimally assigning governmental funds. First, criteria for evaluating clusters are weighted using the best-worst method and clusters are prioritized using the VIKOR method. Second, governmental funding is assigned to the highest priority cluster using robust multi-objective mathematical programming. An innovative method is applied to identify the solution of the Pareto-front with the highest efficiency. In a case study from South Khorasan, computational results show that international market share attraction is the most important criterion and the age of the cluster is the least important criterion in the development of the industrial clusters. The cluster defined for barberry and jujube fruits is determined to be the first-ranked cluster. Most of the total available budget for the development of this cluster is assigned to action plans for marketing and trade development and for investment and financial planning. The proposed methodology thus successfully aided the decision makers to plan their work regarding funding of industrial clusters. We believe that the methodology can be applied as a general tool to help managers of industrial development to better assign governmental funding to develop industrial clusters.

• Abraham, Gyula; Dósa, György; Hvattum, Lars Magnus; Olaj, Tomas Attila Paulsen & Tuza, Zsolt (2023). The board packing problem. European Journal of Operational Research. ISSN 0377-2217. 308(3), p. 1056–1073. doi: 10.1016/j.ejor.2023.01.030. Full text in Research Archive Show summary

  We introduce the board packing problem (BoPP). In this problem we are given a rectangular board with a given number of rows and columns. Each position of the board has an integer value representing a gain, or revenue, that is obtained if the position is covered. A set of rectangles is also given, each with a given size and cost. The objective is to purchase some rectangles to place on the board so as to maximize the profit, which is the sum of the gain values of the covered cells minus the total cost of purchased rectangles. This problem subsumes several natural optimization problems that arise in practice. A mixed-integer programming model for the BoPP problem is provided, along with a proof that BoPP is NP-hard by reduction from the satisfiability problem. An evolutionary algorithm is also developed that can solve large instances of BoPP. We introduce benchmark instances and make extensive computer examinations. Keywords: combinatorial optimization, genetic algorithm, binary integer programming, covering, location problems

• Gjøen, Phillip Sa-Ut; Hvattum, Sofus August; Moltubak, Eirik Malme & Hvattum, Lars Magnus (2023). When is 2 better than 3 in basketball? Statistica Applicata. ISSN 1125-1964. 35(1), p. 1–15. doi: 10.26398/IJAS.0035-003. Full text in Research Archive Show summary

  A recent trend in basketball is that teams are taking more shots outside of the three-point line and fewer shots inside. This is an advantage since the expected number of points scored, in general, is slightly higher for three-point shots. Through simulations, this paper shows that there are game situations where a strategy of taking fewer three-point attempts at the expense of more two-point attempts will improve the probability of winning the game. Keywords: simulation, coaching, strategy, sports

• Balogh, János; Dósa, György; Hvattum, Lars Magnus; Olaj, Tomas Attila Paulsen & Tuza, Zsolt (2022). Guillotine cutting is asymptotically optimal for packing consecutive squares. Optimization Letters. ISSN 1862-4472. 16(9), p. 2775–2785. doi: 10.1007/s11590-022-01858-w. Full text in Research Archive Show summary

  More than half a century ago Martin Gardner popularized a question leading to the benchmark problem of determining the minimum side length of a square into which the squares of sizes 1, 2,..., n can be packed without overlap. Constructions are known for a certain range of n, and summing up the areas yields that a packing in a square of size smaller than N :=√n(n + 1)(2n + 1)/6) is not possible. Here we prove that an asymptotically minimal packing exists in a square of size N +cn+O(√n) with c < 1, and such a packing is achievable with guillotine-cuts. An improved construction is also given for the case where the constraint of guillotine cutting is dropped. Keywords: Square packing · Guillotine cut · Asymptotic analysis · Gardner’s problem · Square the square · Recursive algorithm.

• Zojaji, Amir; Soltaniani, Kiarash; Hvattum, Lars Magnus & Urrutia, Sebastián (2022). Cyclic solutions to a maritime inventory routing problem. Maritime Transport Research. 3, p. 1–13. doi: 10.1016/j.martra.2022.100074. Full text in Research Archive Show summary

  An inventory routing problem occurs when a company manages inventories both at production sites and consumption sites while also being in charge of the transportation of goods. We consider a maritime inventory routing problem where inventories are located at ports and a single product is transported between these ports using a heterogeneous fleet of vessels. As opposed to standard research on such maritime inventory routing problems, a model is developed that produces cyclic plans that are repeatable. Such plans are more costly than plans found using standard non-cyclic models, but the latter suffer from end-of-horizon effects due to being over-optimistic and making myopic decisions in accordance with an objective of minimizing costs.

• Algendi, Abdalrahman; Urrutia, Sebastián & Hvattum, Lars Magnus (2022). Optimizing production levels in maritime inventory routing with load-dependent speed optimization. Flexible Services and Manufacturing Journal. ISSN 1936-6582. 35(1), p. 111–141. doi: 10.1007/s10696-022-09460-z. Full text in Research Archive Show summary

  Maritime inventory routing problems with load-dependent speed optimization involves determining optimal routes, as well as vessel speeds and loads at these routes, so that inventory limits are satisfied at both production and consumption ports. This paper considers a variant where production rates can be selected from several available alternative production levels, as opposed to the normal situation where production rates are chosen a priori. In both cases, production rates remain constant for the duration of the planning horizon. The effect on transportation costs when considering production levels as decision variables is evaluated. The resulting solutions are compared with solutions obtained when production rates are considered as fixed parameters. Computational experiments on a set of benchmark instances from the literature confirm that the process of determining the optimal production levels plays a crucial role in improving the solutions to maritime inventory routing problems with load-dependent speed optimization. Optimizing the production levels can reduce transportation costs by up to 35%.

• Bentsen, Håkon; Hoff, Arild & Hvattum, Lars Magnus (2022). Exponential extrapolation memory for tabu search. EURO Journal on Computational Optimization. ISSN 2192-4406. 10. doi: 10.1016/j.ejco.2022.100028. Full text in Research Archive Show summary

  Tabu search is a well-established metaheuristic framework for solving hard combinatorial optimization problems. At its core, the method uses different forms of memory to guide a local search through the solution space so as to identify high-quality local optima while avoiding getting stuck in the vicinity of any particular local optimum. This paper examines characteristics of moves that can be exploited to make good decisions about steps that lead away from recently visited local optima and towards a new local optimum. Our approach uses a new type of adaptive memory based on a construction called exponential extrapolation. The memory operates by means of threshold inequalities that ensure selected moves will not lead to a specified number of most recently encountered local optima. Computational experiments on a set of one hundred different benchmark instances for the binary integer programming problem suggest that exponential extrapolation is a useful type of memory to incorporate into a tabu search. Keywords: 0-1 Integer programming, binary optimization, adaptive memory, tabu search

• Pluskal, Jaroslav; Šomplák, Radovan; Hrabec, Dušan; Nevrlý, Vlastimír & Hvattum, Lars Magnus (2022). Optimal location and operation of waste-to-energy plants when future waste composition is uncertain. Operational Research. ISSN 1109-2858. 22, p. 5765–5790. doi: 10.1007/s12351-022-00718-w. Full text in Research Archive Show summary

  In many countries, waste management is increasingly geared towards a circular economy, aiming for a sustainable society with less waste generation, fewer landfills, and a higher rate of recycling. Waste-to-Energy (WtE) plants, which convert waste into heat and energy, can contribute to the circular economy by utilizing types of waste that cannot be recycled. Due to the varying quality of sorting and socio-economic conditions in individual regions, the waste composition differs between regions and has an uncertain future development. Waste composition significantly affects the operation of WtE plants due to differences in energy potential. This paper supports strategic capacity planning for waste energy recovery by introducing a two-stage stochastic mixed-integer linear programming model that captures waste composition uncertainty through scenarios of possible future development. The results of the model provide insights into the economics of operation and identify important factors in the sustainability of the waste handling system. The model is demonstrated on an instance with six scenarios for waste management in the Czech Republic for the year 2030. The solution of the proposed model is to build 14 new WtE plants with a total capacity of 1970 kt in addition to the four existing plants with a capacity of 831 kt. The annual energy recovery capacity is expected to increase almost four times to satisfy EU directives that restrict waste landfilling.

• Hrabec, Dušan; Hvattum, Lars Magnus & Hoff, Arild (2022). The value of integrated planning for production, inventory, and routing decisions : a systematic review and meta-analysis. International Journal of Production Economics. ISSN 0925-5273. 248(June), p. 1–13. doi: 10.1016/j.ijpe.2022.108468. Full text in Research Archive Show summary

  This paper presents a comparison of sequential and integrated planning for the production routing problem, in which production, inventory, and routing decisions must be made. The aim is to estimate the expected value of treating the problems as a whole, rather than making decisions sequentially. In particular, the following research questions are posed: What is the expected cost reduction when combining production, inventory, and routing in a single modeling framework, compared to solving the problems individually in a sequence? Under which circumstances is it most beneficial to tackle an integrated problem? In other words, the goal is to establish whether the solutions obtained by the integration are clearly better than approximate solutions obtained by a more simplified process, and if so, under which circumstances this difference is the most pronounced. To answer these research questions, a systematic review was performed, resulting in a set of 20 relevant articles that were analyzed in depth. For the first research question, computational results from 15 articles were obtained and analyzed through a meta-analysis. The analysis estimated an expected cost savings provided by integration of 11.08%, with a 95% confidence interval of [6.58%, 15.58%]. For the second research question, individual results obtained via sensitivity analyses in 20 relevant articles were summarized qualitatively, enabling insights into how the potential savings by integration is influenced by parameters such as the degrees of freedom, the cost, and the capacity. Keywords: sequential planning, value of integration, distribution, production routing problem

• Rodrigues, Filipe; Agra, Agostinho; Hvattum, Lars Magnus & Requejo, Cristina (2022). Weighted iterated local branching for mathematical programming problems with binary variables. Journal of Heuristics. ISSN 1381-1231. 28(3), p. 329–350. doi: 10.1007/s10732-022-09496-2. Full text in Research Archive Show summary

  Local search algorithms are frequently used to handle complex optimization problems involving binary decision variables. One way of implementing a local search procedure is by using a mixed-integer programming solver to explore a neighborhood defined through a constraint that limits the number of binary variables whose values are allowed to change in a given iteration. Recognizing that not all variables are equally promising to change when searching for better neighboring solutions, we propose a weighted iterated local branching heuristic. This new procedure differs from similar existing methods since it considers groups of binary variables and associates with each group a limit on the number of variables that can change. The groups of variables are defined using weights that indicate the expected contribution of flipping the variables when trying to identify improving solutions in the current neighborhood. When the mixed-integer programming solver fails to identify an improving solution in a given iteration, the proposed heuristic may force the search into new regions of the search space by utilizing the group of variables that are least promising to flip. The weighted iterated local branching heuristic is tested on benchmark instances of the optimum satisfiability problem, and computational results show that the weighted method is superior to an alternative method without weights.

• Hvattum, Lars Magnus (2022). Adjusting the order crossover operator for capacitated vehicle routing problems. Computers & Operations Research. ISSN 0305-0548. 148(December), p. 1–8. doi: 10.1016/j.cor.2022.105986. Full text in Research Archive Show summary

  The capacitated vehicle routing problem is a much studied combinatorial optimization problem, reflecting its practical importance within areas such as logistics. The problem is computationally intractable, and heuristics are commonly applied for solving large instances. Among the best heuristics available is a hybrid genetic search that consists of mechanisms from evolutionary algorithms and a range of local search operators. This heuristic applies an order crossover operator that takes as input two existing solutions and produces as output a new solution for the search to explore. An open-source implementation of the heuristic is available, in which the order crossover operator represents 1.4% of the code. This work discusses potential short-comings of the traditional order crossover operator and proposes an adjusted operator. The new operator is evaluated on standard benchmark test instances, and is shown to reduce the gaps to best-known solutions by 4.2%. Keywords: vehicle routing problem, genetic algorithm, open source, genetic operator

• Bentsen, Håkon & Hvattum, Lars Magnus (2022). Variable neighborhood search for binary integer programming problems. International Journal of Metaheuristics (IJMHeur). ISSN 1755-2176. 8, p. 1–26. doi: 10.1504/IJMHEUR.2022.10052729. Full text in Research Archive Show summary

  General solvers exist for several types of optimisation problems, with the commercially available solvers for mixed integer programming (MIP) being a prime example. Although binary integer programming (BIP) can be used to model a wide variety of important combinatorial optimisation problems, relatively few contributions have been made to develop heuristic algorithms for BIP. This paper examines whether variable neighbourhood search can be successfully used to tackle BIP instances, when avoiding very large neighbourhoods explored by the means of external MIP solvers. The results indicate that methods based on variable neighbourhood search are more successful than exact and heuristic commercial solvers on certain types of instances, while the opposite holds true on others. A general variable neighbourhood search proves very effective on instances with up to 200 variables, in particular some instances that are tightly constrained. Keywords: black-box solver, 0-1 integer programming, variable neighbourhood descent, VND, mathematical programming

• Bolstad, Kamilla Hamre; Joshi, Manu; Hvattum, Lars Magnus & Stålhane, Magnus (2022). Composing vessel fleets for maintenance at offshore wind farms by solving a dual-level stochastic programming problem using GRASP. Logistics. 6(1), p. 1–22. doi: 10.3390/logistics6010006. Full text in Research Archive Show summary

  Background: Dual-level stochastic programming is a technique that allows modelling uncertainty at two different levels, even when the time granularity differs vastly between the levels. In this paper we study the problem of determining the optimal fleet size and mix of vessels performing maintenance operations at offshore wind farms. In this problem the strategic planning spans decades, while operational planning is performed on a day-to-day basis. Since the operational planning level must somehow be taken into account when making strategic plans, and since uncertainty is present at both levels, dual-level stochastic programming is suitable. Methods: We present a heuristic solution method for the problem based on the greedy randomized adaptive search procedure (GRASP). To evaluate the operational costs of a given fleet, a novel fleet deployment heuristic (FDH) is embedded into the GRASP. Results: Computational experiments show that the FDH produces near optimal solutions to the operational day-to-day fleet deployment problem. Comparing the GRASP to exact methods, it produces near optimal solutions for small instances, while significantly improving the primal solutions for larger instances, where the exact methods do not converge. Conclusions: The proposed heuristic is suitable for solving realistic instances, and produces near optimal solution in less than 2 h. View Full-Text Keywords: heuristic, fleet size and mix, offshore wind, uncertainty, multi-horizon

• Amaral, Heber F.; Urrutia, Sebastián & Hvattum, Lars Magnus (2021). Delayed improvement local search. Journal of Heuristics. ISSN 1381-1231. 27(5), p. 923–950. doi: 10.1007/s10732-021-09479-9. Full text in Research Archive Show summary

  Local search is a fundamental tool in the development of heuristic algorithms. A neighborhood operator takes a current solution and returns a set of similar solutions, denoted as neighbors. In best improvement local search, the best of the neighboring solutions replaces the current solution in each iteration. On the other hand, in first improvement local search, the neighborhood is only explored until any improving solution is found, which then replaces the current solution. In this work we propose a new strategy for local search that attempts to avoid low-quality local optima by selecting in each iteration the improving neighbor that has the fewest possible attributes in common with local optima. To this end, it uses inequalities previously used as optimality cuts in the context of integer linear programming. The novel method, referred to as delayed improvement local search, is implemented and evaluated using the travelling salesman problem with the 2-opt neighborhood and the max-cut problem with the 1-flip neighborhood as test cases. Computational results show that the new strategy, while slower, obtains better local optima compared to the traditional local search strategies. The comparison is favourable to the new strategy in experiments with fixed computation time or with a fixed target.

• Hvattum, Lars Magnus & Gelade, Garry A. (2021). Comparing bottom-up and top-down ratings for individual soccer players. International Journal of Computer Science in Sport. 20(1), p. 23–42. doi: 10.2478/ijcss-2021-0002. Full text in Research Archive Show summary

  Correctly assessing the contributions of an individual player in a team sport is challenging. However, an ability to better evaluate each player can translate into improved team performance, through better recruitment or team selection decisions. Two main ideas have emerged for using data to evaluate players: Top-down ratings observe the performance of the team as a whole and then distribute credit for this performance onto the players involved. Bottom-up ratings assign a value to each action performed, and then evaluate a player based on the sum of values for actions performed by that player. This paper compares a variant of plus-minus ratings, which is a top-down rating, and a bottom-up rating based on valuing actions by estimating probabilities. The reliability of ratings is measured by whether similar ratings are produced when using different data sets, while the validity of ratings is evaluated through the quality of match outcome forecasts generated when the ratings are used as predictor variables. The results indicate that the plus-minus ratings perform better than the bottom-up ratings with respect to the reliability and validity measures chosen and that plus-minus ratings have certain advantages that may be difficult to replicate in bottom-up ratings. Keywords: association football, ranking, prediction, plus-minus, validity

• Eetvelde, Hans Van; Hvattum, Lars Magnus & Ley, Christophe (2021). The probabilistic final standing calculator : a fair stochastic tool to handle abruptly stopped football seasons. AStA Advances in Statistical Analysis. ISSN 1863-8171. 107(1-2), p. 251–269. doi: 10.1007/s10182-021-00416-6. Full text in Research Archive Show summary

  The COVID-19 pandemic has left its marks in the sports world, forcing the full stop of all sports-related activities in the first half of 2020. Football leagues were suddenly stopped, and each country was hesitating between a relaunch of the competition and a premature ending. Some opted for the latter option and took as the final standing of the season the ranking from the moment the competition got interrupted. This decision has been perceived as unfair, especially by those teams who had remaining matches against easier opponents. In this paper, we introduce a tool to calculate in a fairer way the final standings of domestic leagues that have to stop prematurely: our Probabilistic Final Standing Calculator (PFSC). It is based on a stochastic model taking into account the results of the matches played and simulating the remaining matches, yielding the probabilities for the various possible final rankings. We have compared our PFSC with state-of-the-art prediction models, using previous seasons which we pretend to stop at different points in time. We illustrate our PFSC by showing how a probabilistic ranking of the French Ligue 1 in the stopped 2019–2020 season could have led to alternative, potentially fairer, decisions on the final standing.

• Silva, Rodrigo Ferreira da; Urrutia, Sebastián & Hvattum, Lars Magnus (2021). Extended high dimensional indexing approach for reachability queries on very large graphs. Expert Systems With Applications. ISSN 0957-4174. 181(November), p. 1–11. doi: 10.1016/j.eswa.2021.114962. Full text in Research Archive Show summary

  Given a directed acyclic graph G = (V,A) and two vertices u, v ∈ V , the reachability problem is to answer if there is a path from u to v in the graph. In the context of very large graphs, with millions of vertices and a series of queries to be answered, it is not practical to search the graph for each query. On the other hand, the storage of the full transitive closure of the graph is also impractical due to its O(|V |2) size. Scalable approaches aim to create indices used to prune the search during its execution. Negative indices may be able to determine (in constant time) that a query has a negative answer while positive indices may determine (again in constant time) that a query has a positive answer. In this paper we propose novel scalable approach called LYNX that uses a large number of topological sorts of G as a negative cut index without degrading the query time. A similar strategy is applied regarding a positive cut index. In addition, LYNX proposes a user-defined index size that enables the user to control the ratio between negative and positive cuts depending on the expected query pattern. We show by computational experiments that LYNX consistently outperforms the state-of-the-art approach in terms of query-time using the same index-size for graphs with high reachability ratio. In intelligent computer systems that rely on frequent tests of connectivity in graphs, LYNX can reduce the time delay experience by end users through a reduced query time. This comes at the expense of an increased setup time whenever the underlying graph is updated. Keywords: directed acyclic graphs, topological sorts, reachability queries, graph indexing

• Ahmed, Mohamed Ben; Okoronkwo, Onyemaechi Linda; Okoronkwo, Edwin Chimezie & Hvattum, Lars Magnus (2021). Long‐term effects of short planning horizons for inventory routing problems. International Transactions in Operational Research. ISSN 0969-6016. 29(5), p. 2995–3030. doi: 10.1111/itor.12998. Full text in Research Archive Show summary

  This paper presents a detailed study concerning the importance of the planning horizon when solving inventory routing problems (IRPs). We evaluate the quality of decisions obtained by solving a finite-horizon IRP. We also discuss the relevance of explicitly considering profit maximization models rather than the traditional cost minimization variant. As a means to this end, we describe four classes of the IRP corresponding to different types of markets. Two of them lead to nonlinear models, which are linearized. Furthermore, we provide a deterministic simulator to evaluate the long-term effects arising from using planning horizons of varying lengths when solving the IRP. A computational study is performed on cases generated from benchmark data instances. The results confirm that the long-term performance of the IRP decisions is, in part, contingent on the length of the selected planning horizon. They also show that considering profit maximization instead of cost minimization leads to different decisions, generating considerably more revenue and profits, albeit not nearly as much as suggested by individual solutions to static IRPs with short planning horizons. Keywords: profit maximization, path flow, linearization, end effect, simulation

• Ahmed, Mohamed Ben; Hryhoryeva, Maryia; Hvattum, Lars Magnus & Haouari, Mohamed (2021). A matheuristic for the robust integrated airline fleet assignment, aircraft routing, and crew pairing problem. Computers & Operations Research. ISSN 0305-0548. 137(January), p. 1–14. doi: 10.1016/j.cor.2021.105551. Full text in Research Archive Show summary

  We address an integrated airline scheduling problem that combines three airline planning processes: fleet assignment, aircraft routing, and crew pairing. For a given daily flight schedule, the problem requires simultaneously assigning aircraft and crews to each scheduled flight, taking into account aircraft maintenance restrictions and crew work rules. We propose to solve this complex problem of integrated flight planning while taking into account robustness considerations. In this regard, robustness is achieved by restricting tight connections in the schedule and increasing the number of connections where crews follow the aircraft. We formulate the problem using a very large-scale, yet compact, mixed-integer programming model, and we propose a matheuristic consisting of a decomposition approach and a proximity search algorithm. Computational experiments carried out on real instances from a major airline and having up to 14,014 itineraries, 646 flights, and 202 aircraft provide evidence of the proposed approach’s efficacy. In particular, we find that the average deviation from a conservative bound is at most equal to 0.6%. Keywords: mixed-integer programming, compact formulation, robustness, proximity search

• Rodrigues, Filipe; Agra, Agostinho; Hvattum, Lars Magnus & Requejo, Cristina (2021). Weighted proximity search. Journal of Heuristics. ISSN 1381-1231. 27(3), p. 459–496. doi: 10.1007/s10732-021-09466-0. Full text in Research Archive Show summary

  Proximity search is an iterative method to solve complex mathematical programming problems. At each iteration, the objective function of the problem at hand is replaced by the Hamming distance function to a given solution, and a cutoff constraint is added to impose that any new obtained solution improves the objective function value. A mixed integer programming solver is used to find a feasible solution to this modified problem, yielding an improved solution to the original problem. This paper introduces the concept of weighted Hamming distance that allows to design a new method called weighted proximity search. In this new distance function, low weights are associated with the variables whose value in the current solution is promising to change in order to find an improved solution, while high weights are assigned to variables that are expected to remain unchanged. The weights help to distinguish between alternative solutions in the neighborhood of the current solution, and provide guidance to the solver when trying to locate an improved solution. Several strategies to determine weights are presented, including both static and dynamic strategies. The proposed weighted proximity search is compared with the classic proximity search on instances from three optimization problems: the p-median problem, the set covering problem, and the stochastic lot-sizing problem. The obtained results show that a suitable choice of weights allows the weighted proximity search to obtain better solutions, for 75% of the cases, than the ones obtained by using proximity search and for 96% of the cases the solutions are better than the ones obtained by running a commercial solver with a time limit.

• Turkeš, Renata; Sörensen, Kenneth; Hvattum, Lars Magnus; Barrena, Eva; Chentli, Hayet & Coelho, Leandro C [Show all 20 contributors for this article] (2020). Data for a meta-analysis of the adaptive layer in adaptive large neighborhood search. Data in Brief. 33(December), p. 1–10. doi: 10.1016/j.dib.2020.106568. Full text in Research Archive Show summary

  Meta-analysis, a systematic statistical examination that combines the results of several independent studies, has the potential of obtaining problem- and implementation-independent knowledge and understanding of metaheuristic algorithms, but has not yet been applied in the domain of operations research. To illustrate the procedure, we carried out a meta-analysis of the adaptive layer in adaptive large neighborhood search (ALNS). Although ALNS has been widely used to solve a broad range of problems, it has not yet been established whether or not adaptiveness actually contributes to the performance of an ALNS algorithm. A total of 134 studies were identified through Google Scholar or personal e-mail correspondence with researchers in the domain, 63 of which fit a set of predefined eligibility criteria. The results for 25 different implementations of ALNS solving a variety of problems were collected and analyzed using a random effects model. This dataset contains a detailed comparison of ALNS with the non-adaptive variant per study and per instance, together with the meta-analysis summary results. The data enable to replicate the analysis, to evaluate the algorithms using other metrics, to revisit the importance of ALNS adaptive layer if results from more studies become available, or to simply consult the ready-to-use formulas in the summary file to carry out a meta-analysis of any research question. The individual studies, the meta-analysis and its results are described and interpreted in detail in Renata Turkeš, Kenneth Sörensen, Lars Magnus Hvattum, Meta-analysis of Metaheuristics: Quantifying the Effect of Adaptiveness in Adaptive Large Neighborhood Search, in the European Journal of Operational Research. Keywords: meta-analysis, metaheuristics, adaptive large neighborhood search

• Silva, Rodrigo Ferreira da; Hvattum, Lars Magnus & Glover, Fred (2020). Combining solutions of the optimum satisfiability problem using evolutionary tunneling. The MENDEL Soft Computing journal : International Conference on Soft Computing MENDEL. ISSN 1803-3814. 26(1), p. 23–29. doi: 10.13164/mendel.2020.1.023. Full text in Research Archive Show summary

  The optimum satisfiability problem involves determining values for Boolean vari- ables to satisfy a Boolean expression, while maximizing the sum of coefficients associated with the variables chosen to be true. Existing literature has identified a tabu search heuristic as the best method to deal with hard instances of the prob- lem. This paper combines the tabu search with a simple evolutionary heuristic based on the idea of tunneling between local optima. When combining a set of solutions, variables with common values in all solutions are identified and fixed. The remaining free variables in the problem may be decomposed into several in- dependent subproblems, so that parts of the solutions combined can be extracted and combined in an improved solution. This solution can be further improved by applying the tabu search in an improvement stage. The value of the new heuristic is demonstrated in extensive computational experiments on both existing and new test instances. Keywords: zero-one integer programming, boolean optimization, metaheuristic, tabu search, adaptive memory programming, recombination operator.

• Darmian, Sobhan Mostafayi; Moazzeni, Sahar & Hvattum, Lars Magnus (2020). Multi-objective sustainable location-districting for the collection of municipal solid waste : two case studies. Computers & industrial engineering. ISSN 0360-8352. 150(December), p. 1–17. doi: 10.1016/j.cie.2020.106965. Full text in Research Archive Show summary

  This paper presents a multi-objective location-districting optimization model for sustainable collection of municipal solid waste, motivated by strategic waste management decisions in Iran. The model aims to design an efficient system for providing municipal services by integrating the decisions regarding urban area districting and the location of waste collection centers. Three objectives are minimized, given as 1) the cost of establishing collection centers and collecting waste, 2) a measure of destructive environmental consequences, and 3) a measure of social dissatisfaction. Constraints are formulated to enforce an exclusive assignment of urban areas to districts and that the created districts are contiguous. In addition, constraints make sure that districts are compact and that they are balanced in terms of the amount of waste collected. A multi-objective local search heuristic using the farthest-candidate method is implemented to solve medium and large-scale numerical instances, while small instances can be solved directly by commercial software. A set of randomly generated test instances is used to test the effectiveness of the heuristic. The model and the heuristic are then applied to two case studies from Iran. The obtained results indicate that waste collection costs can be reduced by an estimated 20-30 %, while significantly improving the performance with respect to environmental and social criteria. Thus, the provided approach can provide important decision support for making strategic choices in municipal solid waste management. Keywords: multi-objective optimization, local search, best-worst method

• Håland, Else Marie; Wiig, Astrid Salte; Hvattum, Lars Magnus & Stålhane, Magnus (2020). Evaluating the effectiveness of different network flow motifs in association football. Journal of Quantitative Analysis in Sports (JQAS). 16(4), p. 311–323. doi: 10.1515/jqas-2019-0097. Full text in Research Archive Show summary

  In association football, a network flow motif describes how distinct players from a team are involved in a passing sequence. The flow motif encodes whether the same players appear several times in a passing sequence, and in which order the players make passes. This information has previously been used to classify the passing style of different teams. In this work, flow motifs are analyzed in terms of their effectiveness in terms of generating shots. Data from four seasons of the Norwegian top division are analyzed, using flow motifs representing subsequences of three passes. The analysis is performed with a generalized additive model (GAM), with a range of explanatory variables included. Findings include that motifs with fewer distinct players are less effective, and that motifs are more likely to lead to shots if the passes in the motif utilize a bigger area of the pitch. Keywords: generalized additive model, passing, regression, soccer

• Gelade, Garry A. & Hvattum, Lars Magnus (2020). On the relationship between +/- ratings and event-level performance statistics. Journal of Sports Analytics. ISSN 2215-020X. 6(2), p. 85–97. doi: 10.3233/JSA-200432. Full text in Research Archive Show summary

  This work considers the challenge of identifying and properly assessing the contribution of a single player towards the performance of a team. In particular, we study the use of advanced plus-minus ratings for individual football players, which involves evaluating a player based on the goals scored and conceded with the player appearing on the pitch, while compensating for the quality of the opponents and the teammates as well as other factors. To increase the understanding of plus-minus ratings, event-based data from matches are first used to explain the observed variance of ratings, and then to improve their ability to predict outcomes of football matches. It is found that event-level performance statistics can explain from 22% to 38% of the variance in plus-minus ratings, depending on player positions, while incorporating the event-level statistics only marginally improves the predictive power of plus-minus ratings. Keywords: Association football, key performance indicator, adjusted plus-minus, ranking.

• Arntzen, Halvard & Hvattum, Lars Magnus (2020). Predicting match outcomes in association football using team ratings and player ratings. Statistical Modelling. ISSN 1471-082X. 21(5), p. 449–470. doi: 10.1177/1471082X20929881. Full text in Research Archive Show summary

  The main goal of this article is to compare the performance of team ratings and individual player ratings when trying to forecast match outcomes in association football. The well-known Elo rating system is used to calculate team ratings, whereas a variant of plus-minus ratings is used to rate individual players. For prediction purposes, two covariates are introduced. The first represents the pre-match difference in Elo ratings of the two teams competing, while the second is the average difference in individual ratings for the players in the starting line-ups of the two teams. Two different statistical models are used to generate forecasts. The first type is an ordered logit regression (OLR) model that directly outputs probabilities for each of the three possible match outcomes, namely home win, draw and away win. The second type is based on competing risk modelling and involves the estimation of scoring rates for the two competing teams. These scoring rates are used to derive match outcome probabilities using discrete event simulation. Both types of models can be used to generate pre-game forecasts, whereas the competing risk models can also be used for in-game predictions. Computational experiments indicate that there is no statistical difference in the prediction quality for pre-game forecasts between the OLR models and the competing risk models. It is also found that team ratings and player ratings perform about equally well when predicting match outcomes. However, forecasts made when using both team ratings and player ratings as covariates are significantly better than those based on only one of the ratings. Key words: Elo rating, competing risk, ordered logit regression, plus-minus rating, survival analysis.

• Husakou, Anatol; Hvattum, Lars Magnus; Danielsen, Ketil & Hoff, Arild (2020). An application of the multi-depot heterogeneous fixed fleet open vehicle routing problem. International Journal of Advanced Operations Management (IJAOM). ISSN 1758-938X. 12(2), p. 142–155. doi: 10.1504/IJAOM.2020.108262. Full text in Research Archive Show summary

  This work describes an application of a multi-depot heterogeneous fixed fleet open vehicle routing problem. A contractor owns a fleet of vehicles with different capacities and running costs. The fleet is used to transport craftsmen from their homes to assigned project sites and back, with some of the craftsmen appointed as drivers while others are passengers. An optimisation model is described that enables the contractor to minimise the transportation costs, and a computational study shows that the model can be solved to optimality for realistically sized instances using a standard mixed-integer programming solver. A variant of the problem is also considered, where the assignment of craftsmen to projects is not fixed a priori. For this variant, several simple heuristic rules are investigated to generate project assignments, and computational results show that they are able to find improved assignments. Keywords: mixed integer programming, assignment, transportation

• Eide, Line; Årdal, Gro Cesilie Håhjem; Evsikova, Nataliia; Hvattum, Lars Magnus & Urrutia, Sebastián (2020). Load-dependent speed optimization in maritime inventory routing. Computers & Operations Research. ISSN 0305-0548. 123(November), p. 1–12. doi: 10.1016/j.cor.2020.105051. Full text in Research Archive Show summary

  Maritime inventory routing problems involve determining optimal routes for seagoing vessels between ports while managing the inventory of each port. Normally, such problems are considered with the vessels operating at fixed sailing speeds. However, the speed of vessels can typically be adjusted within an interval, and the actual fuel consumption depends on both the load and the speed of the vessel. The fuel consumption function combines speed and load in a non-linear manner, but can be approximated through linearization. In this work, to evaluate the importance of taking into account that both speeds and load levels influence the fuel costs, the resulting solutions are contrasted with solutions from the case where speeds and travel costs are taken as constants, as well as the case where speed is a decision, but the cost considered to be independent of the load. For either of these cases, load-dependent speed optimization can be added as a post-processing step. Computational experiments show that combining speed and load do have an impact on the selection of routes in maritime inventory routing problems, and that proper modelling of the fuel consumption can reduce sailing costs significantly. On the test instances considered, taking into account speed while ignoring the load leads to cost savings of around 38%. Considering the fuel consumption as a function of speed and load when planning leads to additional cost savings of 28%.

• Hvattum, Lars Magnus (2020). Offensive and defensive plus-minus player ratings for soccer. Applied Sciences. 10(20), p. 1–22. doi: 10.3390/app10207345. Full text in Research Archive Show summary

  Rating systems play an important part in professional sports, for example, as a source of entertainment for fans, by influencing decisions regarding tournament seedings, by acting as qualification criteria, or as decision support for bookmakers and gamblers. Creating good ratings at a team level is challenging, but even more so is the task of creating ratings for individual players of a team. This paper considers a plus–minus rating for individual players in soccer, where a mathematical model is used to distribute credit for the performance of a team as a whole onto the individual players appearing for the team. The main aim of the work is to examine whether the individual ratings obtained can be split into offensive and defensive contributions, thereby addressing the lack of defensive metrics for soccer players. As a result, insights are gained into how elements such as the effect of player age, the effect of player dismissals, and the home field advantage can be broken down into offensive and defensive consequences. View Full-Text Keywords: association football; linear regression; regularization; ranking.

• Pantuso, G. & Hvattum, Lars Magnus (2020). Maximizing performance with an eye on the finances: a chance-constrained model for football transfer market decisions. TOP - An Official Journal of the Spanish Society of Statistics and Operations Research. ISSN 1134-5764. 29, p. 583–611. doi: 10.1007/s11750-020-00584-9. Full text in Research Archive Show summary

  Composing a team of professional players is among the most crucial decisions in association football. Nevertheless, transfer market decisions are often based on myopic objectives and are questionable from a financial point of view. This paper introduces a chance-constrained model to provide analytic support to club managers during transfer windows. The model seeks a top-performing team while adapting to different budgets and financial-risk profiles. In addition, it provides a new rating system that is able to numerically reflect the on-field performance of football players and thus contribute to an objective assessment of football players. The model and rating system are tested on a case study based on real market data. The data from the case study are available online for the benefit of future research.

• Stålhane, Magnus; Bolstad, Kamilla Hamre; Joshi, Manu & Hvattum, Lars Magnus (2020). A dual-level stochastic fleet size and mix problem for offshore wind farm maintenance operations. INFOR: Information Systems and Operational Research. ISSN 0315-5986. 59(2), p. 257–289. doi: 10.1080/03155986.2020.1857629. Full text in Research Archive Show summary

  This paper studies the strategic problem of finding a cost optimal fleet of vessels to support maintenance operations at offshore wind farms. A dual-level stochastic model is formulated, taking into account both long-term strategic uncertainty and short-term operational uncertainty in a single optimization model. The model supports wind farm owners in making strategic decisions regarding the number, placement, charter length, and types of vessels to charter, to meet maintenance demands throughout the lifetime of a wind farm. To evaluate the quality of strategic fleet size and mix decisions, the model also considers the operational decisions of how to utilize the fleet to support maintenance operations. The model accounts for strategic uncertainties that have not been considered in previously developed optimization models for offshore wind, such as uncertainty related to long-term trends in electricity prices and subsidy levels, the stepwise development of wind farms, and technology development in the vessel industry. To solve the proposed stochastic programming model we have developed an ad hoc integer L-shaped method, with customized optimality cuts. The computational experiments show that the proposed method outperforms solving the deterministic equivalent using a commercial MIP solver.

• Hvattum, Lars Magnus; Tirado, Gregorio & Felipe, Ángel (2020). The double traveling salesman problem with multiple stacks and a choice of container types. Mathematics. 8(6), p. 1–11. doi: 10.3390/MATH8060979. Full text in Research Archive Show summary

  The double traveling salesman problem with multiple stacks involves the transportation of goods between two regions. In one region, a vehicle carrying a container visits customers, where pallets of goods are loaded into the container. The container is then shipped to a different region, where another vehicle visits another set of customers where the pallets are unloaded. Pallets are loaded in several rows inside the container, where each row follows the last-in-first-out principle. The standard test instances for the double traveling salesman problem with multiple stacks implies the use of a 45-foot pallet wide container to carry EUR-1 pallets. This paper investigates the effect on transportation costs if an open side container could be used when transporting the pallets. Computational experiments show savings in transportation costs of up to 20%. Moreover, by using a container loaded from the side, rather than from the rear, the defining attributes of the double traveling salesman problem seem to be lost. Keywords: intermodal transportation; vehicle routing; loading; variable neighborhood search.

• Turkeš, Renata; Sörensen, Kenneth & Hvattum, Lars Magnus (2020). Meta-analysis of metaheuristics : quantifying the effect of adaptiveness in adaptive large neighborhood search. European Journal of Operational Research. ISSN 0377-2217. 292(2), p. 423–442. doi: 10.1016/j.ejor.2020.10.045. Full text in Research Archive Show summary

  Research on metaheuristics has focused on (novel) algorithmic development and on competitive testing, both of which have been frequently argued to yield little generalizable knowledge. The main goal of this paper is to promote meta-analysis — a systematic statistical examination that combines the results of several independent studies — as a more suitable way to obtain problem- and implementation-independent insights on metaheuristics. Meta-analysis is widely used in several scientific domains, most notably the medical sciences (e.g., to establish the efficacy of a certain treatment). To the best of our knowledge, this is the first meta-analysis in the field of metaheuristics. To illustrate the approach, we carry out a meta-analysis to gain insights into the importance of the adaptive layer in adaptive large neighborhood search (ALNS). Although ALNS has been widely used to solve a broad range of problems, it has not yet been established whether or not adaptiveness actually contributes to the performance of an ALNS algorithm. A total of 134 studies were identified through Google Scholar or personal e-mail correspondence with researchers in the domain, 63 of which fit our eligibility criteria. After sending requests for data to the authors of the eligible studies, we obtained results for 25 different implementations of ALNS, which were analysed using a random effects model. On average, the addition of an adaptive layer in an ALNS algorithm improves the objective function value by 0.14% (95% confidence interval 0.06% to 0.21%). Although the adaptive layer can (and in a limited number of studies does) have an added value, it also adds complexity and can therefore only be recommended in some specific situations. These findings underline the importance of evaluating the contribution of metaheuristic components. Keywords: metaheuristics, meta-analysis, adaptive large neighborhood search

• Andersen, Robin; Hassel, Vegard; Hvattum, Lars Magnus & Stålhane, Magnus (2020). In-game betting and the Kelly criterion. Mathematics for applications. ISSN 1805-3610. 9(2), p. 67–81. doi: 10.13164/MA.2020.06. Full text in Research Archive Show summary

  When a bet with a positive expected return is available, the Kelly criterion can be used to determine the fraction of wealth to wager so as to maximize the expected logarithmic return on investment. Several variants of the Kelly criterion have been developed and used by investors and bettors to maximize their performance in inefficient markets. This paper addresses a situation that has not, hitherto, been discussed in academic literature: when multiple bets can be placed on the same object and the available odds, true probabilities, or both, vary over time. Such objects are frequently available in sports betting markets, for example, in the case of in-game betting on outcomes of soccer matches. We adapt the Kelly criterion to support decisions in such live betting scenarios, and provide numerical examples of how optimal bet sizes can sometimes be counter-intuitive.

• Skålnes, Jørgen; Dahle, Lars; Andersson, Henrik; Christiansen, Marielle & Hvattum, Lars Magnus (2020). The Multistage Stochastic Vehicle Routing Problem with Dynamic Occasional Drivers. In Lalla-Ruiz, Eduardo; Mes, Martijn & Voß, Stefan (Ed.), Computational logistics : 11th international conference, ICCL 2020, Enschede, The Netherlands, September 28–30, 2020, Proceedings. Springer. ISSN 9783030597467. p. 261–276. doi: 10.1007/978-3-030-59747-4_17. Full text in Research Archive Show summary

  Widespread use of smart phones and cellular networks allow for new solutions to lower the costs of last mile delivery to customers. We consider a setting where a company not only uses its own fleet of vehicles to deliver products from their store, but can also make use of ordinary people who are already on the road. This may include people who visit the store and are willing to take a detour on their way home for a small compensation. The availability of these occasional drivers is naturally highly uncertain, and we assume that some stochastic information is known about them. This leads to a multistage stochastic vehicle routing problem, with dynamic appearance of vehicles. The contributions of this work is to present a formulation of the multistage stochastic programming problem, identifying what type of problem structures that makes this model superior to that of a two-stage formulation, and when a two-stage formulation can be an adequate simplification. Keywords: stochastic programming, uncertainty, crowdshipping, mixed-integer programming

• Rodrigues, Filipe; Agra, Agostinho; Christiansen, Marielle; Hvattum, Lars Magnus & Requejo, Cristina (2019). Comparing techniques for modelling uncertainty in a maritime inventory routing problem. European Journal of Operational Research. ISSN 0377-2217. 277(3), p. 831–845. doi: 10.1016/j.ejor.2019.03.015. Full text in Research Archive Show summary

  Uncertainty is inherent in many planning situations. One example is in maritime transportation, where weather conditions and port occupancy are typically characterized by high levels of uncertainty. This paper considers a maritime inventory routing problem where travel times are uncertain. Taking into account possible delays in the travel times is of main importance to avoid inventory surplus or shortages at the storages located at ports. Several techniques to deal with uncertainty, namely deterministic models with inventory buffers; robust optimization; stochastic programming and models incorporating conditional value-at-risk measures, are considered. The different techniques are tested for their ability to deal with uncertain travel times for a single product maritime inventory routing problem with constant production and consumption rates, a fleet of heterogeneous vessels and multiple ports. At the ports, the product is either produced or consumed and stored in storages with limited capacity. We assume two stages of decisions, where the routing, the visit order of the ports and the quantities to load/unload are first-stage decisions (fixed before the uncertainty is revealed), while the visit time and the inventory levels at ports are second-stage decisions (adjusted to the observed travel times). Several solution approaches resulting from the proposed techniques are considered. A computational comparison of the resulting solution approaches is performed to compare the routing costs, the amount of inventory bounds deviation, the total quantities loaded and unloaded, and the running times. This computational experiment is reported for a set of maritime instances having up to six ports and five ships. Keywords: transportation, maritime inventory routing, travel times uncertainty, stochastic programming

• Brachner, Markus; Stien, Fredrik Berg & Hvattum, Lars Magnus (2019). A mathematical programming framework for planning an emergency response system in the offshore oil and gas industry. Safety Science. ISSN 0925-7535. 113, p. 328–335. doi: 10.1016/j.ssci.2018.11.031. Full text in Research Archive Show summary

  While accidents in the petroleum industry are commonly connected to oil spill disasters, helicopter accidents are, in terms of incidence rates, a more grave concern in Norway. In this paper we present a range of mathematical programming models and a workflow that support decision makers in planning an emergency response system. For the models that are difficult to solve directly, we introduce a tailor-made solution method. With respect to the optimization objectives and constraints, we particularly focus on the performance metrics of response capacity and response time and show that the optimal solutions can differ remarkably, depending on which metric is in the optimization objective. Moreover, we present a multi-objective model that combines the optimization goals to achieve a balanced solution. A case study shows the concrete application of our framework. Keywords: Emergency preparedness, sea rescue, location models, mathematical programming

• Hvattum, Lars Magnus (2019). A comprehensive review of plus-minus ratings for evaluating individual players in team sports. International Journal of Computer Science in Sport. 18(1), p. 1–23. doi: 10.2478/ijcss-2019-0001. Full text in Research Archive Show summary

  The increasing availability of data from sports events has led to many new directions of research, and sports analytics can play a role in making better decisions both within a club and at the level of an individual player. The ability to objectively evaluate individual players in team sports is one aspect that may enable better decision making, but such evaluations are not straightforward to obtain. One class of ratings for individual players in team sports, known as plus-minus ratings, attempt to distribute credit for the performance of a team onto the players of that team. Such ratings have a long history, going back at least to the 1950s, but in recent years research on advanced versions of plus-minus ratings has increased noticeably. This paper presents a comprehensive review of contributions to plusminus ratings in later years, pointing out some key developments and showing the richness of the mathematical models developed. One conclusion is that the literature on plus-minus ratings is quite fragmented, but that awareness of past contributions to the field should allow researchers to focus on some of the many open research questions related to the evaluation of individual players in team sports. Keywords: rating system, ranking, regression, regularization

• Håland, Else Marie; Wiig, Astrid Salte; Stålhane, Magnus & Hvattum, Lars Magnus (2019). Evaluating passing ability in association football. IMA Journal of Management Mathematics. ISSN 1471-678X. 31(1), p. 91–116. doi: 10.1093/Imaman/dpz004. Full text in Research Archive Show summary

  In this paper, the passing ability of football players is determined by building three generalised additive mixed models that each explains a different aspect of a pass’ success: difficulty, risk and potential. The models are built on data from the 2014-2016 seasons of the Norwegian top division Eliteserien, and their predictive power is tested on the 2017 season. The results provide insight into the factors affecting the success of a pass in Eliteserien. These include the location of the pass, the relationship to previous passes and to situations such as throw-ins, corners, free kicks, or tackles, as well as conditions specific to the Eliteserien, such as the time of season and the ground surface type. Finally, the key pass makers in the league are identified.

• Wiig, Astrid Salte; Håland, Else Marie; Stålhane, Magnus & Hvattum, Lars Magnus (2019). Analyzing passing networks in association football based on the difficulty, risk, and potential of passes. International Journal of Computer Science in Sport. 18(3), p. 44–68. doi: 10.2478/ijcss-2019-0017. Full text in Research Archive Show summary

  This paper investigates the use of network analysis to identify key players on teams, and patterns of passing within teams, in association football. Networks are constructed based on passes made between players, and several centrality measures are investigated in combination with three different methods for evaluating individual passes. Four seasons of data from the Norwegian top division are used to identify key players and analyze matches from a selected team. The networks examined in this work have weights based on three different aspects of the passes made: their probability of being completed, the probability that the team keeps possession after the completed pass, and the probability of the pass being part of a sequence leading to a shot. The results show that using different metrics and network weights leads to the identification of key passers in different phases of play and in different positions on the pitch. Keywords: network analysis, pagerank, centrality, sport.

• Denstad, Are Gederaas; Ulsund, Einar Askevold; Christiansen, Marielle; Hvattum, Lars Magnus & Tirado, Gregorio (2019). Multi-objective optimization for a strategic ATM network redesign problem. Annals of Operations Research. ISSN 0254-5330. 296, p. 7–33. doi: 10.1007/s10479-019-03224-z. Full text in Research Archive Show summary

  During the last decades, the banking industry has been facing multiple challenges, from changes in regulations and legal systems, to the irruption of new technologies. A constant adaptation to the rapidly changing business ecosystem is therefore required. This paper deals with one type of efficiency improvement that is required from traditional banking operations as a result of the current shift in the industry towards more use of technology. That is, we deal with the decision-making process related to the redesign of existing ATM networks, which is currently being considered by many banks worldwide. This redesign is mainly a consequence of an increased use of electronic payment methods and card transactions, which have made the demand for cash decrease significantly. We describe a multi-objective mathematical programming model to be used as a tool when making strategic decisions regarding the bank ATM network redesign. Total costs and the coverage of customers and turnover are considered as conflicting performance attributes and analyzed through several multi-criteria techniques, namely the weighted sum and Tchebycheff methods and Archimedean goal programming. Among other insights, the results on a realistic case study show that the potential for cost reductions is high and that the consideration of both customer coverage and turnover coverage is crucial for the performance of the network. Keywords: Multi-criteria, Banking, Mathematical programming, Strategic planning.

• Agra, Agostinho; Christiansen, Marielle; Hvattum, Lars Magnus & Rodrigues, Filipe (2018). Robust optimization for a maritime inventory routing problem. Transportation Science. ISSN 0041-1655. 52(3), p. 509–525. doi: 10.1287/trsc.2017.0814. Full text in Research Archive Show summary

  We consider a single product maritime inventory routing problem in which the production and consumption rates are constant over the planning horizon. The problem involves a heterogeneous fleet and multiple production and consumption ports with limited storage capacity. Maritime transportation is characterized by high levels of uncertainty, and sailing times can be severely influenced by varying and unpredictable weather conditions. To deal with the uncertainty, this paper investigates the use of adaptable robust optimization where the sailing times are assumed to belong to the well-known budget polytope uncertainty set. In the recourse model, the routing, the order of port visits, and the quantities to load and unload are fixed before the uncertainty is revealed, while the visit time to ports and the stock levels can be adjusted to the scenario. We propose a decomposition algorithm that iterates between a master problem that considers a subset of scenarios and an adversarial separation problem that searches for scenarios that make the solution from the master problem infeasible. Several improvement strategies are proposed aiming at reducing the running time of the master problem and reducing the number of iterations of the decomposition algorithm. An iterated local search heuristic is also introduced to improve the decomposition algorithm. A computational study is reported based on a set of real instances.

• Santini, Alberto; Ropke, Stefan & Hvattum, Lars Magnus (2018). A comparison of acceptance criteria for the adaptive large neighbourhood search metaheuristic. Journal of Heuristics. ISSN 1381-1231. 24(5), p. 783–815. doi: 10.1007/s10732-018-9377-x. Full text in Research Archive Show summary

  Adaptive large neighborhood search (ALNS) is a useful framework for solving difficult combinatorial optimisation problems. As a metaheuristic, it consists of some components that must be tailored to the specific optimisation problem that is being solved, while other components are problem independent. The literature is sparse with respect to studies that aim to evaluate the relative merit of different alternatives for specific problem independent components. This paper investigates one such component, the move acceptance criterion in ALNS, and compares a range of alternatives. Through extensive computational testing, the alternative move acceptance criteria are ranked in three groups, depending on the performance of the resulting ALNS implementations. Among the best variants, we find versions of criteria based on simulated annealing, threshold acceptance, and record-to-record travel, with a version of the latter being consistently undominated by the others. Additional analyses focus on the search behavior, and multiple linear regression is used to identify characteristics of search behavior that are associated with good search performance. Keywords: adaptive large neighbourhood search, simulated annealing, threshold acceptance, record-to-record travel, vehicle routing problem, capacitated minimum spanning tree, quadratic assignment problem 

• Pasha, Urooj; Hoff, Arild & Hvattum, Lars Magnus (2018). The multi-period fleet size and mix vehicle routing problem with stochastic demands. In Diez, Pedro; Neittaanmäki, Pekka; Periaux, Jacques; Tuovinen, Tero & Bräysy, Olli (Ed.), Computational Methods and Models for Transport. Springer. ISSN 9783319544908. p. 121–146. doi: 10.1007/978-3-319-54490-8_9. Full text in Research Archive Show summary

  The multi-period fleet size and mix vehicle routing problem with stochastic demands is a new optimization problem that arises from the need to make strategic fleet sizing decisions while taking into consideration tactical planning and operational uncertainty. The setting is a distribution company that delivers goods to a set of customers and where the expected demand for different customers vary from period to period. The actual demand in a given period is stochastic, and is only revealed when visiting the customer. The objective is to minimize total expected costs, consisting of vehicle acquisition costs, routing costs, and the expected cost of route failures. Route failures occur when a vehicle arrives at a customer with an insufficient amount of goods, resulting in the need to refill the vehicle at the depot. The problem is formulated as a mixed integer programming problem. A heuristic for solving the problem is described and implemented, and a computational study is conducted on a set of varied test instances. Keywords: tabu search, heuristic, scenario, stochastic programming, recourse 

• Sæbø, Olav Drivenes & Hvattum, Lars Magnus (2018). Modelling the financial contribution of soccer players to their clubs. Journal of Sports Analytics. ISSN 2215-020X. 5(1), p. 23–34. doi: 10.3233/JSA-170235. Full text in Research Archive Show summary

  This paper presents a framework for evaluating the financial consequences of player transfers as seen from a club’s perspective. To this end, an objective player rating model is designed based on players’ contribution towards creating a positive goals differential for their team. A regression model is then applied to predict match outcomes as a function of the players involved in a match. Finally, Monte Carlo simulation is used to predict the final league standings and the financial gains obtained as a function of sporting success. The framework isillustrated on player transfers from the 2014-2015 English Premier League season. Keywords: association, football, rating, simulation, regression

• Zaitseva, Anna; Hvattum, Lars Magnus & Urrutia, Sebastián (2018). Profit maximization in inventory routing problems. In ., . (Eds.), 2018 IEEE International Conference on Industrial Engineering and Engineering Management (IEEM). IEEE (Institute of Electrical and Electronics Engineers). ISSN 9781538667866. p. 1230–1234. doi: 10.1109/IEEM.2018.8607713. Full text in Research Archive Show summary

  The inventory routing problem (IRP) deals with the transportation of one product from a producer to multiple consumers, which have given demands and inventory capacities, over a discrete time horizon. The traditional goal of the IRP is to minimize the combination of inventory and transportation costs, while avoiding stock outs at customers. This paper proposes two variations of the IRP with profit maximization. First, when the market situation allows prices to be adjusted, the problem involves finding an optimal balance of volume and margin according to a demand function. Second, when prices are fixed, unit production costs depend on the production volume, which can be adjusted to maximize the profit. Both variations lead to non-linear models, which are linearized and then tested on a selection of standard benchmark instances. Computational results show that considering profit maximization instead of cost minimization leads to different decisions, generating a larger revenue and profit.

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• Alteren, Johanne; Hvattum, Lars Magnus; Oskars, Trond Roger; Straume, Solveig & Teryokhin, Sergei (2026). Tid. Fjordantologien 2026. Scandinavian University Press (SCUP). ISBN 9788294167364. 446 p. doi: 10.18261/9788294167371-26. Full text in Research Archive

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• Strøm, Roar & Hvattum, Lars Magnus (2026). Et internasjonalt forskerteam tror de vet hvem som har størst sjanse til å vinne sommerens fotball-VM. [Radio]. NRK P1 Møre og Romsdal . Full text in Research Archive
• Hvattum, Lars Magnus (2025). Operations research as support for football clubs. Full text in Research Archive
• Tirado, Gregorio; Denstad, Are; Ulsund, Einar; Christiansen, Marielle & Hvattum, Lars Magnus (2024). A multi-criteria model for the strategic redesign of ATM networks. Full text in Research Archive
• Hvattum, Lars Magnus (2024). Improving a hybrid genetic search for the capacitated vehicle routing problem. Full text in Research Archive
• Hrydziushka, Darya; Hoff, Arild; Hvattum, Lars Magnus & Dominguez, Gregorio Tirado (2024). Evacuation model under conditions of uncertainty and damaged infrastructure. Full text in Research Archive
• Barstad, Andreas; Schütz, Peter; Msakni, Mohamed Kais & Hvattum, Lars Magnus (2024). Breaking down The Amazon Routing Challenge: A heuristic approach for the clustered TSP. Full text in Research Archive
• Muller, John; Hvattum, Lars Magnus; May, Patrick & Hoac, Edvin Tran (2024). Why do the numbers show that Real Madrid do better without Toni Kroos? [Journal]. The Athletic - New York Times. Full text in Research Archive Show summary

  Why do the numbers show that Real Madrid do better without Toni Kroos?

• Knudseth, Sunniva Haukvik; Hoff, Arild; Oppen, Johan & Hvattum, Lars Magnus (2023). Decision support for allocating farmed fish to customer orders using a bi-objective optimization model. Full text in Research Archive
• Abraham, Gyula; Dósa, György; Olaj, Tomas Attila Paulsen; Tuza, Zsolt & Hvattum, Lars Magnus (2023). Egy téglalap-pakolási feladat, és megoldása különféle módszerekkel. Full text in Research Archive
• Hoff, Arild; Shaabani, Homayoun; Hvattum, Lars Magnus & Laporte, Gilbert (2023). A matheuristic for the multi-product maritime inventory routing problem. Full text in Research Archive
• Knudseth, Sunniva Haukvik; Molland, Even; Hoff, Arild; Hvattum, Lars Magnus & Oppen, Johan (2022). Decision Support for Allocating Farmed Fish to Customer Orders Using a Bi-objective Optimization Model. Full text in Research Archive
• Shaabani, Homayoun; Hoff, Arild; Hvattum, Lars Magnus & Laporte, Gilbert (2021). A matheuristic algorithm for maritime inventory routing problem. Full text in Research Archive
• Hoff, Arild; Hvattum, Lars Magnus & Danielsen, Ketil (2021). An application of the multi-depot heterogeneous fixed fleet open vehicle routing problem. Full text in Research Archive
• Langelo, Erik & Hvattum, Lars Magnus (2021). Solving profit-maximizing lot size problems with customer stockpiling and discrete prices. Full text in Research Archive Show summary

  https://iwls2021.sciencesconf.org/

• Ahmed, Mohamed Ben; Hvattum, Lars Magnus & Haouari, Mohamed (2021). A matheuristic for the robust integrated airline scheduling problem. Full text in Research Archive
• Dósa, György; Hvattum, Lars Magnus; Olaj, Tomas Attila Paulsen & Tuza, Zsolt (2020). The board packing problem : packing rectangles into a board to maximize profit. In Vassanyi, Istvan (Eds.), Proceedings of the Pannonian Conference on Advances in Information Technology (PCIT 2020). University of Pannonia, Faculty of Information Technology. ISSN 9789633961445. p. 10–16. Full text in Research Archive
• Haugen, Kjetil K.; Strandhagen, Jan Ola; Solberg, Harry Arne; Kringstad, Morten; Owren, Brynjulf & Hansson, Lisa [Show all 15 contributors for this article] (2020). Fra toppen av Haugen : svensk norgesmester i verdensklasse. Full text in Research Archive
• Bentsen, Håkon; Hvattum, Lars Magnus & Urrutia, Sebastián (2019). A review of Binary Integer Programming applications and solution methods. Full text in Research Archive Show summary

  Binary Integer Programming (BIP) covers a large variety of different problems, with many real world applications. This work first reviews the scientific literature with the aim of creating an overview of the most important applications of pure BIP models. The literature review is conducted using different search strings in order to find the relevant papers from prominent online databases. The findings are then filtered manually and categorized by application. There are relatively few general purpose solvers for BIP, and computational experiments are conducted to show their performance on benchmark instances from the literature, covering a wide variety of applications. Based on these results, we argue that there is a need for improved general purpose solvers for BIP problems, with a performance level closer to what is found in specialized solvers. Keywords: programming, mixed-integer

• Haugen, Kjetil K.; Owren, Brynjulf; Strandhagen, Jan Ola; Kringstad, Morten; Solberg, Harry Arne & Guvåg, Bjørn [Show all 13 contributors for this article] (2019). Fra toppen av Haugen : tabelltips 2019: stadig norgesmester fra Molde. Full text in Research Archive
• Hvattum, Lars Magnus; Silva, Rodrigo Ferreira da & Glover, Fred (2019). Exploring properties of combining solutions of the Boolean optimization problem. Full text in Research Archive
• Hvattum, Lars Magnus & Pantuso, Giovanni (2019). Maximizing financial and on-field performances when composing teams in soccer. Full text in Research Archive
• Hvattum, Lars Magnus (2019). Professor: – Denne spilleren er viktigst for at Molde skal vinne. [Journal]. Stavanger Aftenblad. Full text in Research Archive
• Hvattum, Lars Magnus & Hustad, Trond (2019). Moldes viktigste spiller. [Journal]. Romsdals Budstikke. Full text in Research Archive
• Dahle, Lars; Andersson, Henrik; Christiansen, Marielle & Hvattum, Lars Magnus (2018). The vehicle routing problem with dynamic occasional drivers - a multistage formulation. Full text in Research Archive
• Hvattum, Lars Magnus; Zaitseva, Anna & Urrutia, Sebastián (2018). Profit maximization in inventory routing problems. Full text in Research Archive
• Bolstad, Kamilla; Joshi, Manu; Stålhane, Magnus & Hvattum, Lars Magnus (2018). Optimizing the vessel fleet size and mix to perform maintenance at offshore wind farms. Full text in Research Archive
• Algendi, Abdalrahman; Urrutia, Sebastián; Hvattum, Lars Magnus & Helgheim, Berit (2024). Home health care staffing, routing, and scheduling problem with multiple shifts and emergency considerations. Høgskolen i Molde - Vitenskapelig høgskole i logistikk. ISSN 9788279623625. Full text in Research Archive Show summary

  Effective planning of human resources is critical in designing an efficient home healthcare system. In this study, we present a novel home healthcare staffing, routing, and scheduling problem inspired by a real-world application. The proposed problem addresses a set of patients, with varying daily visit requirements, being served by a set of caregivers with different qualification levels over a multi-day multi-shift planning horizon. The study aims to achieve three objectives: minimizing the number of additional shifts, maximizing the allocation of caregivers to emergencies, and minimizing the sum of route lengths. These objectives are optimized hierarchically while considering a set of restrictions, including time windows, skill matching, synchronicity, care continuity, and labor regulations. To tackle the problem, we introduce a mixed-integer linear programming model. The model is then extended and two sets of valid inequalities are incorporated to enhance its tightness. Computational experiments are conducted on a set of 20 instances. The results highlight the efficiency of the proposed extension in increasing both the number of instances that can be solved to optimality and the number of instances for which a feasible solution is found. Keywords: Mixed-integer programming; Valid inequalities; Home healthcare; Human resource planning; Multiple shifts; Synchronization.

• Shaabani, Homayoun; Hvattum, Lars Magnus; Laporte, Gilbert & Hoff, Arild (2023). Stability metrics for a maritime inventory routing problem under sailing time uncertainty. Høgskolen i Molde - Vitenskapelig høgskole i logistikk. ISSN 9788279623427. Full text in Research Archive

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