Pub Date : 2025-12-25DOI: 10.1016/j.orl.2025.107403
Ram Krishnamoorthy, Christopher Lourenco
Linear programming (LP) is foundational to operations research; however, nontrivial roundoff-errors may lead to incorrect solutions for 3-5% of LPs within standard test sets. To avoid this, exact LP solvers exist; the forefront of which is SoPlex. SoPlex guarantees exactness by utilizing exact rational-arithmetic factorizations. We modify SoPlex to utilize faster exact integer factorizations, showcasing that, on a test set of LPs, the new approach is a factor of 3.33 and 1.60 times faster in average and geometric mean.
{"title":"Expediting exact linear programming solvers via integer preserving factorization","authors":"Ram Krishnamoorthy, Christopher Lourenco","doi":"10.1016/j.orl.2025.107403","DOIUrl":"10.1016/j.orl.2025.107403","url":null,"abstract":"<div><div>Linear programming (LP) is foundational to operations research; however, nontrivial roundoff-errors may lead to incorrect solutions for 3-5% of LPs within standard test sets. To avoid this, exact LP solvers exist; the forefront of which is SoPlex. SoPlex guarantees exactness by utilizing exact rational-arithmetic factorizations. We modify SoPlex to utilize faster exact integer factorizations, showcasing that, on a test set of LPs, the new approach is a factor of 3.33 and 1.60 times faster in average and geometric mean.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"65 ","pages":"Article 107403"},"PeriodicalIF":0.9,"publicationDate":"2025-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145883328","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-21DOI: 10.1016/j.orl.2025.107399
Joshua Ong, Andrew Mastin, William Yang, Jean-Paul Watson
The interdiction defense (ID) problem solves a defender-attacker-defender model where the defender and attacker share the same set of components to harden and target. We build upon the best response intersection (BRI) algorithm by developing the BRI with suboptimal solutions (BRI-SS) algorithm to solve the ID problem. The BRI-SS algorithm utilizes off-the-shelf optimization solvers that return suboptimal solutions at no additional computation cost. We derive novel cuts from suboptimal solutions, reducing the number of iterations required for the algorithm to converge while maintaining optimality guarantees. We also present a heuristic that utilizes all obtained suboptimal solutions to select the next defense to evaluate at each iteration. We perform computational experiments applied to power grid interdiction on standard test cases. Our results demonstrate that the BRI-SS algorithm consistently outperforms the BRI algorithm across all test cases.
{"title":"Faster solutions to the interdiction defense problem using suboptimal solutions","authors":"Joshua Ong, Andrew Mastin, William Yang, Jean-Paul Watson","doi":"10.1016/j.orl.2025.107399","DOIUrl":"10.1016/j.orl.2025.107399","url":null,"abstract":"<div><div>The interdiction defense (ID) problem solves a defender-attacker-defender model where the defender and attacker share the same set of components to harden and target. We build upon the best response intersection (BRI) algorithm by developing the BRI with suboptimal solutions (BRI-SS) algorithm to solve the ID problem. The BRI-SS algorithm utilizes off-the-shelf optimization solvers that return suboptimal solutions at no additional computation cost. We derive novel cuts from suboptimal solutions, reducing the number of iterations required for the algorithm to converge while maintaining optimality guarantees. We also present a heuristic that utilizes all obtained suboptimal solutions to select the next defense to evaluate at each iteration. We perform computational experiments applied to power grid interdiction on standard test cases. Our results demonstrate that the BRI-SS algorithm consistently outperforms the BRI algorithm across all test cases.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"65 ","pages":"Article 107399"},"PeriodicalIF":0.9,"publicationDate":"2025-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145925117","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-19DOI: 10.1016/j.orl.2025.107401
Zohre Aminifard, Geovani Nunes Grapiglia
We propose a non-monotone line-search method to minimize functions with many non-global local minimizers. Based on a relaxed Armijo condition, the new method allows a controlled increase in the objective function between consecutive iterations, helping iterates escape nearby minimizers. We establish worst-case complexity estimates on the number of iterations required to reach approximate stationary points. Numerical results demonstrate that our method can significantly outperform other non-monotone approaches on functions with spurious minimizers.
{"title":"A non-monotone line-search method for minimizing functions with spurious local minima","authors":"Zohre Aminifard, Geovani Nunes Grapiglia","doi":"10.1016/j.orl.2025.107401","DOIUrl":"10.1016/j.orl.2025.107401","url":null,"abstract":"<div><div>We propose a non-monotone line-search method to minimize functions with many non-global local minimizers. Based on a relaxed Armijo condition, the new method allows a controlled increase in the objective function between consecutive iterations, helping iterates escape nearby minimizers. We establish worst-case complexity estimates on the number of iterations required to reach approximate stationary points. Numerical results demonstrate that our method can significantly outperform other non-monotone approaches on functions with spurious minimizers.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"65 ","pages":"Article 107401"},"PeriodicalIF":0.9,"publicationDate":"2025-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145839751","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-19DOI: 10.1016/j.orl.2025.107400
Dongshuang Hou , Aymeric Lardon , Theo Driessen
We introduce a new class of cooperative games with transferable utility that measure dispersion among players, each associated with a real number representing a specific characteristic (effort level, production cost,...). Cooperation between players is quantified by their dispersion using the statistical concept of squared deviations. These games, called “squared deviations games,” form a subclass of market games and are therefore totally balanced, though not necessarily convex. We also derive their Shapley value through the standard decomposition into unanimity games.
{"title":"Squared deviations games: A subclass of market games and their Shapley value","authors":"Dongshuang Hou , Aymeric Lardon , Theo Driessen","doi":"10.1016/j.orl.2025.107400","DOIUrl":"10.1016/j.orl.2025.107400","url":null,"abstract":"<div><div>We introduce a new class of cooperative games with transferable utility that measure dispersion among players, each associated with a real number representing a specific characteristic (effort level, production cost,...). Cooperation between players is quantified by their dispersion using the statistical concept of squared deviations. These games, called “squared deviations games,” form a subclass of market games and are therefore totally balanced, though not necessarily convex. We also derive their Shapley value through the standard decomposition into unanimity games.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"65 ","pages":"Article 107400"},"PeriodicalIF":0.9,"publicationDate":"2025-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145839752","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-10DOI: 10.1016/j.orl.2025.107398
Melody Qiming Xuan , Jorge Nocedal
This paper investigates a method for solving constrained optimization problems when the derivatives of the objective function are unavailable, while the derivatives of the constraint functions are known. We allow the objective and constraint function to be nonconvex. The method constructs a quadratic model of the objective function via interpolation and computes a step by minimizing this model subject to the original constraints in the problem and a trust region constraint. The step computation requires the solution of a general nonlinear program, which is economically feasible when the constraints and their derivatives are very inexpensive to compute compared to the objective function. The paper includes a summary of numerical results that highlight the method’s promising potential.
{"title":"A feasible method for constrained derivative-free optimization","authors":"Melody Qiming Xuan , Jorge Nocedal","doi":"10.1016/j.orl.2025.107398","DOIUrl":"10.1016/j.orl.2025.107398","url":null,"abstract":"<div><div>This paper investigates a method for solving constrained optimization problems when the derivatives of the objective function are unavailable, while the derivatives of the constraint functions are known. We allow the objective and constraint function to be nonconvex. The method constructs a quadratic model of the objective function via interpolation and computes a step by minimizing this model subject to the original constraints in the problem and a trust region constraint. The step computation requires the solution of a general nonlinear program, which is economically feasible when the constraints and their derivatives are very inexpensive to compute compared to the objective function. The paper includes a summary of numerical results that highlight the method’s promising potential.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"65 ","pages":"Article 107398"},"PeriodicalIF":0.9,"publicationDate":"2025-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145790043","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-29DOI: 10.1016/j.orl.2025.107395
Santanu S. Dey , Frédéric Meunier , Diego Morán Ramírez
Geoffrion’s theorem is a fundamental result from mathematical programming assessing the quality of Lagrangian relaxation, a standard technique to get bounds for integer programs. An often implicit condition is that the set of feasible solutions is finite or described by rational linear constraints. However, we show through concrete examples that the conclusion of Geoffrion’s theorem does not necessarily hold when this condition is dropped. We then provide sufficient conditions ensuring the validity of the result even when the feasible set is not finite and cannot be described using finitely-many rational linear constraints.
{"title":"Geoffrion’s theorem beyond finiteness and rationality","authors":"Santanu S. Dey , Frédéric Meunier , Diego Morán Ramírez","doi":"10.1016/j.orl.2025.107395","DOIUrl":"10.1016/j.orl.2025.107395","url":null,"abstract":"<div><div>Geoffrion’s theorem is a fundamental result from mathematical programming assessing the quality of Lagrangian relaxation, a standard technique to get bounds for integer programs. An often implicit condition is that the set of feasible solutions is finite or described by rational linear constraints. However, we show through concrete examples that the conclusion of Geoffrion’s theorem does not necessarily hold when this condition is dropped. We then provide sufficient conditions ensuring the validity of the result even when the feasible set is not finite and cannot be described using finitely-many rational linear constraints.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"65 ","pages":"Article 107395"},"PeriodicalIF":0.9,"publicationDate":"2025-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145684717","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-27DOI: 10.1016/j.orl.2025.107397
George Dunn , Hadi Charkhgard , Ali Eshragh , Elizabeth Stojanovski
Order picking involves collecting items from their locations within a warehouse. Existing algorithms for finding minimal picker routes consider limited options for travel within a subaisle. One action, traversing a subaisle twice, is not required in rectangular warehouses with two cross-aisles, however, is necessary for larger warehouses. In this work, we demonstrate that double traversals are not required to connect cross-aisle travel regardless of warehouse size. This result simplifies the structure of feasible tours, enabling more efficient algorithms.
{"title":"Double traversals in optimal picker routes for warehouses with multiple blocks","authors":"George Dunn , Hadi Charkhgard , Ali Eshragh , Elizabeth Stojanovski","doi":"10.1016/j.orl.2025.107397","DOIUrl":"10.1016/j.orl.2025.107397","url":null,"abstract":"<div><div>Order picking involves collecting items from their locations within a warehouse. Existing algorithms for finding minimal picker routes consider limited options for travel within a subaisle. One action, traversing a subaisle twice, is not required in rectangular warehouses with two cross-aisles, however, is necessary for larger warehouses. In this work, we demonstrate that double traversals are not required to connect cross-aisle travel regardless of warehouse size. This result simplifies the structure of feasible tours, enabling more efficient algorithms.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"65 ","pages":"Article 107397"},"PeriodicalIF":0.9,"publicationDate":"2025-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145684716","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-25DOI: 10.1016/j.orl.2025.107396
Alexandra Lassota , Adrian Vetta , Bernhard von Stengel
A Condorcet winning set is a set of candidates such that no other candidate is preferred by at least half the voters over all members of the set. The Condorcet dimension, which is the minimum cardinality of a Condorcet winning set, is known to be at most logarithmic in the number of candidates. We study the case of elections where voters and candidates are located in a 2-dimensional space with preferences based upon proximity voting. Our main result is that the Condorcet dimension is at most 3, under both the Manhattan norm and the infinity norm, which are natural measures in electoral systems. We also prove that any set of voter preferences can be embedded into a metric space of sufficiently high dimension for any p-norm, including the Manhattan and infinity norms.
{"title":"The Condorcet dimension of metric spaces","authors":"Alexandra Lassota , Adrian Vetta , Bernhard von Stengel","doi":"10.1016/j.orl.2025.107396","DOIUrl":"10.1016/j.orl.2025.107396","url":null,"abstract":"<div><div>A Condorcet winning set is a set of candidates such that no other candidate is preferred by at least half the voters over all members of the set. The Condorcet dimension, which is the minimum cardinality of a Condorcet winning set, is known to be at most logarithmic in the number of candidates. We study the case of elections where voters and candidates are located in a 2-dimensional space with preferences based upon proximity voting. Our main result is that the Condorcet dimension is at most 3, under both the Manhattan norm and the infinity norm, which are natural measures in electoral systems. We also prove that any set of voter preferences can be embedded into a metric space of sufficiently high dimension for any <em>p</em>-norm, including the Manhattan and infinity norms.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"65 ","pages":"Article 107396"},"PeriodicalIF":0.9,"publicationDate":"2025-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145684718","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-12DOI: 10.1016/j.orl.2025.107387
Deeparnab Chakrabarty, Luc Coté
In this paper we design and analyze a new approximation algorithm for the classic discrete optimization problem of maximizing a monotone submodular function subject to a cardinality constraint. Our algorithm is based on the primal-dual schema and achieves the optimal factor of . While greedy algorithms have been known to achieve this approximation factor, our algorithms also provide a dual certificate which upper bounds the optimum value of any instance. This certificate can be used to certify instance-wise guarantees potentially much better than the worst-case approximation factor.
{"title":"A primal-dual algorithm for monotone submodular maximization","authors":"Deeparnab Chakrabarty, Luc Coté","doi":"10.1016/j.orl.2025.107387","DOIUrl":"10.1016/j.orl.2025.107387","url":null,"abstract":"<div><div>In this paper we design and analyze a new approximation algorithm for the classic discrete optimization problem of maximizing a monotone submodular function subject to a cardinality constraint. Our algorithm is based on the primal-dual schema and achieves the optimal factor of <span><math><mo>(</mo><mn>1</mn><mo>−</mo><mn>1</mn><mo>/</mo><mi>e</mi><mo>)</mo></math></span>. While greedy algorithms have been known to achieve this approximation factor, our algorithms also provide a dual certificate which upper bounds the optimum value of any instance. This certificate can be used to certify instance-wise guarantees potentially much better than the worst-case <span><math><mo>(</mo><mn>1</mn><mo>−</mo><mn>1</mn><mo>/</mo><mi>e</mi><mo>)</mo></math></span> approximation factor.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"65 ","pages":"Article 107387"},"PeriodicalIF":0.9,"publicationDate":"2025-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145532482","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We propose an accelerated algorithm with a Frank-Wolfe method as an oracle for solving strongly monotone variational inequality problems. While standard solution approaches, such as projected gradient descent (aka value iteration), involve projecting onto the desired set at each iteration, a distinctive feature of our proposed method is the use of a linear minimization oracle in each iteration. This difference potentially reduces the projection cost, a factor that can become significant for certain sets or in high-dimensional problems. We validate the performance of the proposed algorithm on the traffic assignment problem, motivated by the fact that the projection complexity per iteration increases exponentially with respect to the number of links.
{"title":"A Frank-Wolfe algorithm for strongly monotone variational inequalities","authors":"Reza Rahimi Baghbadorani , Peyman Mohajerin Esfahani , Sergio Grammatico","doi":"10.1016/j.orl.2025.107388","DOIUrl":"10.1016/j.orl.2025.107388","url":null,"abstract":"<div><div>We propose an accelerated algorithm with a Frank-Wolfe method as an oracle for solving strongly monotone variational inequality problems. While standard solution approaches, such as projected gradient descent (aka value iteration), involve projecting onto the desired set at each iteration, a distinctive feature of our proposed method is the use of a linear minimization oracle in each iteration. This difference potentially reduces the projection cost, a factor that can become significant for certain sets or in high-dimensional problems. We validate the performance of the proposed algorithm on the traffic assignment problem, motivated by the fact that the projection complexity per iteration increases exponentially with respect to the number of links.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"65 ","pages":"Article 107388"},"PeriodicalIF":0.9,"publicationDate":"2025-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145532481","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
扫码关注我们
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号