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On proper separation of convex sets 关于凸集的适当分离
IF 1.2 4区 数学
Mathematical Methods of Operations Research Pub Date : 2024-06-05 DOI: 10.1007/s00186-024-00862-3
Mahmood Mehdiloo
{"title":"On proper separation of convex sets","authors":"Mahmood Mehdiloo","doi":"10.1007/s00186-024-00862-3","DOIUrl":"https://doi.org/10.1007/s00186-024-00862-3","url":null,"abstract":"<p>The aim of this contribution is to propose an alternative but equivalent statement of the proper separation of two closed convex sets in a finite-dimensional Euclidean space. To this aim, we characterize the affine hull of a closed convex set defined by a finite set of equalities and inequalities. Furthermore, we describe algebraically the relative interior of this set by projecting the optimal set of a convex optimization problem onto a subspace of its variables. Then we use this description to develop a system of equalities and inequalities by which the proper separability of the given convex sets is identified. We show that this system is linear in the special case that the given sets are polyhedral.</p>","PeriodicalId":49862,"journal":{"name":"Mathematical Methods of Operations Research","volume":"46 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141253549","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Networks with nonordered partitioning of players: stability and efficiency with neighborhood-influenced cost topology 玩家无序分区网络：受邻域影响成本拓扑的稳定性和效率
IF 1.2 4区 数学
Mathematical Methods of Operations Research Pub Date : 2024-05-29 DOI: 10.1007/s00186-024-00861-4
Ping Sun, Elena Parilina
{"title":"Networks with nonordered partitioning of players: stability and efficiency with neighborhood-influenced cost topology","authors":"Ping Sun, Elena Parilina","doi":"10.1007/s00186-024-00861-4","DOIUrl":"https://doi.org/10.1007/s00186-024-00861-4","url":null,"abstract":"<p>This paper highlights the incentives of individuals to add or sever links in shaping stable and efficient networks when the society is partitioned into groups. In terms of the group partitioning, the players may unequally pay for the link connecting them. To be precise, the cost a player pays for her direct connection is determined by the composition of her neighborhood. In particular, the more members of a group the player has in her neighborhood, the less the average cost of a link is within this group. The main contributions of our paper lie in a detailed analysis of conditions under which particular network configurations—complete network, majority complete network, and complete bipartite network—achieve stability and unique efficiency. The paper examines the impact of the distribution of players across different groups on the stability and efficiency of these networks. We prove that majority complete networks can never be uniquely efficient when there is an equal number of players between two groups, but if they are efficient, the other two types of structures also attain efficiency. Moreover, under certain distributions of players, the unique stability of majority complete networks implies their unique efficiency.</p>","PeriodicalId":49862,"journal":{"name":"Mathematical Methods of Operations Research","volume":"24 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141169268","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Column generation based solution for bi-objective gate assignment problems 基于列生成的双目标门分配问题解决方案
IF 1.2 4区 数学
Mathematical Methods of Operations Research Pub Date : 2024-04-29 DOI: 10.1007/s00186-024-00856-1
Gülesin Sena Daş, Fatma Gzara
{"title":"Column generation based solution for bi-objective gate assignment problems","authors":"Gülesin Sena Daş, Fatma Gzara","doi":"10.1007/s00186-024-00856-1","DOIUrl":"https://doi.org/10.1007/s00186-024-00856-1","url":null,"abstract":"<p>In this paper, we present a column generation-based algorithm for the bi-objective gate assignment problem (GAP) to generate gate schedules that minimize squared slack time at the gates while satisfying passenger expectations by minimizing their walking distance. While most of the literature focuses on heuristic or metaheuristic solutions for the bi-objective GAP, we propose flow-based and column-based models that lead to exact or near optimal solution approaches. The developed algorithm calculates a set of solutions to approximate the Pareto front. The algorithm is applied to the over-constrained GAP where gates are a limited resource and it is not possible to serve every flight using a gate. Our test cases are based on real data from an international airport and include various instances with flight-to-gate ratios between 23.9 and 34.7. Numerical results reveal that a set of solutions representing a compromise between the passenger-oriented and robustness-oriented objectives may be obtained with a tight optimality gap and within reasonable computational time even for these difficult problems.</p>","PeriodicalId":49862,"journal":{"name":"Mathematical Methods of Operations Research","volume":"50 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140842125","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A D.C. approximation approach for optimization with probabilistic constraints based on Chen–Harker–Kanzow–Smale smooth plus function 基于 Chen-Harker-Kanzow-Smale 平滑加函数的概率约束优化 D.C. 近似方法
IF 1.2 4区 数学
Mathematical Methods of Operations Research Pub Date : 2024-04-16 DOI: 10.1007/s00186-024-00859-y
Yonghong Ren, Yuchao Sun, Dachen Li, Fangfang Guo
{"title":"A D.C. approximation approach for optimization with probabilistic constraints based on Chen–Harker–Kanzow–Smale smooth plus function","authors":"Yonghong Ren, Yuchao Sun, Dachen Li, Fangfang Guo","doi":"10.1007/s00186-024-00859-y","DOIUrl":"https://doi.org/10.1007/s00186-024-00859-y","url":null,"abstract":"<p>Many important practical problems can be formulated as probabilistic constrained optimization problem (PCOP), which is challenging to solve since it is usually non-convex and non-smooth. Effective methods for (PCOP) mostly focus on approximation techniques. This paper aims at studying the D.C. (difference of two convex functions) approximation techniques. A D.C. approximation is explored to solve the probabilistic constrained optimization problem based on Chen–Harker–Kanzow–Smale (CHKS) smooth plus function. A smooth approximation to probabilistic constraint function is proposed and the corresponding D.C. approximation problem is established. It is proved that the approximation problem is equivalent to the original one under certain conditions. Sequential convex approximation (SCA) algorithm is implemented to solve the D.C. approximation problem. Sample average approximation method is applied to solve the convex subproblem. Numerical results suggest that D.C. approximation technique is effective for optimization with probabilistic constraints.\u0000</p>","PeriodicalId":49862,"journal":{"name":"Mathematical Methods of Operations Research","volume":"28 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140616891","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Augmenting bi-objective branch and bound by scalarization-based information 利用基于标量的信息增强双目标分支与约束
IF 1.2 4区 数学
Mathematical Methods of Operations Research Pub Date : 2024-04-15 DOI: 10.1007/s00186-024-00854-3
Julius Bauß, Michael Stiglmayr
{"title":"Augmenting bi-objective branch and bound by scalarization-based information","authors":"Julius Bauß, Michael Stiglmayr","doi":"10.1007/s00186-024-00854-3","DOIUrl":"https://doi.org/10.1007/s00186-024-00854-3","url":null,"abstract":"<p>While branch and bound based algorithms are a standard approach to solve single-objective (mixed-)integer optimization problems, multi-objective branch and bound methods are only rarely applied compared to the predominant objective space methods. In this paper we propose modifications to increase the performance of multi-objective branch and bound algorithms by utilizing scalarization-based information. We use the hypervolume indicator as a measure for the gap between lower and upper bound set to implement a multi-objective best-first strategy. By adaptively solving scalarizations in the root node to integer optimality we improve both, upper and lower bound set. The obtained lower bound can then be integrated into the lower bounds of all active nodes, while the determined solution is added to the upper bound set. Numerical experiments show that the number of investigated nodes can be significantly reduced by up to 83% and the total computation time can be reduced by up to 80%.</p>","PeriodicalId":49862,"journal":{"name":"Mathematical Methods of Operations Research","volume":"48 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140585201","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Markov decision processes with risk-sensitive criteria: an overview 具有风险敏感标准的马尔可夫决策过程：概述
IF 1.2 4区 数学
Mathematical Methods of Operations Research Pub Date : 2024-04-01 DOI: 10.1007/s00186-024-00857-0
Nicole Bäuerle, Anna Jaśkiewicz
{"title":"Markov decision processes with risk-sensitive criteria: an overview","authors":"Nicole Bäuerle, Anna Jaśkiewicz","doi":"10.1007/s00186-024-00857-0","DOIUrl":"https://doi.org/10.1007/s00186-024-00857-0","url":null,"abstract":"<p>The paper provides an overview of the theory and applications of risk-sensitive Markov decision processes. The term ’risk-sensitive’ refers here to the use of the Optimized Certainty Equivalent as a means to measure expectation and risk. This comprises the well-known entropic risk measure and Conditional Value-at-Risk. We restrict our considerations to stationary problems with an infinite time horizon. Conditions are given under which optimal policies exist and solution procedures are explained. We present both the theory when the Optimized Certainty Equivalent is applied recursively as well as the case where it is applied to the cumulated reward. Discounted as well as non-discounted models are reviewed.</p>","PeriodicalId":49862,"journal":{"name":"Mathematical Methods of Operations Research","volume":"94 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140585293","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A simple, efficient and versatile objective space algorithm for multiobjective integer programming 多目标整数编程的简单、高效和通用目标空间算法
IF 1.2 4区 数学
Mathematical Methods of Operations Research Pub Date : 2024-03-21 DOI: 10.1007/s00186-023-00841-0
Kerstin Dächert, Tino Fleuren, Kathrin Klamroth
{"title":"A simple, efficient and versatile objective space algorithm for multiobjective integer programming","authors":"Kerstin Dächert, Tino Fleuren, Kathrin Klamroth","doi":"10.1007/s00186-023-00841-0","DOIUrl":"https://doi.org/10.1007/s00186-023-00841-0","url":null,"abstract":"<p>In the last years a multitude of algorithms have been proposed to solve multiobjective integer programming problems. However, only few authors offer open-source implementations. On the other hand, new methods are typically compared to code that is publicly available, even if this code is known to be outperformed. In this paper, we aim to overcome this problem by proposing a new state-of-the-art algorithm with an open-source implementation in <span>C++</span>. The underlying method falls into the class of objective space methods, i.e., it decomposes the overall problem into a series of scalarized subproblems that can be solved with efficient single-objective IP-solvers. It keeps the number of required subproblems small by avoiding redundancies, and it can be combined with different scalarizations that all lead to comparably simple subproblems. Our algorithm bases on previous results but combines them in a new way. Numerical experiments with up to ten objectives validate that the method is efficient and that it scales well to higher dimensional problems.</p>","PeriodicalId":49862,"journal":{"name":"Mathematical Methods of Operations Research","volume":"276 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140205406","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
2023 MMOR best paper award 2023 年网络游戏最佳论文奖
IF 1.2 4区 数学
Mathematical Methods of Operations Research Pub Date : 2024-03-07 DOI: 10.1007/s00186-024-00853-4
Oliver Stein
{"title":"2023 MMOR best paper award","authors":"Oliver Stein","doi":"10.1007/s00186-024-00853-4","DOIUrl":"https://doi.org/10.1007/s00186-024-00853-4","url":null,"abstract":"","PeriodicalId":49862,"journal":{"name":"Mathematical Methods of Operations Research","volume":"66 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140075944","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Trilevel and multilevel optimization using monotone operator theory 利用单调算子理论进行三级和多级优化
IF 1.2 4区 数学
Mathematical Methods of Operations Research Pub Date : 2024-02-28 DOI: 10.1007/s00186-024-00852-5
{"title":"Trilevel and multilevel optimization using monotone operator theory","authors":"","doi":"10.1007/s00186-024-00852-5","DOIUrl":"https://doi.org/10.1007/s00186-024-00852-5","url":null,"abstract":"<h3>Abstract</h3> <p>We consider rather a general class of multi-level optimization problems, where a convex objective function is to be minimized subject to constraints of optimality of nested convex optimization problems. As a special case, we consider a trilevel optimization problem, where the objective of the two lower layers consists of a sum of a smooth and a non-smooth term. Based on fixed-point theory and related arguments, we present a natural first-order algorithm and analyze its convergence and rates of convergence in several regimes of parameters.</p>","PeriodicalId":49862,"journal":{"name":"Mathematical Methods of Operations Research","volume":"170 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140006412","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The non-preemptive ‘Join the Shortest Queue–Serve the Longest Queue’ service system with or without switch-over times 非抢占式 "加入最短队列-为最长队列服务 "服务系统，有无切换时间限制
IF 1.2 4区 数学
Mathematical Methods of Operations Research Pub Date : 2024-02-26 DOI: 10.1007/s00186-023-00848-7
Efrat Perel, Nir Perel, Uri Yechiali
{"title":"The non-preemptive ‘Join the Shortest Queue–Serve the Longest Queue’ service system with or without switch-over times","authors":"Efrat Perel, Nir Perel, Uri Yechiali","doi":"10.1007/s00186-023-00848-7","DOIUrl":"https://doi.org/10.1007/s00186-023-00848-7","url":null,"abstract":"<p>A 2-queue system with a single-server operating according to the combined ‘Join the Shortest Queue–Serve the Longest Queue’ regime is analyzed. Both cases, with or without server’s switch-over times, are investigated under the non-preemptive discipline. Instead of dealing with a state space comprised of two un-bounded dimensions, a non-conventional formulation is constructed, leading to an alternative two-dimensional state space, where only one dimension is infinite. As a result, the system is defined as a quasi birth and death process and is analyzed via both the probability generating functions method and the matrix geometric formulation. Consequently, the system’s two-dimensional probability mass function is derived, from which the system’s performance measures, such as mean queue sizes, mean sojourn times, fraction of time the server resides in each queue, correlation coefficient between the queue sizes, and the probability mass function of the difference between the queue sizes, are obtained. Extensive numerical results for various values of the system’s parameters are presented, as well as a comparison between the current non-preemptive model and its twin system of preemptive service regime. One of the conclusions is that, depending on the variability of the various parameters, the preemptive regime is not necessarily more efficient than the non-preemptive one. Finally, economic issues are discussed and numerical comparisons are presented, showing the advantages and disadvantages of each regime.</p>","PeriodicalId":49862,"journal":{"name":"Mathematical Methods of Operations Research","volume":"32 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139980019","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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