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Mathematical Methods of Operations Research最新文献

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Combining discrete and continuous information for multi-criteria optimization problems 结合离散和连续信息，解决多标准优化问题
IF 1.2 4区 数学
Mathematical Methods of Operations Research Pub Date : 2024-02-23 DOI: 10.1007/s00186-024-00849-0
{"title":"Combining discrete and continuous information for multi-criteria optimization problems","authors":"","doi":"10.1007/s00186-024-00849-0","DOIUrl":"https://doi.org/10.1007/s00186-024-00849-0","url":null,"abstract":"<h3>Abstract</h3> <p>In multi-criteria optimization problems that originate from real-world decision making tasks, we often find the following structure: There is an underlying continuous, possibly even convex model for the multiple outcome measures depending on the design variables, but these outcomes are additionally assigned to discrete categories according to their desirability for the decision maker. Multi-criteria deliberations may then take place at the level of these discrete labels, while the calculation of a specific design remains a continuous problem. In this work, we analyze this type of problem and provide theoretical results about its solution set. We prove that the discrete decision problem can be tackled by solving scalarizations of the underlying continuous model. Based on our analysis we propose multiple algorithmic approaches that are specifically suited to handle these problems. We compare the algorithms based on a set of test problems. Furthermore, we apply our methods to a real-world radiotherapy planning example.</p>","PeriodicalId":49862,"journal":{"name":"Mathematical Methods of Operations Research","volume":"32 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139949805","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 unified approach to inverse robust optimization problems 逆鲁棒性优化问题的统一方法
IF 1.2 4区 数学
Mathematical Methods of Operations Research Pub Date : 2024-02-22 DOI: 10.1007/s00186-023-00844-x
{"title":"A unified approach to inverse robust optimization problems","authors":"","doi":"10.1007/s00186-023-00844-x","DOIUrl":"https://doi.org/10.1007/s00186-023-00844-x","url":null,"abstract":"<h3>Abstract</h3> <p>A variety of approaches has been developed to deal with uncertain optimization problems. Often, they start with a given set of uncertainties and then try to minimize the influence of these uncertainties. The reverse view is to first set a budget for the price one is willing to pay and then find the most robust solution. In this article, we aim to unify these inverse approaches to robustness. We provide a general problem definition and a proof of the existence of its solution. We study properties of this solution such as closedness, convexity, and boundedness. We also provide a comparison with existing robustness concepts such as the stability radius, the resilience radius, and the robust feasibility radius. We show that the general definition unifies these approaches. We conclude with an example that demonstrates the flexibility of the introduced concept.</p>","PeriodicalId":49862,"journal":{"name":"Mathematical Methods of Operations Research","volume":"18 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139949856","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
Complexity of the multiobjective minimum weight minimum stretch spanner problem 多目标最小权重最小拉伸扳手问题的复杂性
IF 1.2 4区 数学
Mathematical Methods of Operations Research Pub Date : 2024-02-15 DOI: 10.1007/s00186-024-00850-7
Fritz Bökler, Henning Jasper
{"title":"Complexity of the multiobjective minimum weight minimum stretch spanner problem","authors":"Fritz Bökler, Henning Jasper","doi":"10.1007/s00186-024-00850-7","DOIUrl":"https://doi.org/10.1007/s00186-024-00850-7","url":null,"abstract":"<p>In this paper, we take an in-depth look at the complexity of a hitherto unexplored <i>multiobjective minimum weight minimum stretch spanner</i> problem; or in short <i>multiobjective spanner (MSp)</i> problem. The MSp is a multiobjective generalization of the well-studied minimum t-spanner problem. This multiobjective approach allows to find solutions that offer a viable compromise between cost and utility—a property that is usually neglected in singleobjective optimization. Thus, the MSp can be a powerful modeling tool when it comes to, e.g., the planning of transportation or communication networks. This holds especially in disaster management, where both responsiveness and practicality are crucial. We show that for degree-3 bounded outerplanar instances the MSp is intractable and computing the non-dominated set is <b>BUCO</b>-hard. Additionally, we prove that if <span>({textbf{P}} ne textbf{NP})</span>, the set of extreme points cannot be computed in output-polynomial time, for instances with unit costs and arbitrary graphs. Furthermore, we consider the directed versions of the cases above.</p>","PeriodicalId":49862,"journal":{"name":"Mathematical Methods of Operations Research","volume":"4 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139759301","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
Stochastic Gauss–Seidel type inertial proximal alternating linearized minimization and its application to proximal neural networks 随机高斯-赛德尔型惯性近端交替线性化最小化及其在近端神经网络中的应用
IF 1.2 4区 数学
Mathematical Methods of Operations Research Pub Date : 2024-02-06 DOI: 10.1007/s00186-024-00851-6
{"title":"Stochastic Gauss–Seidel type inertial proximal alternating linearized minimization and its application to proximal neural networks","authors":"","doi":"10.1007/s00186-024-00851-6","DOIUrl":"https://doi.org/10.1007/s00186-024-00851-6","url":null,"abstract":"<h3>Abstract</h3> <p>In many optimization problems arising from machine learning, image processing, and statistics communities, the objective functions possess a special form involving huge amounts of data, which encourages the application of stochastic algorithms. In this paper, we study such a broad class of nonconvex nonsmooth minimization problems, whose objective function is the sum of a smooth function of the entire variables and two nonsmooth functions of each variable. We propose to solve this problem with a stochastic Gauss–Seidel type inertial proximal alternating linearized minimization (denoted by SGiPALM) algorithm. We prove that under Kurdyka–Łojasiewicz (KŁ) property and some mild conditions, each bounded sequence generated by SGiPALM with the variance-reduced stochastic gradient estimator globally converges to a critical point after a finite number of iterations, or almost surely satisfies the finite length property. We also apply the SGiPALM algorithm to the proximal neural networks (PNN) with 4 layers for classification tasks on the MNIST dataset and compare it with other deterministic and stochastic optimization algorithms, the results illustrate the effectiveness of the proposed algorithm.</p>","PeriodicalId":49862,"journal":{"name":"Mathematical Methods of Operations Research","volume":"18 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139759238","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
Solving quasimonotone and non-monotone variational inequalities 求解准单调和非单调变分不等式
IF 1.2 4区 数学
Mathematical Methods of Operations Research Pub Date : 2024-01-19 DOI: 10.1007/s00186-023-00846-9
V. A. Uzor, T. O. Alakoya, O. T. Mewomo, A. Gibali
{"title":"Solving quasimonotone and non-monotone variational inequalities","authors":"V. A. Uzor, T. O. Alakoya, O. T. Mewomo, A. Gibali","doi":"10.1007/s00186-023-00846-9","DOIUrl":"https://doi.org/10.1007/s00186-023-00846-9","url":null,"abstract":"<p>We present a simple iterative method for solving quasimonotone as well as classical variational inequalities without monotonicity. Strong convergence analysis is given under mild conditions and thus generalize the few existing results that only present weak convergence methods under restrictive assumptions. We give finite and infinite dimensional numerical examples to compare and illustrate the simplicity and computational advantages of the proposed scheme.</p>","PeriodicalId":49862,"journal":{"name":"Mathematical Methods of Operations Research","volume":"13 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139506334","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 fast and robust algorithm for solving biobjective mixed integer programs 求解生物目标混合整数程序的快速稳健算法
IF 1.2 4区 数学
Mathematical Methods of Operations Research Pub Date : 2024-01-12 DOI: 10.1007/s00186-023-00843-y
Diego Pecin, Ian Herszterg, Tyler A. Perini, N. Boland, M. Savelsbergh
{"title":"A fast and robust algorithm for solving biobjective mixed integer programs","authors":"Diego Pecin, Ian Herszterg, Tyler A. Perini, N. Boland, M. Savelsbergh","doi":"10.1007/s00186-023-00843-y","DOIUrl":"https://doi.org/10.1007/s00186-023-00843-y","url":null,"abstract":"","PeriodicalId":49862,"journal":{"name":"Mathematical Methods of Operations Research","volume":"1 6","pages":"1-42"},"PeriodicalIF":1.2,"publicationDate":"2024-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139437844","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
An outer approximation algorithm for generating the Edgeworth–Pareto hull of multi-objective mixed-integer linear programming problems 生成多目标混合整数线性规划问题埃奇沃斯-帕雷托体的外近似算法
IF 1.2 4区 数学
Mathematical Methods of Operations Research Pub Date : 2024-01-04 DOI: 10.1007/s00186-023-00847-8
Fritz Bökler, Sophie N. Parragh, Markus Sinnl, Fabien Tricoire
{"title":"An outer approximation algorithm for generating the Edgeworth–Pareto hull of multi-objective mixed-integer linear programming problems","authors":"Fritz Bökler, Sophie N. Parragh, Markus Sinnl, Fabien Tricoire","doi":"10.1007/s00186-023-00847-8","DOIUrl":"https://doi.org/10.1007/s00186-023-00847-8","url":null,"abstract":"<p>In this paper, we present an outer approximation algorithm for computing the Edgeworth–Pareto hull of multi-objective mixed-integer linear programming problems (MOMILPs). It produces the extreme points (i.e., the vertices) as well as the facets of the Edgeworth–Pareto hull. We note that these extreme points are the extreme supported non-dominated points of a MOMILP. We also show how to extend the concept of geometric duality for multi-objective linear programming problems to the Edgeworth–Pareto hull of MOMILPs and use this extension to develop the algorithm. The algorithm relies on a novel oracle that solves single-objective weighted-sum problems and we show that the required number of oracle calls is polynomial in the number of facets of the convex hull of the extreme supported non-dominated points in the case of MOMILPs. Thus, for MOMILPs for which the weighted-sum problem is solvable in polynomial time, the facets can be computed with incremental-polynomial delay—a result that was formerly only known for the computation of extreme supported non-dominated points. Our algorithm can be an attractive option to compute lower bound sets within multi-objective branch-and-bound algorithms for solving MOMILPs. This is for several reasons as (i) the algorithm starts from a trivial valid lower bound set then iteratively improves it, thus at any iteration of the algorithm a lower bound set is available; (ii) the algorithm also produces efficient solutions (i.e., solutions in the decision space); (iii) in any iteration of the algorithm, a relaxation of the MOMILP can be solved, and the obtained points and facets still provide a valid lower bound set. Moreover, for the special case of multi-objective linear programming problems, the algorithm solves the problem to global optimality. A computational study on a set of benchmark instances from the literature is provided.</p>","PeriodicalId":49862,"journal":{"name":"Mathematical Methods of Operations Research","volume":"16 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139103884","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 spline smoothing homotopy method for nonlinear programming problems with both inequality and equality constraints 具有不等式和等式约束的非线性程序设计问题的样条平滑同调方法
IF 1.2 4区 数学
Mathematical Methods of Operations Research Pub Date : 2023-12-16 DOI: 10.1007/s00186-023-00845-w
Li Dong, Zhengyong Zhou, Li Yang
{"title":"A spline smoothing homotopy method for nonlinear programming problems with both inequality and equality constraints","authors":"Li Dong, Zhengyong Zhou, Li Yang","doi":"10.1007/s00186-023-00845-w","DOIUrl":"https://doi.org/10.1007/s00186-023-00845-w","url":null,"abstract":"<p>In this paper, we construct a new spline smoothing homotopy method for solving general nonlinear programming problems with a large number of complicated constraints. We transform the equality constraints into the inequality constraints by introducing two parameters. Subsequently, we use smooth spline functions to approximate the inequality constraints. The smooth spline functions involve only few inequality constraints. In other words, the method introduces an active set technique. Under some weaker conditions, we obtain the global convergence of the new spline smoothing homotopy method. We perform numerical tests to compare the new method to other methods, and the numerical results show that the new spline smoothing homotopy method is highly efficient.</p>","PeriodicalId":49862,"journal":{"name":"Mathematical Methods of Operations Research","volume":"86 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138687584","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
Analysis of a two-class queueing system with service times dependent on the presence of a certain class 服务时间依赖于某一类的两类排队系统的分析
IF 1.2 4区 数学
Mathematical Methods of Operations Research Pub Date : 2023-12-01 DOI: 10.1007/s00186-023-00842-z
Sara Sasaninejad, Joris Walraevens, Arnaud Devos, Sabine Wittevrongel
{"title":"Analysis of a two-class queueing system with service times dependent on the presence of a certain class","authors":"Sara Sasaninejad, Joris Walraevens, Arnaud Devos, Sabine Wittevrongel","doi":"10.1007/s00186-023-00842-z","DOIUrl":"https://doi.org/10.1007/s00186-023-00842-z","url":null,"abstract":"<p>Most queueing models and their analysis have a rich history and follow a process of increased generality and complexity. In this paper, we introduce a new model, namely a multiclass queueing model where service times depend on the presence of one of the classes. Our model is motivated by road traffic, where the presence of heavy vehicles in a queue slows down the entire system, or, in contrast, where the presence of emergency vehicles may speed up the service. The specific assumption we impose is that the service time of each customer depends on whether at least one customer of that particular class is present in the system at the time of service. Although we study a fairly simple discrete-time model, we show that analysis is not straightforward. Furthermore, numerical examples expose that the impact of particular customers in the system can lead to a substantial slow down (or, in contrast, speed up) of the entire system.</p>","PeriodicalId":49862,"journal":{"name":"Mathematical Methods of Operations Research","volume":"21 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138527230","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
Directional and approximate efficiency in set optimization 集合优化的定向和近似效率
IF 1.2 4区 数学
Mathematical Methods of Operations Research Pub Date : 2023-11-29 DOI: 10.1007/s00186-023-00840-1
Marius Durea, Elena-Andreea Florea
{"title":"Directional and approximate efficiency in set optimization","authors":"Marius Durea, Elena-Andreea Florea","doi":"10.1007/s00186-023-00840-1","DOIUrl":"https://doi.org/10.1007/s00186-023-00840-1","url":null,"abstract":"<p>We investigate, in the framework of set optimization, some issues that are well studied in vectorial setting, that is, penalization procedures, properness of solutions and optimality conditions on primal spaces. Therefore, with this study we aim at completing the literature dedicated to set optimization with some results that have well established correspondence in the classical vector optimization.</p>","PeriodicalId":49862,"journal":{"name":"Mathematical Methods of Operations Research","volume":"26 4","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138527240","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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