{"title":"The circle packing problem: A theoretical comparison of various convexification techniques","authors":"Aida Khajavirad","doi":"10.1016/j.orl.2024.107197","DOIUrl":"10.1016/j.orl.2024.107197","url":null,"abstract":"<div><div>We consider the problem of packing a given number of congruent circles with the maximum radius in a unit square as a mathematical optimization problem. Due to the presence of non-overlapping constraints, this problem is a notoriously difficult nonconvex quadratically constrained optimization problem, which possesses many local optima. We consider several popular convexification techniques, giving rise to linear programming relaxations and semidefinite programming relaxations for the circle packing problem. We compare the strength of these relaxations theoretically, thereby proving the conjectures by Anstreicher. Our results serve as a theoretical justification for the ineffectiveness of existing machinery for convexification of non-overlapping constraints.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"57 ","pages":"Article 107197"},"PeriodicalIF":0.8,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142534930","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}
{"title":"Structured pruning of neural networks for constraints learning","authors":"Matteo Cacciola , Antonio Frangioni , Andrea Lodi","doi":"10.1016/j.orl.2024.107194","DOIUrl":"10.1016/j.orl.2024.107194","url":null,"abstract":"<div><div>In recent years, the integration of Machine Learning (ML) models with Operation Research (OR) tools has gained popularity in applications such as cancer treatment, algorithmic configuration, and chemical process optimization. This integration often uses Mixed Integer Programming (MIP) formulations to represent the chosen ML model, that is often an Artificial Neural Networks (ANNs) due to their widespread use. However, ANNs frequently contain a large number of parameters, resulting in MIP formulations impractical to solve. In this paper we showcase the effectiveness of a ANN pruning, when applied to models prior to their integration into MIPs. We discuss why pruning is more suitable in this context than other ML compression techniques, and we highlight the potential of appropriate pruning strategies via experiments on MIPs used to construct adversarial examples to ANNs. Our results demonstrate that pruning offers remarkable reductions in solution times without hindering the quality of the final decision, enabling the resolution of previously unsolvable instances.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"57 ","pages":"Article 107194"},"PeriodicalIF":0.8,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142441127","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}
{"title":"Worst-case analysis of restarted primal-dual hybrid gradient on totally unimodular linear programs","authors":"Oliver Hinder","doi":"10.1016/j.orl.2024.107199","DOIUrl":"10.1016/j.orl.2024.107199","url":null,"abstract":"<div><div>We analyze restarted PDHG on totally unimodular linear programs. In particular, we show that restarted PDHG finds an <em>ϵ</em>-optimal solution in <span><math><mi>O</mi><mo>(</mo><mi>H</mi><msubsup><mrow><mi>m</mi></mrow><mrow><mn>1</mn></mrow><mrow><mn>2.5</mn></mrow></msubsup><msqrt><mrow><mtext>nnz</mtext><mo>(</mo><mi>A</mi><mo>)</mo></mrow></msqrt><mi>log</mi><mo></mo><mo>(</mo><mi>H</mi><msub><mrow><mi>m</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>/</mo><mi>ϵ</mi><mo>)</mo><mo>)</mo></math></span> matrix-vector multiplies where <span><math><msub><mrow><mi>m</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> is the number of constraints, <span><math><msub><mrow><mi>m</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> the number of variables, <span><math><mtext>nnz</mtext><mo>(</mo><mi>A</mi><mo>)</mo></math></span> is the number of nonzeros in the constraint matrix, <em>H</em> is the largest absolute coefficient in the right hand side or objective vector, and <em>ϵ</em> is the distance to optimality of the outputted solution.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"57 ","pages":"Article 107199"},"PeriodicalIF":0.8,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142441128","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Asymptotic optimality of base-stock policies for lost-sales inventory systems with stochastic lead times","authors":"Shilin Yuan , Jiameng Lyu , Jinxing Xie , Yuan Zhou","doi":"10.1016/j.orl.2024.107196","DOIUrl":"10.1016/j.orl.2024.107196","url":null,"abstract":"<div><div>We consider the lost-sales inventory systems with stochastic lead times and establish the asymptotic optimality of base-stock policies for such systems. Specifically, we prove that as the per-unit lost-sales penalty cost becomes large compared to the per-unit holding cost, the ratio of the optimal base-stock policy's cost to the optimal cost converges to one. Our paper provides a theoretical guarantee of the widely adopted base-stock policies in lost-sales inventory systems with stochastic lead times for the first time.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"57 ","pages":"Article 107196"},"PeriodicalIF":0.8,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142437979","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}
{"title":"Responsibility and solidarity principles in sharing the costs of cleaning a polluted river","authors":"David Lowing","doi":"10.1016/j.orl.2024.107198","DOIUrl":"10.1016/j.orl.2024.107198","url":null,"abstract":"<div><div>To clean a polluted river, some agents must undertake operations that incur costs. The problem is to determine a fair method to share these expenses among agents. We consider the established methods of Local Responsibility Sharing and Upstream Equal Sharing, based on the responsibility principles of Absolute Territorial Sovereignty and Unlimited Territorial Integrity, respectively. We combine these with Total Solidarity, a method based on a solidarity principle. This yields new cost-sharing methods, which we characterize axiomatically.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"57 ","pages":"Article 107198"},"PeriodicalIF":0.8,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142433519","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Tighter ‘uniform bounds for Black–Scholes implied volatility’ and the applications to root-finding","authors":"Jaehyuk Choi , Jeonggyu Huh , Nan Su","doi":"10.1016/j.orl.2024.107189","DOIUrl":"10.1016/j.orl.2024.107189","url":null,"abstract":"<div><div>Using the option delta systematically, we derive tighter lower and upper bounds of the Black–Scholes implied volatility than those in Tehranchi (2016) <span><span>[11]</span></span>. As an application, we propose a Newton–Raphson algorithm on the log price that converges rapidly for all price ranges when using a new lower bound as an initial guess. Our new algorithm is a better alternative to the widely used naive Newton–Raphson algorithm, whose convergence is slow for extreme option prices.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"57 ","pages":"Article 107189"},"PeriodicalIF":0.8,"publicationDate":"2024-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142419780","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}
N. Yekezare , M. Zohrehbandian , M. Maghasedi , F. Bonomo-Braberman
{"title":"Optimality of DSatur algorithm on chordal graphs","authors":"N. Yekezare , M. Zohrehbandian , M. Maghasedi , F. Bonomo-Braberman","doi":"10.1016/j.orl.2024.107185","DOIUrl":"10.1016/j.orl.2024.107185","url":null,"abstract":"<div><div>DSatur is a widely-used heuristic algorithm for graph coloring, proposed by Daniel Brélaz in 1979. It is based on the greedy coloring approach, but selecting the next vertex to be colored from those that maximize the number of colors already used by their neighbors. Though not always optimal, this algorithm is known to be optimal on certain families, like cycles or bipartite graphs. In this paper, we prove the optimality of DSatur on chordal graphs, a superclass of interval graphs.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"57 ","pages":"Article 107185"},"PeriodicalIF":0.8,"publicationDate":"2024-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142419647","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}
{"title":"Complexity analysis and numerical implementation of a new interior-point algorithm for semidefinite optimization","authors":"Billel Zaoui, Djamel Benterki, Samia Khelladi","doi":"10.1016/j.orl.2024.107192","DOIUrl":"10.1016/j.orl.2024.107192","url":null,"abstract":"<div><div>We generalize Zhang and Xu's (2011) <span><span>[22]</span></span> interior point algorithm for linear optimization to semidefinite optimization problems in order to define a new search direction. The symmetrization of the search direction is based on the full Nesterov-Todd scaling scheme. Moreover, we show that the obtained algorithm solves the studied problem in polynomial time and that the short-step algorithm has the best-known iteration bound, namely <span><math><mi>O</mi><mo>(</mo><msqrt><mrow><mi>n</mi></mrow></msqrt><mi>log</mi><mo></mo><mfrac><mrow><mi>n</mi></mrow><mrow><mi>ε</mi></mrow></mfrac><mo>)</mo></math></span>-iterations. Finally, we report a comparative numerical study to show the efficiency of our proposed algorithm.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"57 ","pages":"Article 107192"},"PeriodicalIF":0.8,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142419648","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}
{"title":"Finite horizon partially observable semi-Markov decision processes under risk probability criteria","authors":"Xin Wen , Xianping Guo , Li Xia","doi":"10.1016/j.orl.2024.107187","DOIUrl":"10.1016/j.orl.2024.107187","url":null,"abstract":"<div><div>This paper deals with a risk probability minimization problem for finite horizon partially observable semi-Markov decision processes, which are the fairly most general models for stochastic dynamic systems. In contrast to the expected discounted and average criteria, the optimality investigated in this paper is to minimize the probability that the accumulated rewards do not reach a prescribed profit level at the finite terminal stage. First, the state space is augmented as the joint conditional distribution of the current unobserved state and the remaining profit goal. We introduce a class of policies depending on observable histories and a class of Markov policies including observable process with the joint conditional distribution. Then under mild assumptions, we prove that the value function is the unique solution to the optimality equation for the probability criterion by using iteration techniques. The existence of (<em>ϵ</em>-)optimal Markov policy for this problem is established. Finally, we use a bandit problem with the probability criterion to demonstrate our main results in which an effective algorithm and the corresponding numerical calculation are given for the semi-Markov model. Moreover, for the case of reduction to the discrete-time Markov model, we derive a concise solution.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"57 ","pages":"Article 107187"},"PeriodicalIF":0.8,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142359041","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}
{"title":"A note on the stability of monotone Markov chains","authors":"Bar Light","doi":"10.1016/j.orl.2024.107188","DOIUrl":"10.1016/j.orl.2024.107188","url":null,"abstract":"<div><div>This note studies monotone Markov chains, a subclass of Markov chains with extensive applications in operations research and economics. While the properties that ensure the global stability of these chains are well studied, their establishment often relies on the fulfillment of a certain splitting condition. We address the challenges of verifying the splitting condition by introducing simple, applicable conditions that ensure global stability. The simplicity of these conditions is demonstrated through various examples including autoregressive processes, portfolio allocation problems and resource allocation dynamics.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"57 ","pages":"Article 107188"},"PeriodicalIF":0.8,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142359040","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}