Discrete Optimization最新文献_第8页

LP-based approximation for uniform capacitated facility location problem 均匀容能设施选址问题的lp逼近

IF 1.1 4区数学

Discrete Optimization Pub Date : 2022-08-01 DOI: 10.1016/j.disopt.2022.100723

Sapna Grover , Neelima Gupta , Samir Khuller

{"title":"LP-based approximation for uniform capacitated facility location problem","authors":"Sapna Grover , Neelima Gupta , Samir Khuller","doi":"10.1016/j.disopt.2022.100723","DOIUrl":"10.1016/j.disopt.2022.100723","url":null,"abstract":"<div>In this paper, we study uniform hard capacitated facility location problem. The standard LP for the problem is known to have an unbounded integrality gap. We present constant factor approximation by rounding a solution to the standard LP with a slight <math><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mi>ϵ</mi><mo>)</mo></mrow></math> violation in the capacities.Our result shows that the standard LP is not too bad.Our algorithm is simple and more efficient as compared to the strengthened LP-based true approximation that uses the inefficient ellipsoid method with a separation oracle. True approximations are also known for the problem using local search techniques that suffer from the problem of convergence. Moreover, solutions based on standard LP are easier to integrate with other LP-based algorithms.The result is also extended to give the first approximation for uniform hard capacitated <math><mi>k</mi></math>-facility location problem violating the capacities by a factor of <math><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mi>ϵ</mi><mo>)</mo></mrow></math> and breaking the barrier of 2 in capacity violation. The result violates the cardinality by a factor of <math><mfrac><mrow><mn>2</mn></mrow><mrow><mn>1</mn><mo>+</mo><mi>ϵ</mi></mrow></mfrac></math>.</div>","PeriodicalId":50571,"journal":{"name":"Discrete Optimization","volume":"45 ","pages":"Article 100723"},"PeriodicalIF":1.1,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131270426","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: 1

On the length of L-Grundy sequences 关于L-Grundy序列的长度

IF 1.1 4区数学

Discrete Optimization Pub Date : 2022-08-01 DOI: 10.1016/j.disopt.2022.100725

Rebekah Herrman , Stephen G.Z. Smith

引用次数: 2

A theoretical justification of the set covering greedy heuristic of Caprara et al. capprara等人的集合覆盖贪心启发式的理论证明。

IF 1.1 4区数学

Discrete Optimization Pub Date : 2022-08-01 DOI: 10.1016/j.disopt.2022.100700

Torbjörn Larsson, Nils-Hassan Quttineh

引用次数: 0

The Arc-Item-Load and Related Formulations for the Cumulative Vehicle Routing Problem 累积车辆路径问题的弧项载荷及相关公式

IF 1.1 4区数学

Discrete Optimization Pub Date : 2022-08-01 DOI: 10.1016/j.disopt.2022.100710

Mauro Henrique Mulati , Ricardo Fukasawa , Flávio Keidi Miyazawa

{"title":"The Arc-Item-Load and Related Formulations for the Cumulative Vehicle Routing Problem","authors":"Mauro Henrique Mulati , Ricardo Fukasawa , Flávio Keidi Miyazawa","doi":"10.1016/j.disopt.2022.100710","DOIUrl":"10.1016/j.disopt.2022.100710","url":null,"abstract":"<div>The Capacitated Vehicle Routing Problem (CVRP) consists of finding the cheapest way to serve a set of customers with a fleet of vehicles of a given capacity. While serving a particular customer, each vehicle picks up its demand and carries its weight throughout the rest of its route. While costs in the classical CVRP are measured in terms of a given arc distance, the Cumulative Vehicle Routing Problem (CmVRP) is a variant of the problem that aims to minimize total energy consumption. Each arc’s energy consumption is defined as the product of the arc distance by the weight accumulated since the beginning of the route.The purpose of this work is to propose several different formulations for the CmVRP and to study their Linear Programming (LP) relaxations. In particular, the goal is to study formulations based on combining an arc-item concept (that keeps track of whether a given customer has already been visited when traversing a specific arc) with another formulation from the recent literature, the Arc-Load formulation (that determines how much load goes through an arc).Both formulations have been studied independently before – the Arc-Item is very similar to a multi-commodity-flow formulation in Letchford and Salazar-González (2015) and the Arc-Load formulation has been studied in Fukasawa et al. (2016) – and their LP relaxations are incomparable. Nonetheless, we show that a formulation combining the two (called Arc-Item-Load) may lead to a significantly stronger LP relaxation, thereby indicating that the two formulations capture complementary aspects of the problem. In addition, we study how set partitioning based formulations can be combined with these formulations. We present computational experiments on several well-known benchmark instances that highlight the advantages and drawbacks of the LP relaxation of each formulation and point to potential avenues of future research.</div>","PeriodicalId":50571,"journal":{"name":"Discrete Optimization","volume":"45 ","pages":"Article 100710"},"PeriodicalIF":1.1,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124959123","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: 2

A cut-and-branch algorithm for the Quadratic Knapsack Problem 二次型背包问题的割枝算法

IF 1.1 4区数学

Discrete Optimization Pub Date : 2022-05-01 DOI: 10.1016/j.disopt.2020.100579

Franklin Djeumou Fomeni , Konstantinos Kaparis , Adam N. Letchford

引用次数: 15

Penalty and partitioning techniques to improve performance of QUBO solvers 改进QUBO求解器性能的惩罚和分区技术

IF 1.1 4区数学

Discrete Optimization Pub Date : 2022-05-01 DOI: 10.1016/j.disopt.2020.100594

Amit Verma, Mark Lewis

{"title":"Penalty and partitioning techniques to improve performance of QUBO solvers","authors":"Amit Verma, Mark Lewis","doi":"10.1016/j.disopt.2020.100594","DOIUrl":"10.1016/j.disopt.2020.100594","url":null,"abstract":"<div>Quadratic Unconstrained Binary Optimization (QUBO) modeling has become a unifying framework for solving a wide variety of both unconstrained as well as constrained optimization problems. More recently, QUBO (or equivalent <math><mrow><mo>−</mo><mn>1</mn><mo>/</mo><mo>+</mo><mn>1</mn></mrow></math> Ising Spin) models are a requirement for quantum annealing computers. Noisy Intermediate-Scale Quantum (NISQ) computing refers to classical computing preparing or compiling problem instances for compatibility with quantum hardware architectures. The process of converting a constrained problem to a QUBO compatible quantum annealing problem is an important part of the quantum compiler architecture and specifically when converting constrained models to unconstrained the choice of penalty magnitude is not trivial because using a large penalty to enforce constraints can overwhelm the solution landscape, while having too small a penalty allows infeasible optimal solutions. In this paper we present NISQ approaches to bound the magnitude of the penalty scalar <math><mi>M</mi></math> and demonstrate efficacy on a benchmark set of problems having a single equality constraint and present a QUBO partitioning approach validated by experimentation.</div>","PeriodicalId":50571,"journal":{"name":"Discrete Optimization","volume":"44 ","pages":"Article 100594"},"PeriodicalIF":1.1,"publicationDate":"2022-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.disopt.2020.100594","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126767619","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: 29

Preface: Optimization and Discrete Geometry 前言:优化和离散几何

IF 1.1 4区数学

Discrete Optimization Pub Date : 2022-05-01 DOI: 10.1016/j.disopt.2021.100658

Antoine Deza, Frédéric Meunier, Tal Raviv

引用次数: 0

Preface: Quadratic combinatorial optimization problems 前言:二次组合优化问题

IF 1.1 4区数学

Discrete Optimization Pub Date : 2022-05-01 DOI: 10.1016/j.disopt.2022.100688

Abraham Punnen, Renata Sotirov

引用次数: 0

EXPEDIS: An exact penalty method over discrete sets 离散集上的精确惩罚方法

IF 1.1 4区数学

Discrete Optimization Pub Date : 2022-05-01 DOI: 10.1016/j.disopt.2021.100622

Nicolò Gusmeroli , Angelika Wiegele

引用次数: 8

A two-phase tabu search based evolutionary algorithm for the maximum diversity problem 一种基于两阶段禁忌搜索的最大多样性问题进化算法

IF 1.1 4区数学

Discrete Optimization Pub Date : 2022-05-01 DOI: 10.1016/j.disopt.2020.100613

Xiaolu Liu , Jiaming Chen , Minghui Wang , Yang Wang , Zhouxing Su , Zhipeng Lü

{"title":"A two-phase tabu search based evolutionary algorithm for the maximum diversity problem","authors":"Xiaolu Liu , Jiaming Chen , Minghui Wang , Yang Wang , Zhouxing Su , Zhipeng Lü","doi":"10.1016/j.disopt.2020.100613","DOIUrl":"10.1016/j.disopt.2020.100613","url":null,"abstract":"<div>In this paper, we study the maximum diversity problem (MDP) which is equivalent to the quadratic unconstrained binary optimization (QUBO) problem with cardinality constraint. The MDP aims to select a subset of elements with given cardinality such that the sum of pairwise distances between any two elements in the selected subset is maximized. For solving this computationally challenging problem, we propose a two-phase tabu search based evolutionary algorithm (TPTS/EA), which integrates several distinguishing features to ensure the diversity and the quality of the evolution, such as a two-phase tabu search algorithm which consists of a dynamic candidate list (DCL) strategy-based traditional tabu search in the first phase and a solution-based tabu search procedure to refine the search in the second phase, and two path-relinking based recombination operators to generate new offspring solutions. Tested on three sets of totally 140 public instances in the literature, the study demonstrates the efficacy of the proposed TPTS/EA algorithm in terms of both solution quality and computational efficiency. Specifically, our proposed TPTS/EA algorithm is able to improve the previous best known results for 2 instances, while matching the previous best-known solutions for 130 instances. We also provide experimental evidences to highlight the beneficial effect of several important components in our TPTS/EA algorithm.</div>","PeriodicalId":50571,"journal":{"name":"Discrete Optimization","volume":"44 ","pages":"Article 100613"},"PeriodicalIF":1.1,"publicationDate":"2022-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.disopt.2020.100613","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122460046","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: 5