Discrete Optimization最新文献_第8页

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":null,"pages":null},"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

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":null,"pages":null},"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

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

Reinforcement learning enhanced multi-neighborhood tabu search for the max-mean dispersion problem 强化学习对最大均值分散问题的多邻域禁忌搜索进行了改进

IF 1.1 4区数学

Discrete Optimization Pub Date : 2022-05-01 DOI: 10.1016/j.disopt.2021.100625

Xunhao Gu, Songzheng Zhao, Yang Wang

{"title":"Reinforcement learning enhanced multi-neighborhood tabu search for the max-mean dispersion problem","authors":"Xunhao Gu, Songzheng Zhao, Yang Wang","doi":"10.1016/j.disopt.2021.100625","DOIUrl":"10.1016/j.disopt.2021.100625","url":null,"abstract":"<div>This paper presents a highly effective reinforcement learning enhancement of multi-neighborhood tabu search for the max-mean dispersion problem. The reinforcement learning component uses the Q-learning mechanism that incorporates the accumulated feedback information collected from the actions performed during the search to guide the generation of diversified solutions. The tabu search component employs 1-flip and reduced 2-flip neighborhoods to collaboratively perform the neighborhood exploration for attaining high-quality local optima. A learning automata method is integrated in tabu search to adaptively determine the probability of selecting each neighborhood. Computational experiments on 80 challenging benchmark instances demonstrate that the proposed algorithm is favorably competitive with the state-of-the-art algorithms in the literature, by finding new lower bounds for 3 instances and matching the best known results for the other instances. Key elements and properties are also analyzed to disclose the source of the benefits of our integration of learning mechanisms and tabu search.</div>","PeriodicalId":50571,"journal":{"name":"Discrete Optimization","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.disopt.2021.100625","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127187036","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

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

Approximate separable multichoice optimization over monotone systems 单调系统的近似可分离多选择优化

IF 1.1 4区数学

Discrete Optimization Pub Date : 2022-05-01 DOI: 10.1016/j.disopt.2021.100629

Martin Koutecký , Asaf Levin , Syed M. Meesum , Shmuel Onn

{"title":"Approximate separable multichoice optimization over monotone systems","authors":"Martin Koutecký , Asaf Levin , Syed M. Meesum , Shmuel Onn","doi":"10.1016/j.disopt.2021.100629","DOIUrl":"10.1016/j.disopt.2021.100629","url":null,"abstract":"<div>With each separable optimization problem over a given set of vectors is associated its multichoice counterpart which involves choosing <math><mi>n</mi></math> rather than one solutions from the set so as to maximize the given separable function over the sum of the chosen solutions. Such problems have been studied in various contexts under various names, such as load balancing in machine scheduling, congestion routing, minimum shared and vulnerable edge problems, and shifted optimization. Separable multichoice optimization has a very broad expressive power and can be hard already for explicitly given sets of binary points. In this article we consider the problem over monotone systems, also called independence systems. Typically such a system has exponential size, and we assume that it is presented implicitly by a linear optimization oracle. Our main results for separable multichoice optimization are the following. First, the problem over any monotone system with any separable concave function can be approximated in polynomial time with a constant approximation ratio which is independent of <math><mi>n</mi></math>. Second, the problem over any monotone system with an arbitrary separable function can be approximated in polynomial time with an approximation ratio of <math><mrow><mn>1</mn><mo>/</mo><mrow><mo>(</mo><mi>O</mi><mrow><mo>(</mo><mo>log</mo><mi>n</mi><mo>)</mo></mrow><mo>)</mo></mrow></mrow></math>.</div>","PeriodicalId":50571,"journal":{"name":"Discrete Optimization","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.disopt.2021.100629","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133117962","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

Computational study of a branching algorithm for the maximum k-cut problem 最大k割问题分支算法的计算研究

IF 1.1 4区数学

Discrete Optimization Pub Date : 2022-05-01 DOI: 10.1016/j.disopt.2021.100656

Vilmar Jefté Rodrigues de Sousa , Miguel F. Anjos , Sébastien Le Digabel

引用次数: 1

The Bipartite Boolean Quadric Polytope 二部布尔二次多边形

IF 1.1 4区数学

Discrete Optimization Pub Date : 2022-05-01 DOI: 10.1016/j.disopt.2021.100657

Piyashat Sripratak , Abraham P. Punnen , Tamon Stephen

{"title":"The Bipartite Boolean Quadric Polytope","authors":"Piyashat Sripratak , Abraham P. Punnen , Tamon Stephen","doi":"10.1016/j.disopt.2021.100657","DOIUrl":"10.1016/j.disopt.2021.100657","url":null,"abstract":"<div>We consider the Bipartite Boolean Quadratic Programming Problem (BQP01), which generalizes the well-known Boolean quadratic programming problem (QP01). The model has applications in graph theory, matrix factorization and bioinformatics, among others. The primary focus of this paper is on studying the structure of the Bipartite Boolean Quadric Polytope (BQP<math><msup><mrow></mrow><mrow><mi>m</mi><mo>,</mo><mi>n</mi></mrow></msup></math>) resulting from a linearization of a quadratic integer programming formulation of BQP01.We present some basic properties and partial relaxations of BQP<math><msup><mrow></mrow><mrow><mi>m</mi><mo>,</mo><mi>n</mi></mrow></msup></math>, as well as some families of facets and valid inequalities. We find facet-defining inequalities including a family of odd-cycle inequalities. We discuss various approaches to obtain a valid inequality and facets from those of the related Boolean quadric polytope. The key strategy is based on rounding coefficients, and it is applied to the families of clique and cut inequalities in BQP<math><msup><mrow></mrow><mrow><mi>m</mi><mo>,</mo><mi>n</mi></mrow></msup></math>.</div>","PeriodicalId":50571,"journal":{"name":"Discrete Optimization","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.disopt.2021.100657","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127255795","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

BDD-based optimization for the quadratic stable set problem 基于bdd的二次稳定集问题优化

IF 1.1 4区数学

Discrete Optimization Pub Date : 2022-05-01 DOI: 10.1016/j.disopt.2020.100610

Jaime E. González , Andre A. Cire , Andrea Lodi , Louis-Martin Rousseau

{"title":"BDD-based optimization for the quadratic stable set problem","authors":"Jaime E. González , Andre A. Cire , Andrea Lodi , Louis-Martin Rousseau","doi":"10.1016/j.disopt.2020.100610","DOIUrl":"10.1016/j.disopt.2020.100610","url":null,"abstract":"<div>The quadratic stable set problem (QSSP) is a natural extension of the well-known maximum stable set problem. The QSSP is NP-hard and can be formulated as a binary quadratic program, which makes it an interesting case study to be tackled from different optimization paradigms. In this paper, we propose a novel representation for the QSSP through binary decision diagrams (BDDs) and adapt a hybrid optimization approach which integrates BDDs and mixed-integer programming (MIP) for solving the QSSP. The exact framework highlights the modeling flexibility offered through decision diagrams to handle nonlinear problems. In addition, the hybrid approach leverages two different representations by exploring, in a complementary way, the solution space with BDD and MIP technologies. Machine learning then becomes a valuable component within the method to guide the search mechanisms. In the numerical experiments, the hybrid approach shows to be superior, by at least one order of magnitude, than two leading commercial MIP solvers with quadratic programming capabilities and a semidefinite-based branch-and-bound solver.</div>","PeriodicalId":50571,"journal":{"name":"Discrete Optimization","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.disopt.2020.100610","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126365359","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