A two-phase tabu search based evolutionary algorithm for the maximum diversity problem

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED

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

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引用次数: 5

Abstract

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.

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一种基于两阶段禁忌搜索的最大多样性问题进化算法

本文研究了与具有基数约束的二次型无约束二元优化问题等价的最大分集问题(MDP)。MDP旨在选择具有给定基数的元素子集，使所选子集中任意两个元素之间的成对距离之和最大化。为了解决这一具有计算挑战性的问题，我们提出了一种基于两阶段禁忌搜索的进化算法(TPTS/EA)，该算法集成了几个显著特征，以确保进化的多样性和质量，例如两阶段禁忌搜索算法，该算法在第一阶段由基于动态候选列表(DCL)策略的传统禁忌搜索组成，在第二阶段由基于解的禁忌搜索过程组成，以改进搜索。利用两个基于路径链接的重组算子生成新的子代解。在文献中总共140个公共实例的三组测试中，研究证明了所提出的TPTS/EA算法在解质量和计算效率方面的有效性。具体来说，我们提出的TPTS/EA算法能够在2个实例中改进以前最知名的结果，同时在130个实例中匹配以前最知名的解决方案。我们还提供了实验证据，以突出TPTS/EA算法中几个重要组件的有益效果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Discrete Optimization 管理科学-应用数学

CiteScore

2.10

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： Discrete Optimization publishes research papers on the mathematical, computational and applied aspects of all areas of integer programming and combinatorial optimization. In addition to reports on mathematical results pertinent to discrete optimization, the journal welcomes submissions on algorithmic developments, computational experiments, and novel applications (in particular, large-scale and real-time applications). The journal also publishes clearly labelled surveys, reviews, short notes, and open problems. Manuscripts submitted for possible publication to Discrete Optimization should report on original research, should not have been previously published, and should not be under consideration for publication by any other journal.