High-Order Entropy-Based Population Diversity Measures in the Traveling Salesman Problem

IF 4.6 2区计算机科学 Q2 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

Evolutionary Computation Pub Date : 2020-12-02 DOI:10.1162/evco_a_00268

Yuichi Nagata

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引用次数: 6

Abstract

To maintain the population diversity of genetic algorithms (GAs), we are required to employ an appropriate population diversity measure. However, commonly used population diversity measures designed for permutation problems do not consider the dependencies between the variables of the individuals in the population. We propose three types of population diversity measures that address high-order dependencies between the variables to investigate the effectiveness of considering high-order dependencies. The first is formulated as the entropy of the probability distribution of individuals estimated from the population based on an m-th--order Markov model. The second is an extension of the first. The third is similar to the first, but it is based on a variable order Markov model. The proposed population diversity measures are incorporated into the evaluation function of a GA for the traveling salesman problem to maintain population diversity. Experimental results demonstrate the effectiveness of the three types of high-order entropy-based population diversity measures against the commonly used population diversity measures.

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旅行商问题中基于高阶熵的群体多样性测度

为了保持遗传算法（GA）的种群多样性，我们需要采用适当的群体多样性度量。然而，为排列问题设计的常用种群多样性度量没有考虑种群中个体变量之间的相关性。我们提出了三种类型的种群多样性度量，这些度量解决了变量之间的高阶依赖关系，以研究考虑高阶依赖性的有效性。第一个公式是基于m阶马尔可夫模型从种群中估计的个体概率分布的熵。第二个是第一个的延伸。第三个与第一个相似，但它是基于变阶马尔可夫模型。将所提出的种群多样性测度纳入旅行商问题的遗传算法的评估函数中，以保持种群多样性。实验结果证明了三种基于高阶熵的种群多样性测度对常用种群多样性度量的有效性。

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

Evolutionary Computation 工程技术-计算机：理论方法

CiteScore

6.40

自引率

1.50%

发文量

审稿时长

3 months

期刊介绍： Evolutionary Computation is a leading journal in its field. It provides an international forum for facilitating and enhancing the exchange of information among researchers involved in both the theoretical and practical aspects of computational systems drawing their inspiration from nature, with particular emphasis on evolutionary models of computation such as genetic algorithms, evolutionary strategies, classifier systems, evolutionary programming, and genetic programming. It welcomes articles from related fields such as swarm intelligence (e.g. Ant Colony Optimization and Particle Swarm Optimization), and other nature-inspired computation paradigms (e.g. Artificial Immune Systems). As well as publishing articles describing theoretical and/or experimental work, the journal also welcomes application-focused papers describing breakthrough results in an application domain or methodological papers where the specificities of the real-world problem led to significant algorithmic improvements that could possibly be generalized to other areas.