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

Author:

Nagata Yuichi1

Affiliation:

1. Graduate School of Technology, Industrial and Social Sciences, Tokushima University, 2-1 Minami Josanjima, Tokusima, 770-8506, Japan

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 [Formula: see text]-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.

Publisher

MIT Press - Journals

Subject

Computational Mathematics

Cited by 7 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Evolutionary Multimodal Multiobjective Optimization for Traveling Salesman Problems;IEEE Transactions on Evolutionary Computation;2023

2. Approximately optimal construction of parallel algorithm portfolios by evolutionary intelligence;SCIENTIA SINICA Technologica;2022-08-03

3. Cycle Mutation: Evolving Permutations via Cycle Induction;Applied Sciences;2022-05-29

4. Multi-Modal Multi-Objective Traveling Salesman Problem and its Evolutionary Optimizer;2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC);2021-10-17

5. Computing diverse sets of high quality TSP tours by EAX-based evolutionary diversity optimisation;Proceedings of the 16th ACM/SIGEVO Conference on Foundations of Genetic Algorithms;2021-09-06

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