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A Branch-and-Bound-Based Crossover Operator for the Traveling Salesman Problem

A Branch-and-Bound-Based Crossover Operator for the Traveling Salesman Problem

Thomas Weise, Yan Jiang, Qi Qi, Weichen Liu
Copyright: © 2019 |Volume: 13 |Issue: 3 |Pages: 18
ISSN: 1557-3958|EISSN: 1557-3966|EISBN13: 9781522564584|DOI: 10.4018/IJCINI.2019070101
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MLA

Weise, Thomas, et al. "A Branch-and-Bound-Based Crossover Operator for the Traveling Salesman Problem." IJCINI vol.13, no.3 2019: pp.1-18. http://doi.org/10.4018/IJCINI.2019070101

APA

Weise, T., Jiang, Y., Qi, Q., & Liu, W. (2019). A Branch-and-Bound-Based Crossover Operator for the Traveling Salesman Problem. International Journal of Cognitive Informatics and Natural Intelligence (IJCINI), 13(3), 1-18. http://doi.org/10.4018/IJCINI.2019070101

Chicago

Weise, Thomas, et al. "A Branch-and-Bound-Based Crossover Operator for the Traveling Salesman Problem," International Journal of Cognitive Informatics and Natural Intelligence (IJCINI) 13, no.3: 1-18. http://doi.org/10.4018/IJCINI.2019070101

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Abstract

In this article, the new crossover operator BBX for Evolutionary Algorithms (EAs) for traveling salesman problems (TSPs) is introduced. It uses branch-and-bound to find the optimal combination of the (directed) edges present in the parent solutions. The offspring solutions created are at least as good as their parents and are only composed of parental building blocks. The operator is closer to the ideal concept of crossover in EAs than existing operators. This article provides the most extensive study on crossover operators on the TSP, comparing BBX to ten other operators on the 110 instances of the TSPLib benchmark set in EAs with four different population sizes. BBX, with its better ability to reuse and combine building blocks, surprisingly does not generally outperform the other operators. However, it performs well in certain scenarios. Besides presenting a novel approach to crossover on the TSP, the study significantly extends and refines the body of knowledge on the field with new conclusions and comparison results.

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