Cycle Mutation: Evolving Permutations via Cycle Induction

TL;DR

This paper introduces cycle mutation, a novel mutation operator for evolutionary algorithms that evolves permutations more effectively for assignment problems, supported by fitness landscape analysis and empirical validation.

Contribution

The paper proposes cycle mutation and new permutation distance measures, providing insights into their effectiveness for different problem types and integrating them into open-source libraries.

Findings

Cycle mutation excels on assignment problems like QAP and LCS.

Cycle mutation is less prone to local optima than traditional mutation operators.

Fitness landscape analysis predicts the suitability of cycle mutation for specific problem classes.

Abstract

Evolutionary algorithms solve problems by simulating the evolution of a population of candidate solutions. We focus on evolving permutations for ordering problems like the traveling salesperson problem (TSP), as well as assignment problems like the quadratic assignment problem (QAP) and largest common subgraph (LCS). We propose cycle mutation, a new mutation operator whose inspiration is the well known cycle crossover operator, and the concept of a permutation cycle. We use fitness landscape analysis to explore the problem characteristics for which cycle mutation works best. As a prerequisite, we develop new permutation distance measures: cycle distance, $k$-cycle distance, and cycle edit distance. The fitness landscape analysis predicts that cycle mutation is better suited for assignment and mapping problems than it is for ordering problems. We experimentally validate these findings showing cycle mutation's strengths on problems like QAP and LCS, and its limitations on problems like the TSP, while also showing that it is less prone to local optima than commonly used alternatives. We integrate cycle mutation into the open-source Chips-n-Salsa library, and the new distance metrics into the open-source JavaPermutationTools library.