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CSRX: A novel Crossover Operator for a Genetic Algorithm applied to the Traveling Salesperson Problem

Martin Uray, Stefan Wintersteller, Stefan Huber

TL;DR

This paper addresses improving genetic algorithms for the traveling salesman problem by leveraging inherent solution-space symmetries. It introduces CSRX, a family of crossovers that operate on equivalence classes of permutations to factor out circular shifts and reversals, thereby preserving fitness and substructure. Empirical evaluation on TSPLIB datasets shows CSRX outperforms the state-of-the-art Gog2011 operator in both accuracy and stability. The approach is generalizable to other permutation-based problems and crossover operators, offering a practical pathway to more robust GA performance on symmetric combinatorial tasks.

Abstract

In this paper, we revisit the application of Genetic Algorithm (GA) to the Traveling Salesperson Problem (TSP) and introduce a family of novel crossover operators that outperform the previous state of the art. The novel crossover operators aim to exploit symmetries in the solution space, which allows us to more effectively preserve well-performing individuals, namely the fitness invariance to circular shifts and reversals of solutions. These symmetries are general and not limited to or tailored to TSP specifically.

CSRX: A novel Crossover Operator for a Genetic Algorithm applied to the Traveling Salesperson Problem

TL;DR

This paper addresses improving genetic algorithms for the traveling salesman problem by leveraging inherent solution-space symmetries. It introduces CSRX, a family of crossovers that operate on equivalence classes of permutations to factor out circular shifts and reversals, thereby preserving fitness and substructure. Empirical evaluation on TSPLIB datasets shows CSRX outperforms the state-of-the-art Gog2011 operator in both accuracy and stability. The approach is generalizable to other permutation-based problems and crossover operators, offering a practical pathway to more robust GA performance on symmetric combinatorial tasks.

Abstract

In this paper, we revisit the application of Genetic Algorithm (GA) to the Traveling Salesperson Problem (TSP) and introduce a family of novel crossover operators that outperform the previous state of the art. The novel crossover operators aim to exploit symmetries in the solution space, which allows us to more effectively preserve well-performing individuals, namely the fitness invariance to circular shifts and reversals of solutions. These symmetries are general and not limited to or tailored to TSP specifically.
Paper Structure (9 sections, 1 equation, 4 figures, 2 tables)

This paper contains 9 sections, 1 equation, 4 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Background
  3. tsp
  4. ga
  5. Novel crossover operators exploiting symmetry
  6. Experimental evaluation
  7. Setup.
  8. Results.
  9. Conclusion

Figures (4)

  • Figure 1: The recombination of $\pi_1$ and $\pi_2$ into an offspring $\pi_3$ using .
  • Figure 2: Recombination of $\pi_1$ and $\pi_2$ to candidates $\pi_3$ and $\pi_4$ for .
  • Figure 3: The results on a $95\%$ confidence interval. (reimp) compared with on $1000$ Generations on the eil51 data set. This experiment replicates the results from Gog2011.
  • Figure 4: The second experiment on a $95\%$ confidence interval. The (reimp) compared with on $200$ Generations on the eil51 data set.