[Paper Review] A Powerful Genetic Algorithm for Traveling Salesman Problem

Shujia Liu|arXiv (Cornell University)|Feb 19, 2014

Metaheuristic Optimization Algorithms Research16 references6 citations

TL;DR

This paper proposes a powerful genetic algorithm (GA) for the traveling salesman problem (TSP) that integrates a localized edge-swapping (ES) operator with a dynamic switch to a global ES variant to balance efficiency and solution quality. The method achieves optimal or best-known solutions on 9 out of 10 benchmark instances with up to 16,862 cities, outperforming state-of-the-art LK-based algorithms in solution quality and computation time.

ABSTRACT

This paper presents a powerful genetic algorithm(GA) to solve the traveling salesman problem (TSP). To construct a powerful GA, I use edge swapping(ES) with a local search procedure to determine good combinations of building blocks of parent solutions for generating even better offspring solutions. Experimental results on well studied TSP benchmarks demonstrate that the proposed GA is competitive in finding very high quality solutions on instances with up to 16,862 cities.

Motivation & Objective

• To develop a high-performance genetic algorithm for the TSP that overcomes the high computational cost typical of traditional GAs.
• To improve solution quality by enhancing the edge-swapping (ES) crossover operator through localized and global variants.
• To maintain population diversity while accelerating convergence using a dynamic switching strategy between local and global ES.
• To demonstrate competitive performance against state-of-the-art LK-based algorithms on large-scale TSP instances.

Proposed method

• The algorithm uses a population of 200 solutions initialized via a 2-opt greedy local search to ensure initial solution quality.
• A localized edge-swapping (ES) operator replaces only a few edges from one parent using a block strategy to generate offspring similar to the parent, reducing computational cost to less than O(N).
• The algorithm dynamically switches from localized to global ES when no improvement is observed over a predefined number of generations, enabling escape from local optima.
• The global ES version uses a block strategy to select geographically close M-rings for edge replacement, improving solution quality by preserving structural coherence.
• An alternative evaluation function is used to maintain population diversity, favoring offspring with better spread even if slightly longer in tour length.
• The algorithm terminates when no improvement is observed over a fixed number of generations, with parameters tuned via preliminary experiments.

Experimental results

Research questions

• RQ1 Can a localized edge-swapping operator significantly reduce computational cost in a GA for the TSP while maintaining solution quality?
• RQ2 How does dynamically switching between localized and global edge-swapping improve convergence and solution quality?
• RQ3 To what extent does the block strategy in global ES outperform random or K-multiple strategies in solution quality and diversity?
• RQ4 Can a GA with enhanced ES operators match or exceed the performance of state-of-the-art LK-based algorithms on large-scale TSP instances?

Key findings

• The proposed GA found the optimal or best-known solution for 9 out of 10 benchmark instances, including the largest instance with 16,862 cities.
• On average, the GA achieved a solution error of 0.00% across 9 of the 10 instances, with the highest error being 0.05% on fnl4461.
• The average computation time per run was 650–860 seconds across instances, with the largest instance (it16862) solved in 863 seconds on average.
• The GA outperformed the LKH algorithm in solution quality on several instances, including rl11849 and xrb14233, where it achieved 0.00% error compared to LKH’s 0.04% and 0.02% respectively.
• The dynamic switching from localized to global ES significantly improved performance, especially in escaping local optima on larger instances.
• The block strategy for global ES was empirically superior to the K-multiple strategy in generating high-quality offspring with better structural coherence.