EB-GLS: An Improved Guided Local Search Based on the Big Valley Structure

TL;DR

This paper introduces EB-GLS, an enhanced Guided Local Search method that leverages the big valley structure to better escape local optima, demonstrated to outperform standard GLS on the traveling salesman problem.

Contribution

It proposes a novel penalizing mechanism for GLS based on the big valley structure, maintaining an elite solution to guide the search more effectively.

Findings

EB-GLS outperforms standard GLS in experiments.

The elite solution mechanism improves escape from local optima.

Significant performance gains on the traveling salesman problem.

Abstract

Local search is a basic building block in memetic algorithms. Guided Local Search (GLS) can improve the efficiency of local search. By changing the guide function, GLS guides a local search to escape from locally optimal solutions and find better solutions. The key component of GLS is its penalizing mechanism which determines which feature is selected to penalize when the search is trapped in a locally optimal solution. The original GLS penalizing mechanism only makes use of the cost and the current penalty value of each feature. It is well known that many combinatorial optimization problems have a big valley structure, i.e., the better a solution is, the more the chance it is closer to a globally optimal solution. This paper proposes to use big valley structure assumption to improve the GLS penalizing mechanism. An improved GLS algorithm called Elite Biased GLS (EB-GLS) is proposed. EB-GLS records and maintains an elite solution as an estimate of the globally optimal solutions, and reduces the chance of penalizing the features in this solution. We have systematically tested the proposed algorithm on the symmetric traveling salesman problem. Experimental results show that EB-GLS is significantly better than GLS.