An Indirect Genetic Algorithm for Set Covering Problems

TL;DR

This paper introduces a novel three-stage indirect genetic algorithm for the set covering problem, utilizing an external decoder and hill-climbing to improve solution quality and efficiency compared to traditional methods.

Contribution

It proposes an innovative indirect genetic algorithm with a decoder and post-optimization layer, enhancing solution quality and adaptability for set covering problems.

Findings

Outperforms existing evolutionary approaches in solution quality

Achieves faster convergence and better adaptability

Demonstrates effectiveness on benchmark instances

Abstract

This paper presents a new type of genetic algorithm for the set covering problem. It differs from previous evolutionary approaches first because it is an indirect algorithm, i.e. the actual solutions are found by an external decoder function. The genetic algorithm itself provides this decoder with permutations of the solution variables and other parameters. Second, it will be shown that results can be further improved by adding another indirect optimisation layer. The decoder will not directly seek out low cost solutions but instead aims for good exploitable solutions. These are then post optimised by another hill-climbing algorithm. Although seemingly more complicated, we will show that this three-stage approach has advantages in terms of solution quality, speed and adaptability to new types of problems over more direct approaches. Extensive computational results are presented and compared to the latest evolutionary and other heuristic approaches to the same data instances.