A GRASP-based memetic algorithm with path relinking for the far from most string problem

TL;DR

This paper introduces a memetic algorithm combining GRASP, path relinking, and hill climbing to effectively solve the computationally hard FAR FROM MOST STRING PROBLEM, outperforming existing methods in diverse instances.

Contribution

The paper presents a novel memetic algorithm with integrated heuristics and local search strategies specifically designed for the FFMSP, demonstrating superior performance over state-of-the-art techniques.

Findings

The proposed MA outperforms existing methods with statistical significance.

The algorithm is effective on both random and biological data sets.

Parameter sensitivity analysis confirms robustness of the approach.

Abstract

The FAR FROM MOST STRING PROBLEM (FFMSP) is a string selection problem. The objective is to find a string whose distance to other strings in a certain input set is above a given threshold for as many of those strings as possible. This problem has links with some tasks in computational biology and its resolution has been shown to be very hard. We propose a memetic algorithm (MA) to tackle the FFMSP. This MA exploits a heuristic objective function for the problem and features initialization of the population via a Greedy Randomized Adaptive Search Procedure (GRASP) metaheuristic, intensive recombination via path relinking and local improvement via hill climbing. An extensive empirical evaluation using problem instances of both random and biological origin is done to assess parameter sensitivity and draw performance comparisons with other state-of-the-art techniques. The MA is shown to perform better than these latter techniques with statistical significance.