A Biased Random Key Genetic Algorithm for Solving the Longest Run Subsequence Problem

TL;DR

This paper introduces a Biased Random Key Genetic Algorithm (BRKGA) for efficiently solving the NP-hard Longest Run Subsequence problem, demonstrating state-of-the-art performance with room for further improvements.

Contribution

The paper presents a novel BRKGA approach tailored for the LRS problem, focusing on computational efficiency and comparative analysis with other methods.

Findings

BRKGA outperforms existing heuristics and exact methods

The approach is effective for small to medium alphabet sizes

There is potential for improvement with larger alphabet inputs

Abstract

The longest run subsequence (LRS) problem is an NP-hard combinatorial optimization problem belonging to the class of subsequence problems from bioinformatics. In particular, the problem plays a role in genome reassembly. In this paper, we present a solution to the LRS problem using a Biased Random Key Genetic Algorithm (BRKGA). Our approach places particular focus on the computational efficiency of evaluating individuals, which involves converting vectors of gray values into valid solutions to the problem. For comparison purposes, a Max-Min Ant System is developed and implemented. This is in addition to the application of the integer linear programming solver CPLEX for solving all considered problem instances. The computation results show that the proposed BRKGA is currently a state-of-the-art technique for the LRS problem. Nevertheless, the results also show that there is room for improvement, especially in the context of input strings based on large alphabet sizes.