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

arXiv: https://arxiv.org/abs/2508.14020 · HTML: https://mlsanity.com/paper/2508.14020/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 15 references that are in the map.
- First posted on arXiv 19 Aug 2025.

## Builds on (most cited first, 1 of 1)

- [The Longest Run Subsequence Problem: Further Complexity Results](https://mlsanity.com/paper/2011.08119/) (2020)

## Built on by (most cited first, 1 of 1)

- [LLM-Based Instance-Driven Heuristic Bias In the Context of a Biased Random Key Genetic Algorithm](https://mlsanity.com/paper/2509.09707/) (2025)

## Abstract (arXiv)

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.