# Reinforcement Learning Based Dynamic Selection of Auxiliary Objectives with Preserving of the Best Found Solution

## TL;DR

This paper introduces a reinforcement learning-based method for dynamically selecting auxiliary objectives in optimization, effectively preserving the best solutions and outperforming existing approaches across multiple problems.

## Contribution

It proposes a novel modification of the EA+RL method that prevents losing the best solution during auxiliary objective selection, with theoretical and empirical validation.

## Key findings

- Outperforms EA+RL on all tested problems.
- Surpasses single-objective approach on most instances.
- Provides detailed analysis of algorithm components' influence.

## Abstract

Efficiency of single-objective optimization can be improved by introducing some auxiliary objectives. Ideally, auxiliary objectives should be helpful. However, in practice, objectives may be efficient on some optimization stages but obstructive on others. In this paper we propose a modification of the EA+RL method which dynamically selects optimized objectives using reinforcement learning. The proposed modification prevents from losing the best found solution. We analysed the proposed modification and compared it with the EA+RL method and Random Local Search on XdivK, Generalized OneMax and LeadingOnes problems. The proposed modification outperforms the EA+RL method on all problem instances. It also outperforms the single objective approach on the most problem instances. We also provide detailed analysis of how different components of the considered algorithms influence efficiency of optimization. In addition, we present theoretical analysis of the proposed modification on the XdivK problem.