# New Binary Reptile Search Algorithms for Binary Optimization Problems

## TL;DR

This paper introduces a new binary version of the Reptile Search Algorithm to solve complex binary optimization problems like the Set Covering and Knapsack Problems.

## Contribution

The paper proposes a two-step binarization framework for the Reptile Search Algorithm using transfer functions and binarization rules for binary optimization.

## Key findings

- The Reptile Search Algorithm achieves competitive performance on benchmark binary optimization problems.
- The Z4 transfer function consistently improves performance across all tested algorithms.
- Appropriate binarization strategies are crucial for adapting continuous metaheuristics to binary domains.

## Abstract

Binarizing continuous metaheuristics to solve challenging NP-hard binary optimization problems is a fundamental step in adapting continuous algorithms for discrete domains. Binary optimization problems, such as the Set Covering Problem and the 0–1 Knapsack Problem, demand tailored approaches to efficiently explore and exploit the solution space. The process of binarization often introduces complexities, as it requires balancing the transformation of continuous populations into binary solutions while preserving the algorithm’s capability to navigate the search space effectively. In this context, we explore the performance of the Reptile Search Algorithm (RSA), a continuous metaheuristic, applied to these two benchmark problems. To address the binary nature of the problems, a two-step binarization process is implemented, utilizing combinations of transfer functions with binarization rules. This framework enables the RSA to generate binary solutions while leveraging its inherent strengths in exploration and exploitation. Comparative experiments are conducted with Particle Swarm Optimization and the Grey Wolf Optimizer to benchmark the RSA’s performance under similar conditions. These experiments analyze critical factors such as fitness values, convergence behavior, and exploration–exploitation dynamics, providing insights into the effectiveness of different binarization approaches. The results demonstrate that the RSA achieves competitive performance across both problems, highlighting its flexibility and adaptability, which are attributed to its diverse movement equations. Notably, the Z4 transfer function consistently enhances performance for all algorithms, even when paired with less effective binarization rules. This indicates the potential of Z4 as a robust transfer function for binary optimization. The findings underscore the importance of selecting appropriate binarization strategies to maximize the performance of continuous metaheuristics in binary domains, paving the way for further advancements in hybrid optimization methodologies.