# Binary Pufferfish Optimization Algorithm for Combinatorial Problems

## TL;DR

This paper introduces a binary version of the Pufferfish Optimization Algorithm for solving complex binary optimization problems in industry.

## Contribution

The novel contribution is the development of a binary Pufferfish Optimization Algorithm (BPOA) using transfer functions and binarization rules.

## Key findings

- BPOA was tested on binary problems like the Set Covering and Knapsack Problems with promising results.
- The performance of BPOA is mainly influenced by the pairing of transfer functions and binarization rules.
- Comparisons with other algorithms showed BPOA's effectiveness and flexibility.

## Abstract

Metaheuristics are a fundament pillar of Industry 4.0, as they allow for complex optimization problems to be solved by finding good solutions in a reasonable amount of computational time. One category of important problems in modern industry is that of binary problems, where decision variables can take values of zero or one. In this work, we propose a binary version of the Pufferfish optimization algorithm (BPOA), which was originally created to solve continuous problems. The binary mapping follows a two-step technique, first transforming using transfer functions and then discretizing using binarization rules. We study representative pairings of transfer functions and binarization rules, comparing our algorithm with Particle Swarm Optimization, Secretary Bird Optimization Algorithm, and Arithmetic Optimization Algorithm with identical computational budgets. To validate its correct functioning, we solved binary problems present in industry, such as the Set Covering Problem together with its Unicost variant, as well as the Knapsack Problem. The results we achieved with regard to these problems were promising and statistically validated. The tests performed on the executions indicate that many pair differences are not statistically significant when both methods are already close to the optimal level, and significance arises precisely where the descriptive gaps widen, underscoring that transfer–rule pairing is the main performance factor. BPOA is a competitive and flexible framework whose effectiveness is mainly governed by the discretization design.