Solution of the Binary Knapsack Problem Using the Secretary Bird Optimization Algorithm

Abstract

Many nature-inspired metaheuristic algorithms proposed in the literature are initially designed to operate in continuous search spaces. However, real-world problems are not limited to continuous domains; they also include discrete, combinatorial, and binary problem types.In this study, the performance of the Secretary Bird Optimization Algorithm (SBOA), a recently introduced metaheuristic method, is investigated on the knapsack problem, which belongs to the class of binary optimization problems. Numerous transfer functions have been proposed in the literature to transform continuous search spaces into binary ones. In this work, S-shaped transfer functions are employed for this purpose.Through this transformation, SBOA—originally designed for continuous domains—is adapted to the binary search space and referred to as the Binary SBOA (BSBOA). The performance of BSBOA is evaluated on well-known benchmark knapsack problem instances. While BSBOA achieves optimal solutions on 10 small-scale benchmark problems, it produces near-optimal results for 18 large-scale binary knapsack instances.This study aims to address the SBOA binary optimization problem and evaluate its performance in such an environment.