Chaotic Binary Black Widow Optimization Algorithm based on L-shaped Transfer Function to solve 0-1 Knapsack Problem

Abstract

In this study, a binary chaotic Black Widow Optimization algorithm was introduced to solve the 0-1 knapsack problem. The original Black Widow Optimization algorithm, which was designed for continuous optimization, was modified to work with binary search spaces by introducing L-shaped transfer functions, chaotic initialization, and a greedy repair operator to maintain feasibility given the knapsack capacity constraint. Three transfer functions were analyzed to obtain a better binary version of the algorithm and balance exploration and exploitation. The proposed approach was tested on small-, medium-, and large-scale knapsack benchmark problems. The results of the experiments demonstrate that the improved algorithms achieve better solution quality, stability, convergence speed, and success rate than the basic BBWO-0 algorithm. The CBBWO-L2 and CBBWO-L4 algorithms consistently demonstrate high effectiveness and stability, particularly when applied to medium- and large-scale problems. The results indicate that the proposed method is an efficient metaheuristic approach for solving combinatorial-optimization problems.