Deterministic Parameter Selection of Artificial Bee Colony Based on Diagonalization

Abstract

Artificial Bee Colony (ABC) is a bee inspired swarm intelligence (SI) algorithm well-known for its versatility and simplicity. In crucial steps of the algorithm, employed and scout bees phase, parameters (decision variables) are chosen in a random fashion. Although this randomness may apparently not influence the overall performance of the algorithm, it may contribute to premature convergence towards bad local optima or lack of exploration in multimodal problems featuring rugged surfaces. In this study, a deterministic selection method for decision variables based on Cantor’s proof of uncountability of rational numbers is proposed to be used in the aforementioned steps. The approach seeks to eliminate stochasticity, enhance the exploratory capabilities of the algorithm by verifying all possible variables, and provide a better mechanism to displace solutions out of local optima, introducing more novelty to solutions. In order to analyze potential benefits brought by the proposed approach to the overall performance of the ABC, three variants featuring modifications discussed in this work were designed to be compared in terms of efficiency and stability against the original ABC on 15 instances of unconstrained optimization problems.