A-DVM: A Self-Adaptive Variable Matrix Decision Variable Selection Scheme for Multimodal Problems

Abstract

Artificial Bee Colony (ABC) is a Swarm Intelligence optimization algorithm well known for its versatility. The selection of decision variables to update is purely stochastic, incurring several issues to the local search capability of the ABC. To address these issues, a self-adaptive decision variable selection mechanism is proposed with the goal of balancing the degree of exploration and exploitation throughout the execution of the algorithm. This selection, named Adaptive Decision Variable Matrix (A-DVM), represents both stochastic and deterministic parameter selection in a binary matrix and regulates the extent of how much each selection is employed based on the estimation of the sparsity of the solutions in the search space. The influence of the proposed approach to performance and robustness of the original algorithm is validated by experimenting on 15 highly multimodal benchmark optimization problems. Numerical comparison on those problems is made against the ABC and their variants and prominent population-based algorithms (e.g., Particle Swarm Optimization and Differential Evolution). Results show an improvement in the performance of the algorithms with the A-DVM in the most challenging instances.