An Augmented Lagrangian Artificial Bee Colony with Deterministic Variable Selection for Constrained Optimization

Abstract

Nonlinear constrained optimization problems with nonlinear constraints are common in real-life application models. A viable option to handle such problems is metaheuristics that use proper penalty methods to bound solutions to the feasible space delimited by the constraints. Most penalty methods not only hinder the diversity of solutions but fail to exploit the feasible boundary of constraints from within the infeasible region. In light of this, we propose two methods to be incorporated into derivative-free algorithms for constrained optimization: a deterministic decision variable procedure based on previous works on multimodality; and a penalty method based on the augmented Lagrangian. We limit the study of the effects of our approach to the use of the Artificial Bee Colony algorithm (ABC) and several of its variants due to its simplicity and modular implementation. We validate our hypothesis by means of a numerical experiment using seven distinct nonlinear constrained optimization instances comparing the canonical ABC and some variants made for constrained optimization against their counterparts with the proposed deterministic selection and penalty method. Results suggest a positive outcome in relation to the integration of both methods to the ABC, opening up new avenues of possibilities for our proposed methods to be incorporated into other derivative-free algorithms.