Adaptive boundary constraint-handling scheme for constrained optimization

Nature-inspired optimization algorithms are meta-heuristics that mimic nature for solving optimization problems. Many optimization problems are constrained and have a bounded search space from which some solution vectors leave when the variation operators are applied. Therefore, the use of boundary constraint-handling methods (BCHM) is necessary in order to repair the invalid vectors. This paper presents an adaptive scheme to handling boundary constraints in constrained numerical optimization problems. The proposed adaptive scheme operates in two stages: At the first one, when there are still no feasible solutions, a BCHM that benefits the exploration of the search space is employed, and in the second stage, one of several BCHMs, according to their associated probabilities, is selected. The methods’ probabilities are updated every learning period so that the methods that generate the best repaired solutions will have a greater chance of being selected. The proposed scheme has been tested within two nature-inspired optimization algorithms: Particle Swarm Optimization and Differential Evolution employing their canonical version as well as one state-of-the-art version specialized in constrained optimization. A set of sixty single-objective constrained real-parameter optimization problems are solved. The results show that this adaptive scheme has a major impact on the algorithm’s performance, and it is able to promote better final results mainly within high-dimensional problems.