Evaluation of Active-Set Evolution Strategies for Optimization with Known Constraints

Abstract

Evolution strategy (ES) is most often used to solve unconstrained black-box problems, while active-set methods focus on solving constrained optimization problems. A recent algorithm combines (1+1)-ES and an active-set method to get an active-set evolution strategy to solve problems in which the objective function is considered a black-box, but the constraint functions are known explicitly. We observe that the previous active-set evolution strategies have some settings result in less than optimal performance, so we make some adjustments to the past algorithms. More importantly, we systematically evaluate the performances of the two previous active-set evolution strategies with our modified version on the spherically symmetric functions with mutually orthogonal linear constraints. We also compare the performances of the modified version with three deterministic algorithms and an evolutionary algorithm. The test set we use is from the IEEE Congress on Evolutionary Computation (CEC) Competitions in 2006.