Differential Evolution with Adaptive Penalty and Tournament Selection for Optimization Including Linear Equality Constraints

In order to solve constrained optimization problems, meta-heuristics have to be equipped with a constraint handling scheme. Despite the generality of the meta-heuristics, a large number of objective function (and constraints) evaluations are required so that good results are found. To improve the performance of meta-heuristics it is useful to combine them with exact methods. In this paper, two differential evolution (DE) techniques are proposed to exactly satisfy the linear equality constraints present in a continuous optimization problem that may also include additional non-linear equality and/or inequality constraints. An adaptive penalty method (APM) and a tournament selection technique (TS) are combined to a previous DE variant, called DELEqC-II, to handle the non-linear equality and inequality constraints. Numerical experiments, which include test-problems from the literature, are performed in order to comparatively evaluate the new approaches. The results indicate that the proposed methods outperform the other techniques used in the comparisons.