Adaptive Relaxation Penalty Function Method for Equal Constrained Optimization in Differential Evolution

Differential evolution (DE) algorithm has gained vast application in engineering design community for their global convergence property. Yet it relies on random samplings and is inefficient when dealing with equal constrained optimization, in which the ratio between the size of the feasible search space F and the size of the whole search space S is quite low. To deal with this, adaptive relaxation penalty function method is proposed, which relaxes equal constraints into unequal constrained functions with an adaptive relaxation parameter. The relaxation parameter is employed to create more feasible spaces to facilitate the evolution of DE. It shrinks as the DE locates optimal solutions, which will force these solutions move towards original equal constraint optimum. Numerical examples are used to examine adaptive relaxation penalty function method and encouraging results were achieved, which verify the effectiveness of proposed method.