An Archived Differential Evolution Algorithm for Constrained Global Optimization

Abstract

Many practical engineering problems are naturally global optimization problems with complex constraints and local optimums. However, practicable and effective approaches for those constrained global optimization problems are still insufficient. A modified differential evolution algorithm is put forward for constrained global optimization problems in this work, using a special constraint-handling mechanism based on dynamic penalty functions and fitness calculation of individuals. An archive of solutions is maintained in the evolutionary process so that the best information of previous local optimums can be kept and utilized for the quality estimate of new solutions. Based on the archive of solutions, an iterative control operation is designed in the algorithm to guide the evolutionary process towards a promising space and avoid unnecessary and worthless search processes. Finally, numerical experiments based on a set of eight well-known constrained optimization problems are carried out to investigate the performance of the proposed method, and the experimental results reveal that the proposed algorithm is robust, effective and efficient in solving constrained global optimization problems.

A Robust Archived Differential Evolution Algorithm for Global Optimization Problems

“…We have put forward an archived differential evolution (ADE) for constrained optimization problems based on original DE, using a special dynamic penalty and fitness function for handling constraints and evaluating individuals, a modified selection and an archive of solutions for keeping the best solutions at any generation, and an iterative control operator for regulating and guiding the evolutionary process [6].…”

“…The selection, archivism and Iterative control operators are same as those in ADE [6], so they are just described briefly here.…”

“…The problems P3 and P4 are constrained problems with continuous variables, and 30 independent runs for each of them were performed with G max =200. The results obtained by our approach (RADE) are compared with that obtained by other five state-of-the-art approaches: the archived differential evolution (ADE) [6], the coevolutionary differential evolution (CDE) [23], GA with co-evolution model (GACO) [27], GA with dominancebased tournament selection (GADTS) [28] and coevolutionary particle swarm optimization (CPSO) [29]. The results by comparison in terms of the standard deviation (Std.…”

“…However, DE method was originally proposed, in principle, to solve unconstrained optimization problems, hence we present a modified differential evolution with constraints handling for constrained optimization problems, i.e. the archived differential evolution (ADE) [6].…”