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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 97
Edited by: Y. Tsompanakis, B.H.V. Topping
Paper 49

Normalized Dominance Selection Criteria for Differential Evolution Algorithms in Constrained Optimization Problems

J. Avakian, D. Serio, A. Giannico and G.C. Marano

Department of Environmental Engineering and Sustainable Development, Technical University of Bari, Taranto, Italy

Full Bibliographic Reference for this paper
J. Avakian, D. Serio, A. Giannico, G.C. Marano, "Normalized Dominance Selection Criteria for Differential Evolution Algorithms in Constrained Optimization Problems", in Y. Tsompanakis, B.H.V. Topping, (Editors), "Proceedings of the Second International Conference on Soft Computing Technology in Civil, Structural and Environmental Engineering", Civil-Comp Press, Stirlingshire, UK, Paper 49, 2011. doi:10.4203/ccp.97.49
Keywords: evolutionary algorithm, constrained optimization, dominance based selection methods.

In many scientific, economic and other problems, an optimization problem is the problem of finding the best solution from all feasible solutions, trying to obtain the maximum benefit from a set of limited available resources.

Evolutionary algorithms (EAs) are extremely promising numerical optimization techniques but they suffer lack of efficiency in handling constraints. EAs often perform well approximating solutions to all types of problems because they ideally do not make any assumption about the underlying fitness landscape; these techniques have been successful in fields as diverse as engineering, art, biology, economics, marketing, genetics, operations research, robotics, social sciences, physics, politics and chemistry.

During past decade hybrid algorithms, combining evolutionary computation and constraint-handling techniques, have shown to be effective in specific areas with the use of dominance selection (DS) criterion. Some open questions in using this type of approach are studied in this paper, so that constrained handling problems are approached by different strategies based on normalized dominance selection (NDS) rules. In principle these rules are utilizable in any EAs with a selection phase, so that in this paper they are applied to a differential evolution algorithm (NDS-DEa). The approach proposed here is a modified version of standard DS selection criterion; it adopts a strategy based on preferring feasible to infeasible individuals in any case, independently from solution performances. This methodology presents three possible situations, because comparison should be between two feasible individuals, a feasible and an unfeasible individual, and finally two unfeasible individuals. If the first situation is completely defined, the third one still presents some ambiguity, because of different possible active constraints that do not give an univocally defined ranking. For this reason a specific approach has been developed in this paper introducing a sort of normalization criterion for constraints. It is developed using all unfeasible individuals resulting at each generation. In this way, the case of selecting two unfeasible individuals seemed to be more effective, so that convergence to a feasible space is faster than in the standard approaches. Simulation for comparisons of several well-studied benchmark tests demonstrates the effectiveness, efficiency and robustness of the proposed methodology. Moreover, the effects of several crucial parameters on the performance of the NDS-DEa are studied.

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