Keywords: differential evolution, opposition based optimization, evolutionary algorithms, constraint optimization, optimization, engineering design.

This paper is concerned with optimum design of engineering problems using a recent evolutionary technique, namely opposition based differential evolution. The design of engineering structures and systems can be formulated as optimization problems in which a measure of performance is to be optimized while satisfying all design constraints. Many numerical methods of optimization have been developed and used to design optimal engineering structures.

Evolutionary algorithms which are mostly based on the natural phenomena have attracted a great deal of attention in the last decades. To name a few, the genetic algorithm (GA) [1], evolutionary programming [2], particle swarm optimization [3] are from this family. These algorithms outperform traditional methods in finding the global optimums.

Differential evolution (DE) is an evolutionary algorithm recently developed by Storn, Price and Lampinen [4]. This approach has been successfully applied to solve different optimization problems. DE has proven to be efficient, easy to implement and robust in finding the optimal solution. DE is similar to the GA. The main difference between the GA and DE is that, in the GA, mutation is the result of small perturbation to the genes while in DE mutation is caused by arithmetic combinations of individuals. The concept of opposition based optimization (OBO) has been recently proposed by Rahnamayan, Tizhoosh and Salama [5]. The main idea behind opposition based learning is simultaneous consideration of a point and its corresponding opposite in the feature space. The opposition based differential evolution uses opposition based optimization for population initialization and for generation jumping.

ODE is applied to three constrained engineering design problems. Comparison of the ODE results with the results of other heuristic methods reveals that in all three cases, the proposed approach (ODE) results in a much lower standard deviation for the objective functions. It was also noted that the number of function evaluations is also smaller than those reported by other methods. Therefore, it can be concluded that ODE is a highly efficient and reliable optimization algorithm.

1

C.A.C. Coello, E.M. Montes, "Constraint-handling in genetic algorithms through the use of dominance-based tournament selection", Advanced Engineering Information, 116, 193-203, 2002. doi:10.1016/S1474-0346(02)00011-3

2

C.A.C. Coello, R.L. Becerra, "Efficient evolutionary through the use of a cultural algorithm", Engineering Optimization, 36, 219-236, 2004. doi:10.1080/03052150410001647966

3

Q. He, L. Wang, "An effective co-evolutionary particle swarm optimization for engineering optimization problems", Engineering Application of Artificial Intelligence, 20, 89-99, 2006. doi:10.1016/j.engappai.2006.03.003

4

K.V. Price, R.M. Storn, J.A. Lampinen, "Differential evolution, A practical approach to global optimizations", Springer-Verlag Berlin Heidelberg, 2005.

5

S. Rahnamayan, H.R. Tizhoosh, M.M.A. Salama, "Opposition-Based Differential Evolution", IEEE Transactions on Evolutionary Computation, 12(1), 64-79, 2008. doi:10.1109/TEVC.2007.894200

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