%0 Journal Article
%T Multiobjective Optimization Using Cross-Entropy Approach
%A Karim Sebaa
%A Abdelhalim Tlem£¿ani
%A Mounir Bouhedda
%A Noureddine Henini
%J Journal of Optimization
%D 2013
%R 10.1155/2013/270623
%X A new approach for multiobjective optimization is proposed in this paper. The method based on the cross-entropy method for single objective optimization (SO) is adapted to MO optimization by defining an adequate sorting criterion for selecting the best candidates samples. The selection is made by the nondominated sorting concept and crowding distance operator. The effectiveness of the approach is tested on several academic problems (e.g., Schaffer, Fonseca, Fleming, etc.). Its performances are compared with those of other multiobjective algorithms. Simulation results and comparisons based on several performance metrics demonstrate the effectiveness of the proposed method. 1. Introduction Optimization is a basic tool for several decision making in engineering area. In these fields, we have many conflicting objectives to satisfy. Usually, we convert all objectives to one, single objective (SO) function. The goal is to find out the maximum/minimum of this SO function subject to maintain the physical constraints of the system. The results reflect a compromise between all objectives. The idea is to formulate the function to achieve this desired compromise. By aggregating all objectives in a weighted function, or by transforming all objectives into only one objective, and retaining one objective which will be added to constraints, the conversion from MO to SO is done. But the weakness and the limitation of the aggregation are as follows.(1)The requirement of a prior knowledge about the relative importance of the objectives, and the limits on the objectives that are converted into constraints.(2)The aggregated function leads to only one solution.(3)Trade-offs between objectives cannot be easily evaluated.(4)The solution may not be attainable unless the search space is convex. The aggregation is not recommended for the systems with conflicting objectives. Also, we need to know all possible solutions of all objectives simultaneously. In the business word it is called ¡°the trade-off analysis¡±. There are several areas in engineering where the performing of the trade-off analysis is necessary, such as the following.(1)The design of controllers while reducing the cost, which are two conflicting objectives.(2)The placement of more functional blocks on chip while minimizing the chip area and/or power dissipation.(3)The finding of the vehicle which has the highest range while at the same time consuming minimum amount of energy.(4)The minimization of the operation cost while maintaining a stable work force [1¨C3]. MO problems are more difficult to solve compared to the
%U http://www.hindawi.com/journals/jopti/2013/270623/