Optimization of Weights in Sequential Approximation Multi-Objective Optimization by Using DEA

Abstract

With the development of excellent software in optimization, there is more and more wishes to use these techniques and make epoch developments in their products. However, most of us know that it costs a lot of time and costs to carry out optimization, because it needs to repeat simulations for the number of times. Therefore, most engineers would like to make mathematical models of design problems just enough to express their needs priori to optimization. Let us call these models as light models, in this paper. However, it is very difficult to make a proper light model in the first trial. Recent optimization will find the global solution, so that it will find some modeling miss and lead light model to some strange results. Such phenomenon is not a fault of optimization, but of the light model. We have to revise the light model but it is way difficult to make it rationally with the information we have had from the light model. We have to think of appropriate values of existed constraints, we have to think of new functions for constraints, and so on. It is almost hopeless to revise the light model at one time. The best thing that we can hope for is to give up the light model and make models complex to express the situation of the products. If we do not know proper values for constraints, treat them as objective functions and just go through trade-off analysis to have their relationships information, so that we can give appropriate values. In this sense, it is very important to make models in multi-objective optimization. In multi-objective optimization, it is quite important to carry out trade-off analysis and which might be a key to find epoch design. We had developed approximate multi-objective optimization method, which is composed by satisficing method, convolute radial basis function network and recommendation of new design variables. In satisficing method, we can handle trade-off analysis much easier than weighting methods. However, scalar function composed by satisficing method is not smooth when it gets close to Pareto solution that is indicated by designer’s requirement. Therefore, it is difficult even for convolute RBF to compose better approximate function although we have better approximation for each objective function. In weighting method, it is quite difficult to give proper weights for designer’s requirement. In approximate optimization, fortunately we have a number of data sets. Thus, it is possible to optimize weights which meet for aspiration level in satisficing method. Then, we can have smooth and better approximation for scalar function. In this paper, we are going to show effectiveness of the proposed method through demonstration of numerical examples.