Abstract
With the development of excellent software in optimization, there is more and more wish to use these techniques and make an 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 a simulation 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. 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 result. 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 have developed approximate multi-objective optimization method, which is composed by satisficing method, radial basis function network and recommendation of new design variables. With industrial application, it turned out that we need to have more accuracy especially in approximation of combined scalar objective function. As for approximation, we use radial basis function network with optimization of radius. In this way, it is effective to make smooth function. However, it tends to approximate large wave, so that it is difficult to have bumpy response of the function. And almost always scalar objective function has bumpy characteristics. To overcome this problem, we are going to propose convolute approximation of radial basis function network. It is kind like Fourier series to add more and more higher frequency to add accuracy of the response. From numerical example, we have shown effectiveness of the proposed method.
