Cost-effective Evolutionary Strategies for Pareto Optimal Front Approximation in Multiobjective Shape Design Optimization of Electromagnetic Devices


The role of multiobjective optimization in industrial design of electromagnetic devices is remarkable and is more and more increasing. The availability of powerful and flexible FEM codes for field analysis and the increasing power of computers gives the designer the chance of building complex parametric models to be considered for an automatic optimization procedures. As in almost all design problems, objectives in an electromagnetic devices design are numerous and often in contrast each other. The classical, and still widely used, approach to such a situation is to transform the multiobjective problem into a single-objective one using some extra knowledge, and to solve it with classical techniques for single-objective optimization. Under such a perspective the multi-objective problem is considered as a special case of the single-objective one. This approach has three main drawbacks: 1)the variety of solution of a multiobjective problem is reduced to one with a significant reduction of information, 2)the choice of one solution using some extra knowledge is done a-priori with no complete information about all possible solutions, 3)in some (frequent) multiobjective problems (non-convex problems) the true multiobjective approach gives solutions that would be mathematically impossible to obtain via the classical approach. On the other hand, when Pareto optima theory is considered, no a-priori choice of preferences is required and the perspective is inverted, that is the single-objective problem becomes a special case of the multi-objective one. The aim of the optimization process is the approximation of the infinite Pareto-optimal solution throughout a convergent and equally spaced sampling of the Pareto optimal front. The mathematical theory of multiobjective optimization is mature and gives useful theorems for existence and uniqueness of solutions both when classical scalar formulations are considered and when the problem is tackled via Pareto optima theory. A wide variety of evolutionary and non evolutionary methods being specially devoted to Pareto multiobjective optimization (Multiobjective Evolutionary Algorithms MOEAs) have been developing and are being developed in the scientific community. In order to do this huge amount of different strategies univocally a debate is in progress about test functions, specific convergence criteria and approximation errors because the extension to Pareto Optimal Front (POF) approximation of such concepts is non at all straightforward. This is why, for instance, a special section of the first congress on Evolutionary Multiobjective Optimization (EMO2001, Zurich) was devoted to performance measurements. On the other hand real-life application of MOEAs is often hard and unpractical due to the complexity of methods and the computational cost deriving from the required huge number of objective functions calls. This is particularly true when shape design in electromagnetic industrial devices is concerned, where the evaluation of objective functions often requires FEM computations (sometimes 3D or non-linear or coupled). A special section of EMO2001 was devoted to real-life applications. The effort of this thesis is to link true multiobjective optimization mathematical theory and algorithms with automated optimal design of electromagnetic devices in order to build effective methodologies to be practical in industrial environment. The following key-point will be tackled: 1)Build cost effective strategies requiring a small number of objectives function calls at a given accuracy of Pareto Optimal Front approximation. 2)In order to do this consider the world of Evolutionary multiobjective Optimization methods and try to modify strategies in order them to be practical in electromagnetic shape design. 3)Consider classical non-evolutionary strategies (based of preference function) as well, in a critical way and link them to hybrid stochastic-deterministic search tools. 4)Try to extend neural network based single objective response surface methods to POF approximation. 5)Link developed strategies to commercial FEM field analysis tools. 6)Apply developed strategies to industrial design problem in cooperation with industrial designers.