Inverse Problems and Error Minimisation -- A Paretian Approach to MOSD Theory -- Field Models and Shape Design -- Solving Multiobjective Optimisation Problems -- A Field-Based Benchmark -- Static MOSD -- Moving Along the Pareto Front -- Sensitivity Analysis and MOSD -- Non-Conflicting Multiple Objectives -- Higher-Order Dimensionality -- Multi-Scale Evolution Strategy -- Game Theory and MOSD -- Dynamic MOSD -- An Introduction to Bayesian Probability Theory -- A Bayesian Approach to Multiobjective Optimisation -- Bayesian Imaging and Shape Design -- Conclusion.

Multiobjective Shape Design in Electricity and Magnetism is entirely focused on electric and magnetic field synthesis, with special emphasis on the optimal shape design of devices when conflicting objectives are to be fulfilled. Direct problems are solved by means of finite-element analysis, while evolutionary computing is used to solve multiobjective inverse problems. This approach, which is original, is coherently developed throughout the whole manuscript. The use of game theory, dynamic optimisation, and Bayesian imaging strengthens the originality of the book. Covering the development of multiobjective optimisation in the past ten years, Multiobjective Shape Design in Electricity and Magnetism is a concise, comprehensive and up-to-date introduction to this research field, which is growing in the community of electricity and magnetism. Theoretical issues are illustrated by practical examples. In particular, a test problem is solved by different methods so that, by comparison of results, advantages and limitations of the various methods are made clear. Topics covered include: Maxwell equations and boundary-value problems; Paretian optimality; static optimisation; game theory; dynamic optimisation; Bayesian imaging. Multiobjective Shape Design in Electricity and Magnetism collects the long-lasting experience matured by the author during his research activity both at the university and in cooperation with industrial laboratories.