Pareto optima and Nash equilibria: An effective approach to the shape design in electromagnetics

Abstract

Purpose

This paper seeks to describe an approach to multi‐objective optimization problems (MOOPs) based on game theory (GT) and to provide a comparison with the more standard Pareto approach on a real design problem.

Design/methodology/approach

The GT is first briefly presented, then a possible recasting of MOOPs in terms of GT is described, where players from GT are associated with single objectives and strategies to the choice of degrees of freedom. A comparison with the Pareto approach is performed on the optimized design of a superconducting synchronous generator.

Findings

It was shown that the GT can be applied to the optimized design of real world devices, with results that present a different viewpoint on the problem, yet with device performance comparable with those obtained by standard approaches.

Research limitations/implications

Only the Nash approach to non‐cooperative games has been applied; the conditions for the solution found using GT to belong to the Pareto front have not been fully explored.

Practical implications

Designers and engineers interested in optimal design are presented with a new design technique able to get a balance among conflicting partial objectives, that can also be used to select among different possible designs obtained in other ways (e.g. using the Pareto front approach).

Originality/value

The paper demonstrates the possibility of using GT in the design of real world electromagnetic devices, with reference to the optimal shape design of a high temperature superconducting single‐phase synchronous generator.

Citation

Cioffi, M., Di Barba, P., Formisano, A. and Martone, R. (2008), "Pareto optima and Nash equilibria: An effective approach to the shape design in electromagnetics", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 27 No. 4, pp. 845-854. https://doi.org/10.1108/03321640810878252