Design Optimization Using Game Theory

Abstract

A substantial body of literature on global design optimization techniques is based on an implicit assumption that a system under optimization is designed by a perfectly centralized design team with all team members committed to a global optimum solution. This assumption enables the system engineers to minimize all the objective functions simultaneously while controlling all design decisions at the same time. Recent research suggested that this inherent assumption may need to be revisited. This paper proposes a novel framework for design optimization using game theory, which represents a design process as a normal-form game and unifies two fundamental decisions of discipline designers, namely a system-global or a discipline-local optimum solution. This paper provides a general mathematical formulation of the framework for a design process with any number of discipline designers. The framework introduces the notion of the Nash front, which is a set of design solutions consisting of the Nash equilibria derived through the reallocation of design authority between discipline designers. This paper then tests the framework on a numerical optimization case study of a Stirling micro combined heat and power plant with two discipline designers. The result indicates that for the system capital cost and the system power output the difference between global Pareto-optimum designs and the Nash front designs on average across five different scenarios of design authority allocation was 22% and 16%, correspondingly. The application of the novel framework in different fields of engineering could help to build models that are more realistic and prevent impractical technical objectives.