On the Game-Based Approach to Optimal Design

A game problem of structural design is defined as a problem of playing against external circumstances. There are two classes of players, namely the “ordinal” and “cardinal” players. The ordinal players, designated as the “operator” and “nature”, endeavor to, respectively, minimize or maximize the payoff function, operating within the constraints of limited resources. The fundamental premise of this study is that the action of player “nature” is a priori unknown. Statistical decision theory addresses decision-making scenarios where these probabilities, whether or not they are known, must be considered. The solution to the substratum game is expressed as a value of the game “against nature”. The structural optimization extension of the game considers the value of the game “against nature” as the function of certain parameters. Thus, the value of the game is contingent upon the design parameters. The cardinal players, “designers”, choose the design parameters. There are two formulations of optimization. For the single cardinal player, the pursuit of the maximum and minimum values of the game reduces the problem of optimal design. In the second formulation, there are multiple cardinal players with conflicting objectives. Accordingly, the superstratum game emerges, which addresses the interests of the superstratum players. Finally, the optimal design problems for games with closed forms are presented. The game formulations could be applied for optimal design with uncertain loading, considering “nature” as the source of uncertainty.