An Interval-Based Focalization Method for Decision-Making in Decentralized, Multi-Functional Design

Multi-functional design problems are characterized by strong coupling between design variables that are controlled by stakeholders from different disciplines. This coupling necessitates efficient modeling of interactions between multiple designers who want to achieve conflicting objectives but share control over design variables. Various game-theoretic protocols such as cooperative, non-cooperative, and leader/follower have been used to model interactions between designers. Non-cooperative game theory protocols are of particular interest for modeling cooperation in multi-functional design problems. These are the focus of this paper because they more closely reflect the level of information exchange possible in a distributed environment. Two strategies for solving such non-cooperative game theory problems are: a) passing Rational Reaction Sets (RRS) among designers and combining these to find points of intersection and b) exchanging single points in the design space iteratively until the solution converges to a single point. While the first strategy is computationally expensive because it requires each designer to consider all possible outcomes of decisions made by other designers, the second strategy may result in divergence of the solution. In order to overcome these problems, we present an interval-based focalization method for executing decentralized decision-making problems that are common in multi-functional design scenarios. The method involves propagating ranges of design variables and systematically eliminating infeasible portions of the shared design space. This stands in marked contrast to the successive consideration of single points, as emphasized in current multifunctional design methods. The key advantages of the proposed method are: a) targeted reduction of design freedom and b) non-divergence of solutions. The method is illustrated using two sample scenarios — solution of a decision problem with quadratic objectives and the design of multi-functional Linear Cellular Alloys (LCAs). Implications include use of the method to guide design space partitioning and control assignment.