Decentralized Design Under Uncertainty: Investigating the Impact of Designer Mistakes

The design of products and processes within a decentralized design framework requires different design teams or distributed subsystems to solve their local optimization problems and pass their optimal designs to the other subsystems. It is common for subsystems to not cooperate with each other by sharing objective or gradient information and the only information communicated between subsystems is the values of coupled design variables. Non local design variables are treated as constraints in local subsystem optimization. The subsystems iterate by communicating design variable values back and forth until they all converge upon a solution. For subsystems with multiple, conflicting objectives, the converged solution lies at the intersection of the Rational Reaction Set and is called the “Nash Equilibrium”. It is known that the Nash Equilibrium solution is rarely Pareto optimal, the ideal solution set for multiobjective optimization problems. A common assumption in design decision making is that the designer makes no errors in the selection of the optimal design in the iterative process. In this paper, a framework for distributed design is presented that preserves the general assumptions of non cooperation between subsystems but models mistakes made by designers in the selection of optimal designs. It is assumed that the designers of the initial decision making subsystem within the decentralized design process make errors in selecting the optimal design. A set based approach is used to model these errors which are then propagated through the design process. Subsystems utilize metamodeling techniques to develop approximations of the non local rational reaction sets which are then used to determine a representation of the non local objective functions. It is seen that solutions from this modified decentralized design framework are better than the Nash Equilibrium. The proposed framework includes concepts from game theory, uncertainty modeling, error propagation, set based design and metamodeling techniques.