Separating Design Optimization Problems for Bounded Rational Designers

This paper presents a method for assessing the quality of progressive design processes that seek to maximize the profitability of the product that is being designed. The proposed approach uses separations, a type of problem decomposition, to model progressive design processes. The subproblems in the separations correspond roughly to phases in the progressive design processes. We simulate the choices of a bounded rational designer for each subproblem using different search algorithms. We consider different types and versions of these search processes in order to determine if the results are robust to the decision-making model. We use a simple twovariable problem to help describe the approach and then apply the approach to assess motor design processes. Methods for assessing the quality of engineering design processes can be used to guide improvements to engineering design processes and generate more valuable products. INTRODUCTION In general, design optimization determines values for design variables such that an objective function is optimized while performance and other constraints are satisfied [1, 2, 3]. The study of design optimization has yielded many useful techniques for solving optimization problems. Design engineers may use these techniques during a design process whenever appropriate mathematical models are available to represent the objective function and constraints in terms of the design variables [2]. Decomposition-based design optimization methods divide a large optimization problem into a set of smaller subproblems but require multiple iterations to converge to a feasible, optimal solution. Model coordination and goal coordination are two common methods for the decomposition of large scale design optimization problems [4, 5]. Multidisciplinary optimization (MDO) problems have been the focus of decomposition approaches such as the bi-level integrated system synthesis (BLISS) approach [6], analytical target cascading [7-9], collaborative optimization [10], and coupled subspace optimization (CSSO) [11, 12]. Yoshimura et al. [13] decompose a multi-objective optimization problem into a hierarchy of problems that have two objectives. One can assess the quality of a decomposition-based design optimization method by evaluating the solution that is generated by the method using the objective function of the original design optimization problem and comparing that to the optimal value. For instance, if a decomposition-based design optimization method is used to solve an aircraft design optimization problem in which the objective function is to minimize the aircraft’s gross takeoff weight, then one can assess the quality of that method by comparing the gross takeoff weight of the method’s solution to the optimal gross takeoff weight (found by solving the original design optimization problem). Decomposition-based design optimization methods are a form of problem decomposition, which is one type of decomposition in engineering design [14]. A second type is product decomposition, which divides the physical elements of a product (or system) into subassemblies and components. A third type is process decomposition, which divides the entire design task (from gathering requirements to detailed design) into the various activities that form engineering design processes. In this paper, we will consider a certain class of engineering design processes that we call progressive design. A progressive design process is an engineering design process that creates a product or system design through a series of distinct phases. (Thus, this term would not cover prototypebased design processes that iterate through generate-build-test cycles.) Each phase generates intermediate results by making decisions about different aspects of the design and generates increasingly detailed information. (The name reflects the similarity to a progressive die, which makes an increasingly complex part through a series of punches.) Pahl and Beitz [15], Proceedings of the ASME 2009 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference IDETC/CIE 2009 August 30 September 2, 2009, San Diego, California, USA