Rules for trajectory updating in decision based design

Abstract

Optimization is an indispensable tool in decision based design (DBD). There is an emerging consensus in DBD that the only correct objective to maximize is the decision maker's utility from a design. However, a utility function assessed a priori may not capture the preferences of the decision maker over the entire design space. As a result, when the optimizer searches for the optimal design, it may traverse (or end up) in regions in the design space where the preference order among different solutions is different from that used to build the utility function. For a highly non-convex design space, this can lead to convergence to a grossly suboptimal design depending on where we start the solution search. In this article, we propose two approaches to address this issue. First, we track the trajectory of the solution as generated by the optimizer and generate ranking questions that are presented to the designer to verify the correctness of the utility function, and second we propose backtracking rules if a local utility function is very different from the initially assessed function. We demonstrate our methodology using a mathematical example and a welded-beam design problem.