Session: 02-03-01: Optimization

Paper Number: 144099

144099 - On a Sampling Based Method for Multi-Objective Robust Optimization 

Many engineering design optimization problems pose challenges when solving, as they often involve trade-offs between multiple conflicting objectives, constraints, and uncertainties in parameters or variables. Thus, in such cases it is desirable to obtain solutions that are robustly optimum. A robust optimal solution not only achieves the desired objectives, but also maintains feasibility, despite perturbations or variations in the uncertain parameters.

This paper presents a scenario-generation based method for solving multi-objective robust optimization (MORO) problems. The approach follows an iterative, sequential, single-level optimization problem workflow, which, unlike most methods presented in the literature, only requires the optimization problem to be solved once per iteration, thus reducing the computational cost of solving the problem. The prosed approach is designed to be very general in nature and can be applied to a range of problems – constrained and unconstrained, linear and non-linear, continuous and discrete, as well as problems where the objectives and constraints are black-box or simulation-based. Additionally, this approach can handle various uncertainty types – interval, distributional, or a mix of both.

The proposed MORO approach relies on concepts related to the Monte Carlo method and worst case analysis to handle the uncertainty and return a robust solution. The first step of the MORO algorithm requires defining the problem, along with setting the uncertain parameters to their nominal values or assumed initial values. Next, the optimization problem is solved to obtain a set of non-dominated solutions - the solver can be chosen by the user and can be adapted to the specific problem. Then, achieving robustness is handled by generating a set of new samples (or realizations) of the uncertain parameters. Depending on how the uncertain parameters are defined (e.g., as interval uncertainty or following a distribution), the sampling is performed from the range or distribution accordingly. Next, all the constraints are evaluated for all non-dominated points and for each uncertainty sample, and a feasibility check is performed. The constraint with the maximum violation, i.e., the worst case, is added to the optimization problem, and the algorithm continues to the next iteration. For the next iteration, the problem is resolved (now with the additional constraint), a new set of non-dominated solutions is obtained, and the procedure is repeated. The algorithm stops once all the uncertainty constraints are satisfied – i.e., at this point no realization of uncertain parameters has violated any of the constraints for the current set of non-dominated solutions. Thus, the solutions found in the current iteration are returned as the robust optimal solutions.

The proposed approach is applied to some example problems and compared against an existing MORO approach. To further demonstrate the applicability of this approach to a real world problem, it was implemented on an Unmanned Surface Vessel (USV) case study. The results obtained and subsequent performance analysis show that the proposed approach generally performs well, in some cases even outperforming existing approaches, and that the method's framework is flexible enough to be applicable to a wide variety of problems.

Presenting Author: Elizabeth Jordan University of Maryland

Presenting Author Biography: Elizabeth Jordan received the B.S. degree (Hons.) in mechanical engineering from the University of Maryland (UMD), College Park, MD, USA, in December 2020, where she is currently pursuing the Ph.D. degree in mechanical engineering. Her engineering work experience includes seven internships and co-ops with GE Aviation and AEDC Wind Tunnel 9. She is currently a Graduate Research Assistant. Her research interests include optimization, modeling, and decision support systems and their applications in the design and operation of engineering and healthcare systems. Ms. Jordan has received several honors and awards, including the President’s Scholarship, the Dean’s List Award for five semesters, and the University Honors Citation, while at UMD. Most recently, she was awarded the Clark Doctoral Fellowship, which is one of the most prestigious fellowships for graduate engineering students at UMD.

Authors:

Elizabeth Jordan University of Maryland
Arko Chatterjee University of Maryland
Ruochen Yang University of Maryland
Katrina Groth University of Maryland
Shapour Azarm University of Maryland