Multi-Objective Robust Optimization Under Interval Uncertainty Using Online Approximation and Constraint Cuts

Abstract

Many engineering optimization problems are multi-objective, constrained and have uncertainty in their inputs. For such problems it is desirable to obtain solutions that are multi-objectively optimum and robust. A robust solution is one that as a result of input uncertainty has variations in its objective and constraint functions which are within an acceptable range. This paper presents a new approximation-assisted MORO (AA-MORO) technique with interval uncertainty. The technique is a significant improvement, in terms of computational effort, over previously reported MORO techniques. AA-MORO includes an upper-level problem that solves a multi-objective optimization problem whose feasible domain is iteratively restricted by constraint cuts determined by a lower-level optimization problem. AA-MORO also includes an online approximation wherein optimal solutions from the upper- and lower-level optimization problems are used to iteratively improve an approximation to the objective and constraint functions. Several examples are used to test the proposed technique. The test results show that the proposed AA-MORO reasonably approximates solutions obtained from previous MORO approaches while its computational effort, in terms of the number of function calls, is significantly reduced compared to the previous approaches.

Robust design optimization with bivariate quality characteristics

“…With a single quality characteristic and its quality loss function, the optimization model involves only a single objective. If designers are interested in a trade-off between the standard deviation and the mean deviation of a quality characteristic, they may formulate the problem with a multi-objective optimization model McAllister et al 2004;Messac and IsmailYahaya 2002;Hu et al 2011;Li and Azarm 2008). The two objectives are the standard deviation and mean deviation of the quality characteristic.…”

Adaptive efficient global optimization of systems with independent components

“…Improving systems by adaptively sampling component metamodels is also a fairly well known concept (Li et al 2006;Hu et al 2011). Optimization of multilevel decomposed systems that have a hierarchical structure has also received attention (Kokkolaras et al 2004).…”

Metamodel-based multi-objective robust design optimization of structures

“…Gunawan and Azarm [1] and Li et al [3] propose a double loop optimization approach with interval uncertainty. These approaches can be computationally intractable, especially in high-dimensional problems [4], since two optimization problems need to be resolved for each design. In order to reduce the computational cost, some authors such as Hu et al [4] and Shimoyama et al [5] suggest the use of approximations to assist the multi-objective optimization problem.…”

“…These approaches can be computationally intractable, especially in high-dimensional problems [4], since two optimization problems need to be resolved for each design. In order to reduce the computational cost, some authors such as Hu et al [4] and Shimoyama et al [5] suggest the use of approximations to assist the multi-objective optimization problem. In this respect, Hu et al [4] propose a two-level optimization with uncertainty intervals assisted by Kriging models.…”

“…In order to reduce the computational cost, some authors such as Hu et al [4] and Shimoyama et al [5] suggest the use of approximations to assist the multi-objective optimization problem. In this respect, Hu et al [4] propose a two-level optimization with uncertainty intervals assisted by Kriging models. In the work proposed by Shimoyama et al [5], Kriging models are used to obtain mean and standard deviation of the objective functions efficiently.…”