Bi-Level Adaptive Weighted Sum Method for Multidisciplinary Multi-Objective Optimization

Abstract

The primary goal of this research is to develop a framework for dealing with multi-objective, multidisciplinary optimization problems with a large number of variables. The proposed method is expected to provide a relatively uniformly spaced, widely distributed Pareto front. To achieve this end, a novel integration of the adaptive weighted sum method within a concurrent subspace optimization framework is presented. In the bilevel framework of concurrent subspace optimization, the adaptive weighted sum is used to make tradeoffs among multiple, conflicting objectives. To obtain better distributed solutions, two modifications are made. First, an additional equality constraint in suboptimization for each expected solution is relaxed because it causes slow convergence within the bilevel optimization framework. The probability of entrapment in local minima can also be reduced. Second, the mesh of the Pareto front patches is modified due to the low efficiency of the original scheme. The proposed method is demonstrated with three multidisciplinary design optimization problems: 1) a numerical multidisciplinary design optimization test problem with a convex Pareto front, available within the NASA multidisciplinary design optimization Test Suite; 2) a test problem with a nonconvex Pareto front, which is not easily solved; and 3) a conceptual design of a subsonic passenger aircraft, which consists of two objectives, four design variables, five coupling behavior variables, seven constraints in aerodynamics, and weight discipline. The primary results show that the proposed method is promising with regard to obtaining a uniformly spaced, widely distributed, and smooth Pareto front and is applicable in the design of large-scale, complex engineering systems such as aircraft.