Bi-level adaptive weighted sum method for multidisciplinary multi-objective optimization

Multidisciplinary design optimization (MDO) is a concurrent design tool for large-scale, complex engineering systems that can be affected through the optimal design of several smaller functional units or subsystems. Due to the multi-objective nature of most MDO problems, in recent years more work has focused on extending existing MDO method to handle such multi-objective MDO problems, by means of integrating multi-objective optimization method within MDO framework. In this paper, a novel integration of Adaptive weighted sum (AWS) method within Concurrent Subspace Optimization (CSSO) framework is presented and investigated. In the bi-level framework of CSSO, AWS is used to make tradeoff between multiple, conflicting objectives. And our developed multi-objective MDO method is called AWSCSSO method. In order to obtain better distributed solutions, two modifications are made on AWSCSSO. On one hand, additional equality constraint in suboptimization for each expected solution is relaxed since it causes difficulty of convergence within bi-level optimization framework. And the probability of entrapment in local minima can also be decreased. On the other hand, the mesh of Pareto front patches is modified due to the low efficiency of the original one. The proposed method is demonstrated with three MDO problems: 1) a numerical MDO test problem with convex Pareto front, from the NASA Langley Research Center MDO Test Suite; 2) a test problem with non-convex Pareto front, which is not easy to be solved; 3) conceptual design of a subsonic passenger aircraft, which consists of 2 objectives, 4 design variables, 5 coupling behavior variables, 7 constraints in aerodynamics and weight discipline. The proposed method is validated by example 1 and example 2. It is also compared with other multi-objective CSSO method. The comparison shows more uniformly-spaced, more widely-distributed, smoother Pareto front is computed using the proposed method. In example 3, the proposed method is used in an aircraft conceptual design problem and the Pareto front is successfully acquired, which preliminarily shows that AWSCSSO is applicable in aircraft design.