A Genetic Algorithms Based Approach for Multidisciplinary Multiobjective Collaborative Optimization

Abstract

*† A new genetic algorithm based approach for multiobjective collaborative optimization is presented. The objective is to extend the bi-level formulation of collaborative optimization which has been essentially developed for single objective optimization problems to those problems with multiple objectives at the system and subsystem levels with interdisciplinary couplings between the subsystems. In the proposed approach, the overall problem is formulated such that the subsystem analyzers can only be accessed by the respective subsystems and objectives in each subproblem are related to the physical problem being addressed. The system and subsystem subproblems attempt at optimizing their respective objectives while satisfying various constraints using a Multi-Objective Genetic Algorithm (MOGA). MOGA solves system level subproblem with respect to shared variables. For each generation at the system level, the subsystems are optimized for each candidate design from the population. In each iteration, each subsystem subproblem has multiple solutions in the form of a Pareto optimal set. A decision is made in each subsystem to select a single solution from its Pareto set. This single solution can be chosen based on the best or worst value for any one objective. The selected solutions from all subsystems are collected and passed up to the system level. The objective and constraint values returned from each of the subsystems are used to assign a fitness value to the candidate designs at the system level. The proposed approach is implemented using object-oriented programming and multithreading techniques. In this regard, multiple subsystems in a given problem can use different optimization algorithms. The different subproblems that need to be solved during each MOGA iteration at the system level are solved in-parallel taking advantage of a multiprocessor computing hardware. The proposed approach is applied to a numerical and an engineering test problem. The solutions obtained from the proposed approach compare well with those obtained from a non-decomposition based (“all-at-once”) optimization approach.