Development of multi-objective concurrent subspace optimization and visualization methods for multidisciplinary design

Most real-world design problems are complex and multidisciplinary, as there is always more than one objective (cost) function to be extremized in each problem. Hence, the primary goal of this research is to extend the capability of the Concurrent Subspace Optimization (CSSO) method to handle multi-objective optimization problems (MOPs) in Multidisciplinary Design Optimization (MDO).; The conventional CSSO approach is easily able to deal with such problems by applying the Weighted Sum approach. However, it is well known that the main disadvantage of the Weighted Sum approach is that it is unable to capture Pareto points on any non-convex part of the Pareto Front. Moreover, an aggregate objective function simply cannot reflect the true spirit of the CSSO method, which was developed to allow groups of specialists to independently have more control over their own design criteria and goals, even while maintaining system level coordination. In this study, the framework of Multi-Objective Concurrent Subspace Optimization (MOCSSO) methods is proposed in which each discipline has substantial control over its own objective function during the design process. By means of MOCSSO, an aggregate objective function is not required before solving an MOP. Instead, each subspace optimizes its own objective function while obtaining a Pareto optimum. This is accomplished by incorporating the concept of Pareto optimality into the subspace optimizations.; The Modified Concurrent Subspace Optimization (MDCSSO) method is presented first, in which the original CSSO approach is tailored to accommodate a multi-objective formulation. Once feasibility is demonstrated, the method is then extended to full-fledged multi-objective Pareto approaches based on designer's preferences. These methods are formed the Multi-Objective Concurrent Subspace Optimization (MOCSSO) methods, and include the Multi-Objective Pareto Concurrent Subspace Optimization (MOPCSSO) method, the Multi-Objective Range Concurrent Subspace Optimization (MORCSSO) method, the Multi-Objective Target Concurrent Subspace Optimization (MOTCSSO) method, and the Multi-Objective Range/Target Concurrent Subspace Optimization (MORTCSSO) method. Additionally, the Multi-Objective Pareto Front Visualization (MOPFV) and Interactive Multi-Objective Pareto Front Visualization (IMOPFV) frameworks are developed and presented. These visualization capabilities provide a means of real-time ‘steering’ during the solution process.; This dissertation demonstrates that CSSO-based multi-objective optimization methods developed in this research enable substantial flexibility and autonomy amongst participating analysis groups in an MDO problem.