Most engineering design problems are complex and multidisciplinary in nature, and quite often require more than one objective (cost) function to be extremized simultaneously. For multi-objective optimization problems, there is not a single optimum solution, but a set of optimum solutions called the Pareto set. The primary goal of this research is to develop a heuristic solution strategy to enable multi-objective optimization of highly coupled multidisciplinary design applications, wherein each discipline is able to retain some degree of autonomous control during the process. To achieve this goal, this research extends the capability of the Multi-Objective Pareto Concurrent Subspace Optimization (MOPCSSO) method to generate large numbers of non-dominated solutions in each cycle, with subsequent update and refinement, thereby greatly increasing efficiency.
While the conventional MOPCSSO approach is easily able to generate Pareto solutions, it will only generate one Pareto solution at a time. In order to generate the complete Pareto front, MOPCSSO requires multiple runs (translating into many system convergence cycles) using different initial staring points. In this research, a Genetic Algorithm-based heuristic solution strategy is developed for multi-objective problems in coupled multidisciplinary design. The Multi-Objective Genetic Algorithm Concurrent Subspace Optimization (MOGACSSO) method allows for the generation of relatively evenly distributed Pareto solutions in a faster and more efficient manner than repeated implementation of MOPCSSO.
While achieving an optimum design, it is often also desirable that the optimum design be robust to uncontrolled parameter variations. In this research, the capability of the MOGACSSO method is also extended to generate Pareto points that are robust in terms of performance and feasibility, for given uncontrolled parameter variations. The Roust-MOGACSSO method developed in this research can generate a large number of designs that are truly Pareto (or close to the Pareto front) while still being robust according to the designer's specifications. The Robust-MOGACSSO method allows the designer to select a design based on his preferences for performance as well as robustness.
This research also investigates the use of the Hyperspace Pareto Frontier (HPF) visualization technique to convey robustness information (associated with the Pareto points) to the designer. It is shown that the robustness of Pareto points can be evaluated as a post-processing step and visualized in an intuitive fashion using HPF visualizations. The designer can specify a preference structure for robustness together with a preference structure for performance values. Visualizing his preference structures in HPF allows the designer to perform a unique trade-off investigation and thereby select a design that satisfies his preference for performance as well as robustness.
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