Application of the modified physical programming method to generating the entire Pareto frontier in multiobjective optimization
Sergey Vladimirovich Utyuzhnikov, Paolo Fantini · Research Explorer (The University of Manchester) · 2005
In an industrial design setting, the decision-maker (DM) has to trade-off many conflicting criteria such as minimum weight, acquisition and lifecycle costs, and desirable performance characteristics. In this process it is natural to exclude from the consideration any design solution which can be improved without any trade-off and violation of the constraints. It leads to the Pareto optimal solutions. The DM selects the ultimate solution among the Pareto set on the basis of additional subjective (qualitative) requirements. Unfortunately, wider industrial application of vector optimization methods seems to be constrained by the high computational resources required and the limited time scales available to perform extensive optimisation search. Thus, when considering the design of complex products such as aircraft, the DM is able to consider only a few possible (Pareto) solutions. Under such conditions, it is necessary to minimize the computational time required to find a Pareto optimal solution. The choice of an appropriate numerical optimization method is therefore important, in particular, with respect to the ability to generate an even distribution of the complete Pareto frontier in order to gain maximum information on the Pareto surface with minimum computational time. The Physical Programming (PP) Method recently suggested by Messac appears to match many of the above requirements. The PP has been modified by the authors to make it simpler and more efficient for practical applications. The modification is based on shrinking the search domain to make its location in the objective space easier. The algorithm to obtain an even distribution of the Pareto set is outlined. It is shown that the method is able to find the Pareto surface for different test cases including the optimization of the wing having a Zhukowskii profile. It is also shown in this paper that the method generates the entire Pareto frontier for both the convex and concave surfaces in the cases of bi- objective and multiobjective optimisation.