New Evolutionary Algorithm for Multi-objective Optimization and its Application to Engineering Design Problems

1 Abstract Multi-objective optimization addresses problems with several design objectives, which are often conflicting, placing different demands on the design variables. In contradiction to traditional optimization methods, which combine all objectives into a single figure of merit, parallel optimization strategies such as evolutionary algorithms allow direct convergence to the Pareto front. This permits a designer to choose a posteriori a design from a variety of Pareto-optimal solutions. In this paper, we introduce a new evolutionary approach called the subdivision method (SDM), using geometrical relations for the fitness assignment in the population, which guaranty diversity preservation and fast convergence to the Pareto set. New properties of the SDM are the constraint-free integration of target objective regions, and the ability to converge to the nondominated bounds of the objective space (Pareto solutions) as well as to the dominated bounds. The algorithm is applied to structural optimization problems and compared with state-of-the-art optimization algorithms.