On e-constraint based methods for the generation of Pareto frontiers

Abstract

Over the years, a number of methods have been proposed for the generation of uniform and globally optimal Pareto frontiers in multi-objective optimization problems. This has been the case irrespective of the problem definition. The most commonly applied methods are the normal constraint method and the normal boundary intersection method. The former suffers from the deficiency of an uneven Pareto set distribution in the case of vertical (or horizontal) sections in the Pareto frontier, whereas the latter suffers from a sparsely populated Pareto frontier when the optimization problem is numerically demanding (ill-conditioned). The method proposed in this paper, coupled with a simple Pareto filter, addresses these two deficiencies to generate a uniform, globally optimal, well-populated Pareto frontier for any feasible bi-objective optimization problem. A number of examples are provided to demonstrate the performance of the algorithm.