Exploration of Pareto Frontier Using a Fuzzy Controlled Hybrid Line Search

This paper proposes a new approach for multicriteria optimization which aggregates the objective functions and uses a line search method in order to locate an approximate efficient point. Once the first Pareto solution is obtained, a simplified version of the former one is used in the context of Pareto dominance to obtain a set of efficient points, which will assure a thorough distribution of solutions on the Pareto frontier. In the current form, the proposed technique is well suitable for problems having multiple objectives (it is not limited to bi-objective problems) and require the functions to be continuous twice differentiable. In order to assess the effectiveness of this approach, some experiments were performed and compared with two well known population-based meta-heuristics. When compared to the population-based meta-heuristic, the proposed approach not only assures a better convergence to the Pareto frontier but also illustrates a good distribution of solutions. We propose a fuzzy logic controller to adapt the parameter required to control the distribution of solutions in the spreading phase. Our goal is to find a good distribution of solutions as quick as possible. From a computational point of view, both stages of the line search converge within a short time (average about 150 milliseconds for the first stage and about 20 milliseconds for the second stage). Apart from this, the proposed technique is very simple, easy to implement to solve multiobjective problems.