Hybrid Line Search for Multiobjective Optimization

Abstract

The aggregation of objectives in multiple criteria programming is one of the simplest and widely used approach. But it is well known that these techniques sometimes fail in different aspects for determining the Pareto frontier. This paper proposes a new line search based approach for multicriteria optimization. The objectives are aggregated and the problem is transformed into a single objective optimization problem. Then the line search method is applied and an approximate efficient point is lacated. 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). the functions to be optimized must be continuous twice differentiable. In order to assess the effectiveness of this approach, some experiments were performed and compared with two recent well known population-based metaheuristics ParEGO [8] and NSGA II [2]. When compared to ParEGO and NSGA II, the proposed approach not only assures a better convergence to the Pareto frontier but also illustrates a good distribution of solutions. From a computational point of view, of the line search converge within a short time (average about 150 milliseconds) and the generation of well distributed solutions on the Pareto frontier is also very fast (about 20 milliseconds). Apart from this, the proposed technique is very simple, easy to implement and use to solve multiobjective problems.