Local Search for Multiobjective Function Optimization: Pareto Descent Method

Many real-world problems entail multiple conflicting objectives, which makes multiobjective optimization an important subject. Much attention has been paid to Genetic Algorithm (GA) as a potent multiobjective optimization method, and the effectiveness of its hybridization with local search (LS) has recently been reported in the literature. However, there have been a relatively small number of studies on LS methods for multiobjective function optimization. Although each of the existing LS methods has some strong points, they have respective drawbacks such as high computational cost and inefficiency of improving objective functions. Hence, a more effective and efficient LS method is being sought, which can be used to enhance the performance of the hybridization. Pareto descent directions are defined in this paper as descent directions to which no other descent directions are superior in improving all objective functions. Moving solutions in such directions is expected to maximally improve all objective functions simultaneously. This paper proposes a new LS method, Pareto Descent Method (PDM), which finds Pareto descent directions and moves solutions in such directions. In the case part or all of them are infeasible, it finds feasible Pareto descent directions or descent directions as necessary and moves solutions in these directions. PDM finds these directions by solving linear programming problems. Thus, it is computationally inexpensive. Experiments have shown that PDM is superior to existing methods.