Local search for multiobjective function optimization: pareto descent method

Genetic Algorithm (GA) is known as a potent multiobjective optimization method, and the effectiveness of hybridizing it with local search (LS) has recently been reported in the literature. However, there is 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 in 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.Defining Pareto descent directions as descent directions to which no other descent directions are superior in improving all objective functions, this paper proposes a new LS method, Pareto Descent Method (PDM), which finds Pareto descent directions and moves solutions in such directions thereby improving all objective functions simultaneously. In the case part or all of them are infeasible, it finds feasible Pareto descent directions or descent directions as appropriate. PDM finds these directions by solving linear programming problems, which is computationally inexpensive. Experiments have shown PDM's superiority over existing methods.