A Genetic Algorithm Approach for an Equitable Treatment of Objective Functions in Multi-objective Optimization Problems

摘要

A reasonable solution to a multi-objective problem is to determine an entire Pareto optimal solution set. Another general approach is to transform a multi-objective optimization problem into a mono-objective one. Determination of a single objective is possible with methods such as weighted sum method, but the problem lies in the right selection of the weights to characterize the decision makers preferences. In this paper, we study the problem where the decision maker tries to balance the objective function weights. This task is not easy for both decision maker and system analyser. To remedy this problem we introduce a solution method based on a genetic algorithm which automates the choice of the weights by varying them at each iteration of the algorithm. Our algorithm is tested on five academic problems and is applied to a UMTS base station location planning problem. The obtained results show that the proposed approach ensures an equitable treatment of each objective function.