Dynamic Lexicographic Approach for Heuristic Multi-objective Optimization

This paper proposes a dynamic lexicographic approach to tackle multi-objective optimization problems. In this method, the ordering of objectives, which reflects their relative preferences, is changed in a dynamic fashion during the search. This approach eliminates the need for the decision-maker to establish fixed preferences among the competing objectives, which is often difficult. At the same time, the approach offers more flexibility to navigate constrained combinatorial search spaces than Pareto dominance, which treats all objectives with the same importance. The proposed dynamic lexicographic ordering is tested within a multiobjective particle swarm optimization algorithm and experiments are carried out on a number of instances of the vehicle routing problem with time windows. Our current results show that dynamic lexicographic ordering produces better results than Pareto dominance on instances with clustered sets of customers.