A Simple yet Efficient Multiobjective Combinatorial Optimization Method Using Decomposition and Pareto Local Search

Combining ideas from evolutionary algorithms, decomposition approaches and Pareto local search, this paper suggests a simple yet efficient memetic algorithm for combinatorial multiobjective optimization problems: MoMad. It decomposes a combinatorial multiobjective problem into a number of single objective optimization problems using an aggregation method. MoMad evolves three populations: population PL for recording the current solution to each subproblem, population PP for storing starting solutions for Pareto local search, and an external population PE for maintaining all the nondominated solutions found so far during the search. A problem-specific single objective heuristic can be applied to these subproblems to initialize the three populations. At each generation, a Pareto local search method is first applied to search a neighborhood of each solution in PP to update PL and PE . Then a single objective local search is applied to each perturbed solution in PL for improving PL and PE , and re-initializing PP . The procedure is repeated until a stopping condition is met. MoMad provides a generic hybrid algorithmic framework to use problem specific knowledge and employ well developed single objective local search and heuristics, and Pareto local search methods for dealing with combinatorial multiobjective problems. It is a population based iteration method and thus an anytime algorithm. Extensive experiments have been conducted in this paper to study MoMad and compare it with some other state of the art algorithms on the multiobjective traveling salesman problem and the multiobjective knapsack problem. The experimental results show that our proposed algorithm outperforms or performs similarly to the best so far heuristics on these two problems.