MEDACO: Solving Multiobjective Combinatorial Optimization with Evolution, Decomposition and Ant Colonies

We propose a novel multiobjective evolutionary algorithm, MEDACO, a shorter acronym for MOEA/D-ACO, combining ant colony optimization (ACO) and multiobjective evolutionary algorithm based on decomposition (MOEA/D). The motivation is to use the online-learning capabilities of ACO, according to the Reactive Search Optimization (RSO) paradigm of ”learning while optimizing”, to further improve the effectiveness of the original MOEA/D algorithms. Following other MOEA/D-like algorithms, MEDACO decomposes a multiobjective optimization problem into a number of single-objective optimization tasks solved by different iterated greedy construction processes (a.k.a. ants). Each ant has an individual heuristic information matrix and several neighboring ants, characterized by a similar combination of the individual objectives. All ants are divided into groups, with each group maintaining a different pheromone matrix. During the search, each ant records the best solution found so far for its subproblem. To construct a new solution, an ant combines information from its group’s pheromone matrix, its own heuristic information matrix and its current solution. Extensive experimental comparisons are executed. On the multiobjective 0-1 knapsack problem, MEDACO outperforms MOEA/D-GA on all the nine test instances. Furthermore, we demonstrate that the heuristic information matrices in MEDACO are crucial to significantly improve the performance. On the biobjective traveling salesman problem, MEDACO performs much better than the previously proposed BicriterionAnt algorithm on the 12 test instances. We also critically evaluate the effects of the group, the neighborhood and the location information of current solutions on the performance of MEDACO.