Multiobjective Combinatorial Optimization by Using Decomposition and Ant Colony

Combining ant colony optimization (ACO) and multiobjective evolutionary algorithm based on decomposition (MOEA/D), this paper proposes a multiobjective evolutionary algorithm, MOEA/D-ACO. Following other MOEA/D-like algorithms, MOEA/D-ACO decomposes a multiobjective optimization problem into a number of single objective optimization problems. Each ant (i.e. agent) is responsible for solving one subproblem. All the ants are divided into a few groups and each ant has several neighboring ants. An ant group maintains a pheromone matrix and an individual ant has a heuristic information matrix. During the search, each ant also 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. An ant checks the new solutions constructed by itself and its neighbors, and updates its current solution if it has found a better one in terms of its own objective. Extensive experiments have been conducted in this paper to study and compare MOEA/D-ACO with other algorithms on two set of test problems. On the multiobjective 0-1 knapsack problem, MOEA/D-ACO outperforms MOEA/D-GA on all the nine test instances. We also demonstrate that the heuristic information matrices in MOEA/D-ACO are crucial to the good performance of MOEA/D-ACO for the knapsack problem. On the biobjective traveling salesman problem, MOEA/D-ACO performs much better than BicriterionAnt on all the 12 test instances. We also evaluate the effects of grouping, neighborhood and the location information of current solutions on the performance of MOEA/D-ACO. The work in this paper shows that reactive search optimization scheme, i.e., the “learning while optimizing” principle, is effective in improving multiobjective optimization algorithms.