A Multi-Objective Decomposition-Based Ant Colony Optimisation Algorithm With Negative Pheromone

Existing ant colony algorithms only have one kind of pheromone. They use non-dominated solutions to update it while not making use of dominated solutions, which can provide valuable information for guiding the subsequent foraging process. To make full use of dominated solutions, we create a new kind of pheromone temporarily called a negative pheromone and propose a new ant colony optimisation algorithm called NMOACO/D, which combines MOEA/D-ACO with the negative pheromone. Many experiments have been carried out in this study to compare NMOACO/D with MOEA/D-ACO and other algorithms on several bi-objective travelling salesman problems. We demonstrate that NMOACO/D outperforms the MOEA/D-ACO and six different recently proposed related algorithms on all nine test instances. We also evaluate the effect of negative pheromone on the performance of the NMOACO/D. The results in this paper show that correctly making use of the information related to dominated solutions can further improve the ant colony algorithm performance.