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Classical vehicle routing problems (VRP) involves supply of goods/services from a central depot to geographically scattered customers. Besides the classical objective of minimizing the total travelled distance, the present work also considers simultaneous optimization of two additional objectives namely minimizing make span and minimizing distance imbalance. A mathematical model for this multi-objective version of VRP (MO-VRPTW) has been developed. A meta-heuristic based on multiple ant colony system for solving this MO-VRPTW has also been proposed. Firefly algorithm (FA) has also been applied to avoid local optima. Two new migration operators named Migration-I and Migration-II and multi-pheromone matrices have been developed to further improve the solution set. The proposed algorithm has been tested on a number of benchmark problems and its superiority over other state of art approaches and NSGA-II one of the commonly used method for multi-objective optimization problems is demonstrated.

Improved Multi-Ant-colony algorithm for solving Multi-Objective Vehicle Routing Problems