A velocity-based ACO algorithm for optimizing routes and social cost

Abstract

Intrinsically, the attainment of optimal solution via the Ant Colony System (ACS) algorithm essentially depends on the attractiveness of the quantity of pheromone on a given path. This leads to neglecting the velocity of the ant which constitutes an important nature-based heuristic information. The aim of this paper is to improve an existing ACS algorithm by integrating ant velocity, an insight gained from the Intelligent Water Drops (IWD) algorithm. A bi-objective model was formulated and adapted into the proposed ACS algorithm to optimize route length and social cost associated with various activities along the route. The solution technique was based on the min-max approach. A 14-node road network data, measuring distances and social costs was used in validating the algorithm. Both the benchmark algorithm and our proposed ant velocity-based ACS algorithm yielded the same bi-optimal solution (12km,GHS7) of distance and social cost along the path 1→4→7→11→12→14. The proposed ACS algorithm converges at the 127th iteration, corresponding to approximately 3 s execution time. Obviously, the proposed ACS algorithm outperforms the benchmark algorithm which converges at the 207th iteration, with approximately 5 s execution time. Therefore, the proposed ACS algorithm has outperformed the benchmark ACS algorithm in respect of time (or the number of iterations needed for convergence) by approximately 39 %. Evidently, with a velocity of 0.2445 ms−2, the optimal time taken by the best ant to complete the tour is approximately 27 s.