Visibility Adaptation in Ant Colony Optimization for Solving Traveling Salesman Problem

Abstract

Ant Colony Optimization (ACO) is a practical and well-studied bio-inspired algorithm to generate feasible solutions for combinatorial optimization problems such as the Traveling Salesman Problem (TSP). ACO is inspired by the foraging behavior of ants, where an ant selects the next city to visit according to the pheromone on the trail and the visibility heuristic (inverse of distance). ACO assigns higher heuristic desirability to the nearest city without considering the issue of returning to the initial city or starting point once all the cities are visited. This study proposes an improved ACO-based method, called ACO with Adaptive Visibility (ACOAV), which intelligently adopts a generalized formula of the visibility heuristic associated with the final destination city. ACOAV uses a new distance metric that includes proximity and eventual destination to select the next city. Including the destination in the metric reduces the tour cost because such adaptation helps to avoid using longer links while returning to the starting city. In addition, partial updates of individual solutions and 3-Opt local search operations are incorporated in the proposed ACOAV. ACOAV is evaluated on a suite of 35 benchmark TSP instances and rigorously compared with ACO. ACOAV generates better solutions for TSPs than ACO, while taking less computational time; such twofold achievements indicate the proficiency of the individual adoption techniques in ACOAV, especially in AV and partial solution update. The performance of ACOAV is also compared with the other ten state-of-the-art bio-inspired methods, including several ACO-based methods. From these evaluations, ACOAV is found as the best one for 29 TSP instances out of 35 instances; among those, optimal solutions have been achieved in 22 instances. Moreover, statistical tests comparing the performance revealed the significance of the proposed ACOAV over the considered bio-inspired methods.

Three-dimensional continuous picking path planning based on ant colony optimization algorithm

“…The method fully validates that SMACFA outperforms the performance of other algorithms in solving TSP. Shahadat et al [25] proposed an improved ACO-based approach called ACO with Adaptive Visibility PLOS ONE (ACOAV). This method uses a new distance metric that incorporates partial updates of individual solutions and 3-Opt local search operations.…”

A Discrete JAYA Algorithm Based on Reinforcement Learning and Simulated Annealing for the Traveling Salesman Problem

“…Traditional exact algorithms have prominent disadvantages in the face of this difficulty, making it difficult to effectively solve this optimization problem [4]. To overcome this difficulty, researchers have designed many meta-heuristic algorithms inspired by the laws of physical change and biological systems in nature, such as Genetic Algorithm (GA) [5], Cuckoo Search (CS) [6], Particle Swarm Optimization (PSO) [7][8][9], Bat Algorithm (BA) [2], Simulated Annealing (SA) [10], Ant Colony Optimization algorithm (ACO) [8,[11][12][13][14], Frog-Leaping Algorithm (FLA) [15], and Artificial Bee Colony (ABC) [16][17][18][19][20]. Those kinds of meta-heuristic algorithms are simple in principle, are flexible in mechanism, and easily find the approximate optimal solution in a short time.…”

An Adaptive Ant Colony Optimization for Solving Large-Scale Traveling Salesman Problem

“…In the traditional ant colony algorithm, the heuristic information is obtained by the reciprocal of the distance between nodes, without considering the need to return to the starting city in the last step. Shahadat et al [30] adopted the general formula of visibility heuristic associated with the final destination city to intelligently deal with the problem of returning to the starting city. Yu et al [31] found that the traditional ant colony algorithm would fall into the local optimum when increasing the pheromone concentration factor.…”