Annealing Ant Colony Optimization with Mutation Operator for Solving TSP

Abstract

Ant Colony Optimization (ACO) has been successfully applied to solve a wide range of combinatorial optimization problems such as minimum spanning tree, traveling salesman problem, and quadratic assignment problem. Basic ACO has drawbacks of trapping into local minimum and low convergence rate. Simulated annealing (SA) and mutation operator have the jumping ability and global convergence; and local search has the ability to speed up the convergence. Therefore, this paper proposed a hybrid ACO algorithm integrating the advantages of ACO, SA, mutation operator, and local search procedure to solve the traveling salesman problem. The core of algorithm is based on the ACO. SA and mutation operator were used to increase the ants population diversity from time to time and the local search was used to exploit the current search area efficiently. The comparative experiments, using 24 TSP instances from TSPLIB, show that the proposed algorithm outperformed some well-known algorithms in the literature in terms of solution quality.

Traveling-Salesman-Problem Algorithm Based on Simulated Annealing and Gene-Expression Programming

“…To verify the performance of the proposed algorithm, two experiments were conducted for six benchmark instances obtained from the TSPLIB, and the experimental results of TSP-SAGEP were compared with three other heuristic algorithms. Results show that TSP-SAGEP outperformed the other heuristic algorithms proposed in [10,17,23,26]. Specifically, compared with traditional GEP, Ezugwu2017, Mohsen2016, and Wang2016, TSP-SAGEP had the best solution quality, low error between the best solution, a known optimal solution for all instances, and high convergent speed.…”

“…Simulation results demonstrated that the proposed algorithm had advantages in terms of stability and optimization capacity. Mohsen et al [17] proposed a hybrid ant-colony optimization algorithm based on the simulated annealing algorithm to solve the traveling-salesman problem. El-Samak et al [19] applied the affinity propagation clustering technique to optimize the genetic algorithm for finding the best solutions to the traveling-salesman problem.…”

“…From Figure 4, we can also find that, in all 10 runs, the number of solving the best solution based on TSP-SAGEP is 7, 7, 7, 6, 5 and 5 for the fri26, st70, gr120, pcb442, gr666, and rl1304 datasets, respectively. [17], and Wang 2016 [23] in terms of the best solution, the worst solution, and rate of difference, which is obtained by the Equation (2). Results are shown in Table 4.…”

“…To solve the problem, besides traditional backtracking algorithms, branch-and-bound algorithms, and greedy algorithms, we mainly use heuristic search algorithms to optimize. These heuristic algorithms include the simulated annealing algorithm [8][9][10][11][12], tabu-search algorithm [13][14][15], ant-colony optimization algorithm [16][17][18], and genetic algorithm [19][20][21][22][23][24]. However, the optimization time of the simulated annealing algorithm is very long, the tabu-search algorithm has a strong dependence on the initial solution and can only be serialized, genetic algorithm is easy to fall into local optimization and has poor convergence performance, and the ant-colony algorithm also has long optimization time and is also prone to falling into local optimization [25].…”

Dynamic Reduction-Expansion Operator to Improve Performance of Genetic Algorithms for the Traveling Salesman Problem

“…Due to this situation, development of metaheuristics has been performed to provide high-quality solutions in a reasonable time for different combinatorial optimization problems such as the TSP [6]. Among the most efficient metaheuristics for the TSP the following can be mentioned: Genetic Algorithms (GA), Particle Swarm Optimization (PSO), Tabu Search (TS), Simulated Annealing (SA), Ant Colony Optimization (ACO), and Artificial Neural Networks (ANNs) [3,6].…”