A novel hybrid approach for solving the multiple traveling salesmen problem

Abstract

The multiple Travelling Salesmen Problem (mTSP) is one of the most popular and important operational research problems. It is a problem where n salesmen have to visit m cities such that each salesman has to visit at least one city and all the cities should be visited exactly once, starting and ending at one specific city. In this paper a new hybrid approach called AC2OptGA is proposed to solve the mTSP. AC2OptGA is a combination of three algorithms: Modified Ant Colony, 2-Opt, and Genetic Algorithm. Ant Colony-based algorithm is used to generate solutions on which the 2-Opt edge exchange algorithm is applied to enhance the obtained solutions. A Genetic Algorithm is then used to again improve the quality of the solutions. The reason behind combining the above-mentioned algorithms is to exploit their strengths in both global and local searches. The proposed approach is evaluated using various data instances from standard benchmarks. Using the TSPLIB benchmarks for large-sized instances, AC2OptGA shows better results than M-GELS, the current best known approach. For medium and small-sized data instances, AC2OptGA shows better results than other approaches and comparable results to M-GELS. Using the MTSP benchmarks (MTSP-51, MTSP-100 and MTSP-150), AC2OptGA outperforms other methods for number of salesmen less than 10 and is competitive with NMACO (BKS) for 10 salesmen. ARTICLE HISTORY

Experimental Study of a Hybrid Genetic Algorithm for the Multiple Travelling Salesman Problem

“…en a hybrid GA (HGA) is developed using a heuristic method for creating initial population, SCX, swap mutation, local search approach, and an immigration approach for finding highquality solution to the reduced problem. e usefulness of our proposed HGA is observed against some ACO-based algorithms [21][22][23], GAs [24,25], and a gravitational emulation approach [26] on some symmetric instances from TSPLIB [27]. e computational experiences demonstrate the usefulness of the proposed HGA.…”

“…A novel hybrid approach, named AC2OptGA, by combining a modified ACO, 2-opt, and GA is proposed in [21] to find solution to the problem. Initially, solutions are generated using ACO, then enhanced the obtained solutions using the 2-opt method, and finally, once again improved solution quality using GA. is approach is evaluated using various instances from TSPLIB and found better than the existing algorithm.…”

“…We compare our proposed HGA with some state-of-theart algorithms on the abovementioned six instances using m � 5. e state-of-the-art algorithms are a hybrid approach that combines ACO, 2-opt, and GA algorithms (AC2OptGA) [21], GA with local operators (GAL) [25], modified sweep and ant colony algorithm (SW + AS elite ) [22], modified gravitational emulation local search (M-GELS) [26], modified GA (MGA) [24], and novel modified ACO (NMACO) [23]. We used the same parameters for our HGA which are used for all of these algorithms.…”

Solving the Multiple Traveling Salesman Problem Using Memetic Algorithm

“…ACO approaches are used to produce solutions that use the 2-opt edge exchange approach to improve the solutions obtained. The basic concept of using ACO to solve the MTSP is the salesmen on their tours simulate or act like ants in their search for food, they go separately leaving a pheromone in the path they follow while searching for food [8].…”

Using genetic algorithm to solve multiple traveling salesman problem and considering Carbon emissions

“…Results showed that seeker genetic algorithm obtains a path with the lowest cost. (18) Liao, T.-Y. (2017) proposed details and a crossover meta-heuristic algorithm to address on-line vehicle routing problem, for reducing costs which surrounds financial matters and emissions.…”