An Improved Discrete Bat Algorithm for Symmetric and Asymmetric Traveling Salesman Problems (1604.04138v1)

Abstract: Bat algorithm is a population metaheuristic proposed in 2010 which is based on the echolocation or bio-sonar characteristics of microbats. Since its first implementation, the bat algorithm has been used in a wide range of fields. In this paper, we present a discrete version of the bat algorithm to solve the well-known symmetric and asymmetric traveling salesman problems. In addition, we propose an improvement in the basic structure of the classic bat algorithm. To prove that our proposal is a promising approximation method, we have compared its performance in 37 instances with the results obtained by five different techniques: evolutionary simulated annealing, genetic algorithm, an island based distributed genetic algorithm, a discrete firefly algorithm and an imperialist competitive algorithm. In order to obtain fair and rigorous comparisons, we have conducted three different statistical tests along the paper: the Student's $t$-test, the Holm's test, and the Friedman test. We have also compared the convergence behaviour shown by our proposal with the ones shown by the evolutionary simulated annealing, and the discrete firefly algorithm. The experimentation carried out in this study has shown that the presented improved bat algorithm outperforms significantly all the other alternatives in most of the cases.

• The paper presents an improved discrete Bat Algorithm (IBA) for TSP and ATSP, using strategies like dynamic search operator switching based on distance to enhance efficiency.
• Experimental evaluation demonstrates IBA consistently outperforms benchmark algorithms on 37 instances, finding optimal or near-optimal solutions more efficiently and robustly.
• The successful adaptation has practical implications for solving real-world routing problems and suggests potential for applying IBA to other complex combinatorial optimization tasks.

A Comprehensive Analysis of an Improved Discrete Bat Algorithm for the Traveling Salesman Problems

The paper presents a novel adaptation of the Bat Algorithm (BA) for solving both the Symmetric and Asymmetric Traveling Salesman Problems (TSP and ATSP). The original bat algorithm, rooted in the echolocation method used by bats, was developed for continuous optimization problems. This research not only adapts BA for discrete problems but also proposes an enhanced version, the Improved Bat Algorithm (IBA), which introduces unique strategies to increase the algorithm's efficiency.

Overview of the Discrete Bat Algorithm

In adapting the BA for TSP and ATSP, the researchers made several key modifications to the algorithm's structure. The traditional BA uses parameters such as pulse rate, loudness, frequency, and velocity, which are transformed in the discrete setting. The paper introduces the Hamming Distance function as a mechanism to determine the 'velocity' of bats, allowing them to explore the space of possible solutions effectively. Bats represent feasible solutions, and their movements are guided by neighborhood searches using 2-opt and 3-opt operators.

Proposed Improvements: The Improved Bat Algorithm

The IBA builds upon the foundational structure of the discrete BA by introducing intelligence in bat movements. Bats modify their search patterns depending on their distance, represented by the Hamming Distance, from the best solution found by the population. If a bat is close to the best-known solution, a 2-opt move is employed for local optimization, whereas a 3-opt move is used for global exploration when they are further. This dynamic switching enhances the algorithm's ability to escape local optima and maintains diversity in the candidate solutions.

Experimental Evaluation

The effectiveness of the proposed IBA is validated through rigorous experiments conducted on 37 instances of TSP and ATSP, comparing its performance against several notable algorithms, including the Genetic Algorithm (GA), Evolutionary Simulated Annealing (ESA), Distributed Genetic Algorithm (IDGA), Discrete Firefly Algorithm (DFA), and Discrete Imperialist Competitive Algorithm (DICA).

The experiments demonstrate that IBA consistently outperforms these alternatives across most instances. The results indicate that IBA secured optimal or near-optimal solutions in a significant number of cases with relatively lower computational overhead. Moreover, statistical analyses employing Student's t-test, Holm's test, and Friedman's test confirm the superiority of the IBA with high confidence levels.

Convergence and Robustness

A notable advantage of the IBA is its convergence behavior. The algorithm requires fewer evaluations of the objective function to converge to competitive solutions compared to other benchmarked methods. Additionally, the standard deviation of the results suggests that IBA provides more stable solutions, highlighting its robustness in addressing the inherent complexities of TSP and ATSP.

Potential Implications and Future Directions

The successful adaptation and enhancement of the BA for discrete optimization problems, specifically TSP and ATSP, have practical implications for solving real-world routing challenges in logistics, transportation, and supply chain management. The paper paves the way for extending the application of IBA to other NP-hard combinatorial problems such as Vehicle Routing Problems (VRPs) and Rich Routing Problems.

Future work may focus on investigating hybrid approaches by combining IBA with exact methods or commercial solvers to further refine the optimization process. Additionally, expanding the algorithm to tackle multi-objective optimization scenarios could provide a wider scope of utility in various industrial applications.

In conclusion, the paper presents a significant advancement in metaheuristic optimization by enhancing the Bat Algorithm for discrete problems. Its refined methodological approach and insightful experiments underscore its potential value in the academic and practical fields.