Simulated annealing based symbiotic organisms search optimization algorithm for traveling salesman problem

Symbiotic Organisms Search (SOS) algorithm is an effective new metaheuristic search algorithm, which has recently recorded wider application in solving complex optimization problems. SOS mimics the symbiotic relationship strategies adopted by organisms in the ecosystem for survival. This paper, presents a study on the application of SOS with Simulated Annealing (SA) to solve the well-known traveling salesman problems (TSPs). The TSP is known to be NP-hard, which consist of a set of (n − 1)!/2 feasible solutions. The intent of the proposed hybrid method is to evaluate the convergence behaviour and scalability of the symbiotic organism’s search with simulated annealing to solve both small and large-scale travelling salesman problems. The implementation of the SA based SOS (SOS-SA) algorithm was done in the MATLAB environment. To inspect the performance of the proposed hybrid optimization method, experiments on the solution convergence, average execution time, and percentage deviations of both the best and average solutions to the best known solution were conducted. Similarly, in order to obtain unbiased and comprehensive comparisons, descriptive statistics such as mean, standard deviation, minimum, maximum and range were used to describe each of the algorithms, in the analysis section. The oneway ANOVA and Kruskal-Wallis test were further used to compare the significant difference in performance between SOS-SA and the other selected state-of-the-art algorithms. The performances of SOS-SA and SOS are evaluated on different sets of TSP benchmarks obtained from TSPLIB (a library containing samples of TSP instances). The empirical analysis’ results show that the quality of the final results as well as the convergence rate of the new algorithm in some cases produced even more superior solutions than the best known TSP benchmarked results

Finding the best tour for travelling salesman problem using artificial ecosystem optimization

This paper presents a new method based on the artificial ecosystem optimization (AEO) algorithm for finding the shortest tour of the travelling salesman problem (TSP). Wherein, AEO is a newly developed algorithm based on the idea of the energy flow of living organisms in the ecosystem consisting of production, consumption and decomposition mechanisms. In order to improve the efficiency of the AEO for the TSP problem, the 2-opt movement technique is equipped to enhance the quality of the solutions created by the AEO. The effectiveness of AEO for the TSP problem has been verified on four TSP instances consisting of the 14, 30, 48 and 52 cities. Based on the calculated results and the compared results with the previous methods, the proposed AEO method is one of the effective approaches for solving the TSP problem

Simulated Annealing Algorithm for Determining Travelling Salesman Problem Solution and Its Comparison with Branch and Bound Method

Travelling Salesman Problem (TSP) is a problem where a person must visit some places, starting from one city and then moving on to the next city with the conditions that the places visited can only be passed precisely once and then back to the starting city. TSP is an NP-hard, an important problem in operations research. TSP problems can be solved by an exact method or an approximation method, namely the metaheuristic method. This research aims to solve the TSP problem with an approximation method called the Simulated Annealing (SA), and then compare the results of this approximation method with the exact Branch and Bound method. The results indicated that the SA method could accomplish TSP problems. However, like other metaheuristic methods, SA only accomplishes it using an approach to get good results. Still, it cannot be determined that SA has the most optimal results, but the time needed by the SA method is faster than the Branch and Bound method. In case I, the percentage difference between the distance generated using the SA method with the B-and-B method is 0%, in case II it is 7% and in case III it is 8%