A perturbation based modified BAT algorithm for priority based covering salesman problem

Abstract

In this study, Bat algorithm (BA) is modified along with K-opt operation and one newly proposed perturbation approach to solve the well known covering salesman problem (CSP). Here, along with the restriction of the radial distances of the unvisited cities from the visited cities another restriction is imposed where a priority is given to some cities for the inclusion in the tour, i.e., some clusters to be created where the prioritised cities must be the visiting cities and the corresponding CSP is named as Prioritised CSP (PCSP). In the algorithm, 3-opt and 4-opt operations are used for two different purposes. The 4-opt operation is applied for generating an initial solution set of CSP for the BA and the 3-opt operation generates some perturbed solutions of a solution. A new perturbation approach is proposed for generating neighbour solutions of a potential solution where the exchange of some cities in the tour is made and is named as K-bit exchange operation. The proposed solution approach for the CSP and PCSP is named as the modified BA embedded with K-bit exchange and K-opt operation (MBAKEKO). It is a two-stage algorithm where in the first stage of the algorithm the clustering of the cities is done with respect to a fixed visiting city of each cluster in such a manner that the distances of the other cities of the cluster must lie with in the fixed covering distance of the problem and in the second stage the BA is applied to find the minimum cost Hamiltonian circuit by passing through the visiting cities of the clusters. MBAKEKO is tested with a set of benchmark test problems with significantly large sizes from the TSPLIB. To measure the performance of MBAKEKO, its results are compared with the results of different well-known approaches for CSPs available in the literature. It is observed from the comparison studies that MBAKEKO searches the minimum cost tour for any of the considered instances compared to all other well-known algorithms in the literature. It can be concluded from the numerical studies that the performance of MBAKEKO is better with respect to the state-of-the-art algorithms available in the literature.