A modified discrete antlion optimizer for the ring star problem with secondary sub-depots

Abstract

This paper introduces a new problem in the field of combinatorial optimization. This problem can be named as the ring star problem with secondary sub-depots (RSPSSD). RSPSSD has one fixed main depot, and it allows a network to be divided into three types of nodes, namely primary sub-depots (includes the main depot too), secondary sub-depots and left out nodes. The challenge of the problem is to select some primary and secondary sub-depots that minimize the total routing cost which has three components. The first one is the routing cost of the main circuit that covers all the primary sub-depots including the main depot. The second one is the total routing cost of all the secondary circuits, each of which covers a set of few secondary sub-depots and their nearest primary sub-depot. The secondary circuits also have a constraint on the number of secondary sub-depots in it. The last one is the assignment cost of the left out nodes to their nearest concentrators which is nothing but anyone from the main depot, primary or secondary sub-depots. The proposed RSPSSD problem is solved with the proposed modified discrete antlion optimizer and tested using some TSP benchmark instances. The random walk of an antlion and an ant is encoded with ternary number system. The statistical analysis and comparison of the result against some other algorithms are also presented. A real-life case study has also been shown to validate the proposed model and algorithm.