Covering Solid Travelling Salesman Problem - An Algorithamic Study

Abstract

In this paper we model a Covering Solid Travelling Salesman Problem (CSTSP), a generalization of a two dimensional Covering Sales-man Problem (CSP) which is reduced to a Solid Travelling sales man problem (STSP) and solved by using a modified Genetic Algorithm (MGA). A salesman starts from an initial node and visits a subset of nodes only for once so that unvisited nodes are within a predetermined distance from the visited nodes, and comes back to the initial node. Here, a set of conveyances is available at the above mentioned nodes and the salesman uses the appropriate conveyance for minimum cost. Thus the problem reduces to finding the optimal covering set of nodes and the proper conveyance for travel so that total travel cost is minimum. This reduced STSP is solved by an MGA, which consists of roulette-wheels election, cyclic crossover, 2-inversemutation. A teach selected node, a random mutation for vehicle is introduced. Hence the CSTSP is solved by a random search (RS) for covering set and MGA, i.e, RS-MGA. The model is illustrated with some randomly generated cost and distance matrices.