An open close multiple travelling salesman problem with single depot

This paper introduces a novel practical variant, namely an open close multiple travelling salesmen problem with single depot (OCMTSP) that concerns the generalization of classical travelling salesman problem (TSP). In OCMTSP, the overall salesmen can be categorized into internal/permanent and external/outsourcing ones, where all the salesmen are positioned at the depot city. The primary objective of this problem is to design the optimal route such that all salesmen start from the depot/base city, and then visit a given set of cities. Each city is to be visited precisely once by exactly one salesman, and only the internal salesmen have to return to the depot city whereas the external ones need not return. To find optimal solutions, an exact pattern recognition technique based Lexi-search algorithm (LSA) is developed which has been subjected in Matlab. Comparative computational results of the LSA have been made with the existing methods for general multiple travelling salesman problem (MTSP). Further, to test the performance of LSA, computational experiments have been carried out on some benchmark as well as randomly generated test instances for OCMTSP, and results are reported. The overall computational results demonstrate that the proposed LSA is efficient in providing optimal and sub-optimal solutions within the considerable CPU times

Solving open travelling salesman subset-tour problem through a hybrid genetic algorithm

In open travelling salesman subset-tour problem (OTSSP), the salesman needs to traverse a set of k (≤n) out of n cities and after visiting the last city, the salesman does not necessarily return to the central depot. The goal is to minimize the overall traversal distance of covering k cities. The OTSSP model comprises two types of problems such as subset selection and permutation of the cities. Firstly, the problem of selection takes place as the salesman’s tours do not contain all the cities. On the other hand, the next problem is about to determine the optimal sequence of the cities from the selected subset of cities. To deal with this problem efficiently, a hybrid nearest neighbor technique based crossover-free Genetic algorithm (GA) with complex mutation strategies is proposed. To the best of the author’s knowledge, this is the first hybrid GA for the OTSSP. As there are no existing studies on OTSSP yet, benchmark instances are not available for OTSSP. For computational experiments, a set of test instances is created by using TSPLIB. The extensive computational results show that the proposed algorithm is having great potential in achieving better results for the OTSSP. Our proposed GA being the first evolutionary-based algorithm that will help as the baseline for future research on OTSSP

The degree constrained k-cardinality minimum spanning tree problem: a lexi-search algorithm

This paper deals with the degree constrained k-cardinality minimum spanning tree (k-MSTPD) problem defined on a connected, edge weighted and undirected graph. The aim of this problem is to determine the least weighted spanning tree with exactly k vertices such that except the root vertex, no other vertex in the resultant spanning tree exceeds the specified degree limit. The k-MSTPD problem has many practical applications for the design of electric, communication, and transportation networks. The problem is then formulated as a zero-one programming. In this paper, an exact algorithm known as Lexi-search algorithm (LSA) is developed to tackle the k-MSTPD problem. Furthermore, the developed LSA is programmed in Matlab and tested on some benchmark instances as well as on random instances and the respective results are reported. The obtained experimental results showed that the developed LSA takes significantly less time to find the optimal solutions