Abstract
The minimum travel cost is a new approach to solve the Travelling Salesman Problem (TSP). The TSP library website (TSPLIB) provides several TSP problems with their best knownsolutions as a means to test any proposed algorithm. The present paper successfully applies the minimum travel cost algorithmto the 43 nodes P43problem which has the value of 5620 for its best knownsolution.This paper provides the details of the solution for value of 5621.
Highlights
The Travelling Salesman Problem (TSP) is defined as a set of nodes that represent a number N of cities, where the distance between each two nodes is known, and it is required the tour with least cost that starts from one node and visits all other nodes and returns back to the start node, in condition that each node is visited only once
Website provides sample TSP problems with known solutions in order to test the validity of proposed solutions for this interesting problem
This paper addresses the P43 problem which is a symmetrical graph that has a value of 5620 for the least cost tour visiting all nodes
Summary
The Travelling Salesman Problem (TSP) is defined as a set of nodes that represent a number N of cities, where the distance (cost) between each two nodes is known, and it is required the tour with least cost that starts from one node and visits all other nodes and returns back to the start node, in condition that each node is visited only once. TSP is mathematically presented as a full graph with number of nodes N. TSP is a prototype of hard combinatorial optimization problem where the possible solutions are (N-1)!. The new approach of minimum travel cost provides convergent solution for the TSP problem (Eleiche and Markus 2010). This paper addresses the P43 problem which is a symmetrical graph that has a value of 5620 for the least cost tour visiting all nodes. The P43 problem was selected to be solved using the new algorithm as it is the smallest problem in size after the previously solved problem with 17 nodes
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