Heuristic approach and its application to solve NP-complete traveling salesman problem

Since long ago, a suitable solution to the traveling salesman problem in different scenarios has always been a popular problem for research. Various heuristic and evolutionary approaches have been designed for it. We developed a simple heuristic approach to identify n optimal routes from nC2 routes abiding a degree constraint, where only those routes are selected in the set of feasible routes (Hx), which have a degree less than or equal to 2. We implemented the present tactic on the milk delivery problem, that is, to determine the best route for a milk van supplying milk to (i) 10 houses and (ii) 20 houses, in an area including dairy. For (i), out of 45 possible routes, 10 optimal routes of Hamiltonian cycle length 188 have been selected in 0.1344 s. Similarly, for (ii), 20 optimal routes of Hamiltonian cycle length 328 have been selected in 0.2488 s from 190 total routes. In this way, the time complexity of the proposed heuristic approach is O(n2 log2n), where its solution always lies in the right neighborhood of 0.