Heuristics for K-Independent Average Traveling Salesperson Problem

Abstract

This paper deals with heuristic solution of K-independent average traveling salesperson (KIATSP) problem which is a recent extension of the well-known traveling salesperson problem (TSP). This problem seeks finding of K mutually independent Hamiltonian tours with no common edge such that the weighted sum of the average and standard deviation of the cost of these K tours is as small as possible. Like TSP, KIATSP is also an $$\mathcal{N}\mathcal{P}$$ -hard problem. We have designed seven constructive heuristics to address this problem. Our first two heuristics build K tours one after the other, whereas all the other heuristics construct K tours parallelly. A detailed comparative study of the performances of these seven heuristics on 40 TSPLIB instances has been presented. It is observed that those heuristics which build tours in parallel generally performed better than those heuristics where tours are built one after the other.