Optimising Tours for the Weighted Traveling Salesperson Problem and the Traveling Thief Problem: A Structural Comparison of Solutions

TL;DR

This paper compares the structure and solution quality of the Weighted Traveling Salesperson Problem (W-TSP) and the Traveling Thief Problem (TTP), revealing insights into their solution distributions and fitness function impacts.

Contribution

It provides a structural comparison of W-TSP and TTP, analyzing how different fitness functions influence solution quality and distribution.

Findings

W-TSP can often be better solved using TTP's fitness function.

W-TSP and TTP solutions differ significantly from optimal TSP or greedy solutions.

Using TTP's fitness function improves W-TSP solution quality.

Abstract

The Traveling Salesperson Problem (TSP) is one of the best-known combinatorial optimisation problems. However, many real-world problems are composed of several interacting components. The Traveling Thief Problem (TTP) addresses such interactions by combining two combinatorial optimisation problems, namely the TSP and the Knapsack Problem (KP). Recently, a new problem called the node weight dependent Traveling Salesperson Problem (W-TSP) has been introduced where nodes have weights that influence the cost of the tour. In this paper, we compare W-TSP and TTP. We investigate the structure of the optimised tours for W-TSP and TTP and the impact of using each others fitness function. Our experimental results suggest (1) that the W-TSP often can be solved better using the TTP fitness function and (2) final W-TSP and TTP solutions show different distributions when compared with optimal TSP or weighted greedy solutions.