A Fully Polynomial Time Approximation Scheme for Packing While Traveling

TL;DR

This paper introduces an FPTAS for the packing while traveling problem, a component of the traveling thief problem, providing efficient approximation methods and demonstrating superior performance over existing approaches.

Contribution

The paper develops an exact dynamic programming algorithm and a fully polynomial time approximation scheme for the PWT problem, advancing solution techniques for TTP.

Findings

FPTAS achieves near-optimal solutions efficiently.

Experimental results outperform current state-of-the-art methods.

Approach is effective on diverse benchmark instances.

Abstract

Understanding the interactions between different combinatorial optimisation problems in real-world applications is a challenging task. Recently, the traveling thief problem (TTP), as a combination of the classical traveling salesperson problem and the knapsack problem, has been introduced to study these interactions in a systematic way. We investigate the underlying non-linear packing while traveling (PWT) problem of the TTP where items have to be selected along a fixed route. We give an exact dynamic programming approach for this problem and a fully polynomial time approximation scheme (FPTAS) when maximising the benefit that can be gained over the baseline travel cost. Our experimental investigations show that our new approaches outperform current state-of-the-art approaches on a wide range of benchmark instances.