# The Packing While Traveling Problem

arXiv: https://arxiv.org/abs/1512.08831 · HTML: https://mlsanity.com/paper/1512.08831/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Dec 2015.

## Built on by (most cited first, 2 of 2)

- [Benchmarking Algorithms for Submodular Optimization Problems Using IOHProfiler](https://mlsanity.com/paper/2302.01464/) (2023)
- [Solving Travelling Thief Problems using Coordination Based Methods](https://mlsanity.com/paper/2310.07156/) (2023)

## Abstract (arXiv)

This paper introduces the Packing While Traveling problem as a new non-linear knapsack problem. Given are a set of cities that have a set of items of distinct profits and weights and a vehicle that may collect the items when visiting all the cities in a fixed order. Each selected item contributes its profit, but produces a transportation cost relative to its weight. The problem asks to find a subset of the items such that the total gain is maximized. We investigate constrained and unconstrained versions of the problem and show that both are NP-hard. We propose a pre-processing scheme that decreases the size of instances making them easier for computation. We provide lower and upper bounds based on mixed-integer programming (MIP) adopting the ideas of piecewise linear approximation. Furthermore, we introduce two exact approaches: one is based on MIP employing linearization technique, and another is a branch-infer-and-bound (BIB) hybrid approach that compounds the upper bound procedure with a constraint programming model strengthened with customized constraints. Our experimental results show the effectiveness of our exact and approximate solutions in terms of solution quality and computational time.