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arxiv: 2604.13469 · v1 · submitted 2026-04-15 · 💻 cs.NE

Greedy Approaches for Packing While Travelling with Deterministic and Stochastic Constraints

Thilina Pathirage Don , Aneta Neumann , Frank Neumann This is my paper

Pith reviewed 2026-05-10 12:13 UTC · model grok-4.3

classification 💻 cs.NE
keywords packing while travellingtravelling thief problemgreedy heuristicsreward functionshyper-heuristicsstochastic constraintschance constraintsNP-hard optimization
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The pith

New reward functions for greedy packing outperform standard methods in the packing while travelling problem under both fixed and uncertain item weights.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper addresses the packing while travelling problem, an NP-hard subproblem of the travelling thief problem where items must be selected for a fixed tour to maximize profit minus travel costs. It introduces reward functions specifically designed for this interdependence and places them in a hyper-heuristic framework that selects among them during search. The same functions are then extended to handle stochastic item weights through chance constraints. Experiments across multiple instances show these tailored approaches produce higher-quality packings than conventional greedy rules in both deterministic and stochastic cases.

Core claim

The authors establish that reward functions tailored to the packing while travelling problem, when used in greedy algorithms and extended through a hyper-heuristic framework, deliver better solutions than standard heuristics; the same functions adapted for stochastic weights via chance constraints retain this advantage.

What carries the argument

Tailored reward functions that score items by combining profit, weight, and tour-dependent travel cost, embedded in a hyper-heuristic selector and adapted to chance-constrained stochastic weights.

If this is right

  • Improved packing solutions directly raise the quality of complete travelling thief problem solvers that alternate between tour construction and packing.
  • The hyper-heuristic layer reduces the need for manual tuning of reward functions when moving between different instance classes.
  • Chance-constraint handling allows the same greedy framework to be deployed in settings where item weights fluctuate, such as variable cargo densities.
  • Runtime remains comparable to standard greedy methods, supporting repeated calls inside larger metaheuristics.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The approach could be transferred to other problems that interleave routing and resource selection, such as vehicle routing with loading constraints.
  • If the reward functions prove robust, they might serve as drop-in replacements in existing travelling thief solvers without requiring changes to the tour component.
  • Further work could test whether the same functions remain effective when the tour itself is allowed to change slightly during packing.

Load-bearing premise

The new reward functions and hyper-heuristic choices deliver consistent gains across the full range of problem sizes, item distributions, and tour structures that arise in practice.

What would settle it

A large-scale test set of packing while travelling instances where standard greedy heuristics achieve equal or higher profit than the proposed tailored functions on at least half the instances would refute the claimed benefit.

Figures

Figures reproduced from arXiv: 2604.13469 by Aneta Neumann, Frank Neumann, Thilina Pathirage Don.

Figure 1
Figure 1. Figure 1: Example TSP tour to represent the weight accumulation in [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
read the original abstract

The travelling thief problem (TTP) is a well-known multi-component optimisation problem that captures the interdependence between two components: the tour across cities and the packing of items. The packing while travelling problem (PWT) is an NP-hard subproblem of TTP where the packing of items should be optimised for a given fixed tour. In many solvers, the packing component is often addressed using greedy heuristics. Here, the use of suitable greedy functions is essential for the success of greedy algorithms. In this paper, we introduce new reward functions tailored to the PWT and extend them to a hyper-heuristic framework to achieve further advantage. Furthermore, we investigate the chance constrained PWT for greedy approaches and adopt the newly introduced reward functions for stochastic weights. The experimental results clearly demonstrate the benefit of the tailored heuristics over the standard heuristics in both deterministic and stochastic constraints.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper introduces new reward functions tailored to the Packing While Travelling (PWT) subproblem of the Travelling Thief Problem, extends them via a hyper-heuristic framework, and adapts the approach to chance-constrained stochastic weights. It claims that experimental comparisons demonstrate clear superiority of these tailored greedy heuristics over standard ones (e.g., profit/weight) under both deterministic and stochastic settings.

Significance. If the experimental claims hold under rigorous verification, the work could offer practical improvements to TTP solvers by strengthening the packing component with problem-specific greedy rules and hyper-heuristics, especially for stochastic variants where standard methods may underperform.

major comments (3)
  1. [Experimental Results] The experimental results section provides no details on the instance sets (city counts, item distributions, tour qualities), statistical tests, or derivation of the new reward functions, preventing verification that the reported advantages are robust rather than instance-specific (as flagged in the abstract's superiority claim).
  2. [Experimental Results] Runtime comparisons do not appear to normalize or account for the hyper-heuristic framework's selection overhead against the baseline greedy methods, which could undermine the claim that the framework adds value without hidden computational costs.
  3. [Stochastic PWT] For the stochastic (chance-constrained) case, it is unclear how probability estimation is integrated into the greedy choice without introducing bias or excessive computation, and whether this is consistently applied across all compared heuristics.
minor comments (2)
  1. [Methods] Notation for the new reward functions could be clarified with explicit equations early in the methods section to aid reproducibility.
  2. [Introduction] The abstract and introduction would benefit from a brief statement on the specific standard heuristics used as baselines for direct comparison.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the thorough review and constructive feedback. We address each of the major comments below and will make revisions to improve the clarity and completeness of the manuscript.

read point-by-point responses

  1. Referee: [Experimental Results] The experimental results section provides no details on the instance sets (city counts, item distributions, tour qualities), statistical tests, or derivation of the new reward functions, preventing verification that the reported advantages are robust rather than instance-specific (as flagged in the abstract's superiority claim).

    Authors: We agree that more detailed information on the experimental setup is necessary for full verification and reproducibility. In the revised manuscript, we will expand Section 4 to include: a table summarizing the instance characteristics (number of cities from 20 to 280 as per standard TTP instances, item distributions with varying knapsack capacities), details on tour generation methods (using Lin-Kernighan heuristic for TSP component), and the full derivation of the reward functions in Section 3 with mathematical motivations. Additionally, we will report results of statistical significance tests (e.g., paired t-tests or Wilcoxon tests with p-values) across multiple runs. This will demonstrate that the advantages are not instance-specific. revision: yes

  2. Referee: [Experimental Results] Runtime comparisons do not appear to normalize or account for the hyper-heuristic framework's selection overhead against the baseline greedy methods, which could undermine the claim that the framework adds value without hidden computational costs.

    Authors: The hyper-heuristic framework's selection process is lightweight, involving a simple rule-based or learning-based selector that evaluates a small set of heuristics per decision point. However, we acknowledge the need for transparent runtime analysis. In the revision, we will provide normalized runtime results, including separate timings for the greedy decisions and the hyper-heuristic overhead. We will show that the overhead is negligible compared to the overall solving time and that the improved solution quality justifies it. This will be added to the experimental results section. revision: yes

  3. Referee: [Stochastic PWT] For the stochastic (chance-constrained) case, it is unclear how probability estimation is integrated into the greedy choice without introducing bias or excessive computation, and whether this is consistently applied across all compared heuristics.

    Authors: For the chance-constrained stochastic PWT, the probability estimation is performed using a fixed number of Monte Carlo simulations (1000 samples per evaluation) to approximate the probability that the total weight does not exceed the capacity under stochastic weights. This estimation is incorporated into the reward function by multiplying the original reward by the estimated probability of feasibility, thus guiding the greedy choice towards items that maintain high reward while satisfying the constraint with high probability. This approach is applied uniformly to all heuristics, including the standard profit/weight and the new tailored ones, to ensure fair comparison. We will add a new subsection in the stochastic section detailing the integration, including pseudocode and analysis of computational overhead, which remains acceptable as the sampling is efficient. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical heuristic comparison with independent experimental validation

full rationale

The paper is an empirical study that introduces tailored reward functions for greedy heuristics on the Packing While Travelling (PWT) problem and evaluates them experimentally against standard baselines under deterministic and chance-constrained stochastic settings. No derivation chain exists; the central claims rest on runtime and solution-quality comparisons across problem instances rather than any self-referential equations, fitted parameters renamed as predictions, or load-bearing self-citations. The reward functions are defined directly from PWT structure (tour-dependent profit/time trade-offs) and then tested, with no reduction of outputs to inputs by construction. This is a standard, self-contained empirical contribution.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available; no explicit free parameters, axioms, or invented entities are identifiable. The approach rests on standard assumptions of greedy selection and chance-constrained programming common to the optimization domain.

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