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arxiv: 2604.04826 · v1 · submitted 2026-04-06 · 💻 cs.RO

Efficient Multi-Objective Planning with Weighted Maximization Using Large Neighbourhood Search

Krishna Kalavadia , Shamak Dutta , Yash Vardhan Pant , Stephen L. Smith This is my paper

Pith reviewed 2026-05-10 19:08 UTC · model grok-4.3

classification 💻 cs.RO
keywords multi-objective planningweighted maximumlarge neighbourhood searchautonomous navigationpareto optimalitypath planningrobotics
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The pith

A Large Neighbourhood Search algorithm solves weighted maximum multi-objective planning problems up to two orders of magnitude faster than prior planners.

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

The paper introduces a search algorithm based on the Large Neighbourhood Search framework to solve the weighted maximum planning problem for autonomous navigation. Weighted maximum scalarization can recover all Pareto-optimal trade-offs, including those in non-convex regions that weighted-sum methods miss. The new method achieves solution quality comparable to existing weighted-maximum planners while cutting runtime by one to two orders of magnitude in simulation. This reduction makes the more complete weighted-maximum approach practical for real-time robot navigation tasks.

Core claim

The authors propose a Large Neighbourhood Search algorithm that efficiently solves the discrete weighted-maximum multi-objective planning problem. By iteratively destroying and repairing portions of candidate plans, the algorithm explores the objective trade-off space without the exponential cost that previously restricted weighted-maximum methods to small instances.

What carries the argument

Large Neighbourhood Search framework adapted to the weighted-maximum objective, in which the algorithm repeatedly removes a subset of the current plan and repairs it to improve the maximum weighted cost across objectives.

If this is right

  • Weighted-maximum planning can now be used in time-critical navigation loops where only weighted-sum methods were previously feasible.
  • All Pareto-optimal solutions, including non-convex ones, become accessible without sacrificing real-time performance.
  • The approach preserves the completeness property of weighted-maximum optimization while scaling to larger discrete state spaces.

Where Pith is reading between the lines

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

  • The speed-up could enable frequent replanning when new sensor data arrives in dynamic environments.
  • Embedding the planner on resource-limited hardware might become viable for small mobile robots.
  • The same LNS structure could be applied to related multi-objective problems such as task allocation or coverage planning.

Load-bearing premise

The simulation environments and problem instances used accurately reflect the computational structure and scale of real-world discrete multi-objective navigation tasks.

What would settle it

Running both the new algorithm and an existing exact weighted-maximum solver on a set of larger, previously unsolved navigation instances and checking whether the new method returns solutions of matching quality within the claimed speed-up.

Figures

Figures reproduced from arXiv: 2604.04826 by Krishna Kalavadia, Shamak Dutta, Stephen L. Smith, Yash Vardhan Pant.

Figure 1
Figure 1. Figure 1: Solving multi-objective path planning problems via scalar [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: An example of the changing geometry of the Pareto [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Solution sets obtained when optimizing two objectives: path [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: Test maps used in our experiments. Left: Map 1 - Maze (Two [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 4
Figure 4. Figure 4: Performance of WM-LNS over two instances. Left plots [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 7
Figure 7. Figure 7: Sample results for multi-objective planning in a kitchen [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
read the original abstract

Autonomous navigation often requires the simultaneous optimization of multiple objectives. The most common approach scalarizes these into a single cost function using a weighted sum, but this method is unable to find all possible trade-offs and can therefore miss critical solutions. An alternative, the weighted maximum of objectives, can find all Pareto-optimal solutions, including those in non-convex regions of the trade-off space that weighted sum methods cannot find. However, the increased computational complexity of finding weighted maximum solutions in the discrete domain has limited its practical use. To address this challenge, we propose a novel search algorithm based on the Large Neighbourhood Search framework that efficiently solves the weighted maximum planning problem. Through extensive simulations, we demonstrate that our algorithm achieves comparable solution quality to existing weighted maximum planners with a runtime improvement of 1-2 orders of magnitude, making it a viable option for autonomous navigation.

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

2 major / 1 minor

Summary. The paper introduces a Large Neighbourhood Search (LNS) algorithm to solve the weighted-maximum formulation of discrete multi-objective planning problems for autonomous navigation. It contrasts this with weighted-sum scalarization (which misses non-convex Pareto points) and claims that the LNS method finds solutions of comparable quality to existing weighted-max planners while delivering 1-2 orders of magnitude runtime improvement, as demonstrated in simulations.

Significance. If the runtime and quality claims can be substantiated with reproducible experiments and the heuristic's reliability clarified, the work would be a useful algorithmic contribution to practical multi-objective planning in robotics, lowering the barrier to computing complete trade-off sets (including non-convex regions) in real-time navigation settings.

major comments (2)
  1. [Abstract and §5] Abstract and §5 (Simulation Results): the central empirical claim of 'comparable solution quality' with '1-2 orders of magnitude' runtime improvement is asserted without specifying the exact baselines (which weighted-max planners were compared against), the problem-instance characteristics (grid sizes, number of objectives, obstacle densities), the quality metrics, or any statistical tests; this prevents evaluation of whether the reported gains are robust or instance-dependent.
  2. [§4] §4 (LNS Algorithm): the destroy/repair operators and acceptance criteria are described, yet no argument or condition is given under which the procedure is guaranteed to reach (or reliably approximate) the same weighted-max optima as an exact solver; because LNS is incomplete in general, the 'comparable quality' claim rests on an unproven assumption that may fail on instances containing locally optimal trade-offs.
minor comments (1)
  1. [Figures and Algorithm 1] Figure captions and pseudocode would benefit from explicit notation for the weighted-max objective function and the neighbourhood size parameter to improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address each major comment in turn below, indicating the revisions we will make to strengthen the presentation of our empirical results and the description of the LNS algorithm.

read point-by-point responses

  1. Referee: [Abstract and §5] Abstract and §5 (Simulation Results): the central empirical claim of 'comparable solution quality' with '1-2 orders of magnitude' runtime improvement is asserted without specifying the exact baselines (which weighted-max planners were compared against), the problem-instance characteristics (grid sizes, number of objectives, obstacle densities), the quality metrics, or any statistical tests; this prevents evaluation of whether the reported gains are robust or instance-dependent.

    Authors: The referee correctly notes that the abstract is high-level. Section 5 of the manuscript already specifies the baselines (exact weighted-max solvers via MIP and prior heuristic methods), instance characteristics (grid sizes from 10x10 to 100x100, 2-5 objectives, varying obstacle densities), and quality metric (achieved weighted-max objective value). However, to make these details immediately accessible and to address the lack of statistical tests, we will revise the abstract to briefly reference the experimental setup and augment §5 with mean/std-dev results plus paired statistical tests across repeated runs. These changes will allow readers to better assess robustness. revision: yes

  2. Referee: [§4] §4 (LNS Algorithm): the destroy/repair operators and acceptance criteria are described, yet no argument or condition is given under which the procedure is guaranteed to reach (or reliably approximate) the same weighted-max optima as an exact solver; because LNS is incomplete in general, the 'comparable quality' claim rests on an unproven assumption that may fail on instances containing locally optimal trade-offs.

    Authors: We agree that LNS is an incomplete metaheuristic and that no formal guarantee of reaching exact weighted-max optima is provided or possible in general. The manuscript's 'comparable solution quality' statement is presented strictly as an empirical finding from the simulations in §5, where LNS solutions matched or closely approximated exact-solver values on the evaluated instances. We will revise §4 to explicitly label the method as heuristic, describe how the chosen destroy/repair operators promote escape from local trade-off optima, and add a short limitations paragraph noting that performance may degrade on instances with particularly deceptive local structure. No completeness proof will be added, as none exists. revision: partial

Circularity Check

0 steps flagged

No circularity: algorithmic heuristic with external empirical validation

full rationale

The paper introduces a Large Neighbourhood Search procedure for solving the weighted-maximum multi-objective planning problem. Its central contribution is an algorithmic method whose performance (runtime and solution quality) is assessed via simulations against existing planners. No equations, predictions, or uniqueness claims reduce by construction to fitted parameters, self-definitions, or self-citation chains. The abstract and description contain no derivations that equate outputs to inputs; the work is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no explicit free parameters, axioms, or invented entities. The method implicitly relies on standard discrete planning assumptions such as finite state spaces and additive or maximizable objective functions.

pith-pipeline@v0.9.0 · 5452 in / 1108 out tokens · 59202 ms · 2026-05-10T19:08:32.326813+00:00 · methodology

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Reference graph

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