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arxiv: 2605.10634 · v1 · submitted 2026-05-11 · 💻 cs.AI

Teacher-Aware Evolution of Heuristic Programs from Learned Optimization Policies

Minyu Chen , Song Qin , Ling-I Wu , Jianxin Xue , Guoqiang Li This is my paper

Pith reviewed 2026-05-12 05:29 UTC · model grok-4.3

classification 💻 cs.AI
keywords heuristic evolutionLLM heuristic designcombinatorial optimizationbehavioral feedbacklearned optimization policiesschedulingroutinggraph optimization
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The pith

Learned optimization policies can guide the evolution of better static heuristics by supplying local behavioral feedback instead of relying only on final performance scores.

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

LLM methods for automatically designing heuristics for combinatorial problems have relied on delayed endpoint performance as the main signal for guiding search. This paper proposes querying separately trained learned optimization policies on the states encountered during candidate heuristic execution and using their preferred actions as immediate local feedback to steer the evolutionary process. The resulting heuristics are executable programs that incorporate both performance outcomes and these teacher-derived signals. Experiments across scheduling, routing, and graph benchmarks show gains over performance-only baselines, with the added benefit that no neural inference is needed once the heuristic is discovered. Readers would care because the approach turns existing learned policies into reusable sources of guidance that produce deployable, lightweight code rather than requiring ongoing model calls.

Core claim

The paper shows that independently trained learned optimization policies can be repurposed as behavioral teachers: by querying them for action preferences on states visited by evolving candidate programs, the search discovers static executable heuristics that outperform those evolved using only task performance, as validated on scheduling, routing, and graph optimization benchmarks without any neural inference required at deployment.

What carries the argument

Teacher-aware evolutionary framework that extracts local action preferences from learned policies to supplement endpoint performance in LLM-driven heuristic search.

If this is right

  • Heuristics discovered this way achieve higher performance on standard combinatorial optimization benchmarks than performance-driven LLM evolution baselines.
  • The final heuristics are static executable programs that require no neural network inference or model deployment at runtime.
  • Learned optimization policies can be reused as sources of behavioral guidance rather than being directly imitated or deployed.
  • The method applies to multiple problem classes including scheduling, routing, and graph optimization.

Where Pith is reading between the lines

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

  • The separation of policy training from heuristic deployment allows one trained policy to potentially inform many different heuristic design tasks without repeated neural costs.
  • This feedback style could be tested in domains outside combinatorial optimization where learned models exist but fast rule-based implementations are preferred.
  • Multiple policies trained under different objectives might be queried together to produce richer behavioral signals for evolution.

Load-bearing premise

Querying learned optimization policies on the intermediate states visited by candidate heuristics produces reliable local behavioral feedback that meaningfully improves evolution beyond endpoint performance signals alone.

What would settle it

An experiment in which heuristics evolved with the teacher-derived action preferences show no consistent performance advantage over those evolved with performance feedback only, across the same scheduling, routing, and graph benchmarks.

Figures

Figures reproduced from arXiv: 2605.10634 by Guoqiang Li, Jianxin Xue, Ling-I Wu, Minyu Chen, Song Qin.

Figure 1
Figure 1. Figure 1: summarizes the overall search loop. At generation g, the current population Pg consists of executable heuristic programs. Each program is rolled out on design instances to obtain its task objective and on-policy states. The learned teacher is queried only on these visited states, producing action-level diagnostics such as top-1 agreement, normalized teacher value, and percentile rank. These diagnostics, to… view at source ↗
Figure 2
Figure 2. Figure 2: compares the best-so-far objective over generations on JSSP 20 × 20 and TSP50. Our method reaches better solutions earlier and maintains a lower best-so-far objective throughout the search. This suggests that teacher-aware feedback improves not only the final selected heuristic, but also the efficiency of the evolutionary search process. 0 1 2 3 4 5 Generation 1810 1820 1830 1840 1850 1860 Best-so-far obje… view at source ↗
read the original abstract

LLM-based automatic heuristic design has shown promise for generating executable heuristics for combinatorial optimization, but existing methods mainly rely on delayed endpoint performance. We propose a \emph{teacher-aware evolutionary framework} that uses independently trained learned optimization policies as behavioral teachers. Instead of deploying or imitating the teacher, our method queries it on states visited by candidate heuristic programs and uses its action preferences as local feedback for evolution. The resulting search discovers static executable heuristics guided by both task performance and teacher-derived behavioral signals. Experiments on scheduling, routing, and graph optimization benchmarks show that our method improves over performance-driven LLM heuristic evolution baselines while requiring no neural inference at deployment. These results suggest that learned optimization policies can be repurposed as behavioral feedback sources for automatic heuristic discovery.

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

1 major / 2 minor

Summary. The paper proposes a teacher-aware evolutionary framework for LLM-based automatic design of executable heuristic programs for combinatorial optimization tasks. Independently trained learned optimization policies serve as behavioral teachers: candidate heuristics are evaluated not only on endpoint performance but also by querying the teacher on visited states to obtain local action-preference feedback that guides the evolutionary search. The resulting static heuristics require no neural inference at deployment. Experiments on scheduling, routing, and graph optimization benchmarks report improvements over performance-driven LLM heuristic evolution baselines.

Significance. If the central claim holds, the work offers a way to repurpose learned optimization policies as sources of dense behavioral signals for heuristic evolution without imitation or deployment costs. This addresses the delayed-feedback limitation of prior performance-only methods and produces directly executable programs. The approach is notable for its parameter-free integration of teacher signals and its focus on falsifiable benchmark improvements.

major comments (1)
  1. [§4 and §5] §4 (Method) and §5 (Experiments): The fitness function combines endpoint performance with teacher-derived action preferences, yet no ablation is reported that removes only the teacher-action-preference term while preserving identical performance evaluation, search budget, and LLM prompt structure. Without this control, the reported gains on scheduling/routing/graph benchmarks cannot be attributed to the teacher component rather than the evolutionary loop or baseline LLM capabilities.
minor comments (2)
  1. [Abstract] Abstract: states that the method 'improves over performance-driven LLM heuristic evolution baselines' but supplies no quantitative deltas, error bars, number of runs, or statistical tests.
  2. [§4] Notation for the combined fitness function is introduced without an explicit equation number; cross-referencing the exact weighting between performance and teacher signals is difficult.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their thoughtful review and for identifying a point that merits clarification. We respond to the major comment below.

read point-by-point responses

  1. Referee: [§4 and §5] §4 (Method) and §5 (Experiments): The fitness function combines endpoint performance with teacher-derived action preferences, yet no ablation is reported that removes only the teacher-action-preference term while preserving identical performance evaluation, search budget, and LLM prompt structure. Without this control, the reported gains on scheduling/routing/graph benchmarks cannot be attributed to the teacher component rather than the evolutionary loop or baseline LLM capabilities.

    Authors: We thank the referee for this observation. The performance-driven LLM heuristic evolution baseline reported in §5 is constructed precisely as the requested control: it employs the same evolutionary loop, identical search budget, and the same LLM prompt structure for generating and refining candidate heuristics. The only difference is the fitness function, which uses solely endpoint performance and omits the teacher-action-preference term. The reported improvements are therefore measured against this exact ablation. To remove any potential ambiguity, we will revise the manuscript to state this equivalence explicitly in §4 and §5 and to add a short paragraph confirming that all other experimental factors (prompt wording, population size, number of generations, etc.) are held constant. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivation relies on independent teacher training and external benchmarks

full rationale

The paper's core method trains optimization policies independently, then queries them on states from candidate heuristics to supply behavioral feedback during LLM-driven evolution. This feedback is combined with endpoint performance but does not reduce to a self-definition, fitted parameter renamed as prediction, or self-citation chain. The central claim rests on experimental gains versus performance-only baselines on scheduling/routing/graph tasks, with no equations or steps that equate the output to the input by construction. The absence of an ablation isolating the teacher term is an evidence gap, not a circularity in the derivation itself.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides no explicit free parameters, axioms, or invented entities; assessment limited to high-level description.

pith-pipeline@v0.9.0 · 5425 in / 974 out tokens · 60762 ms · 2026-05-12T05:29:57.582891+00:00 · methodology

discussion (0)

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