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REVIEW 3 major objections 5 minor 50 references

Synergizing Reinforcement Learning and Genetic Algorithms for Neural Combinatorial Optimization

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Training neural combinatorial-optimization policies with a genetic-augmentation loop cuts optimality gaps on TSP, CVRP, PCTSP, and OP and speeds convergence, without changing inference behavior.

desk verdict EAM's stability bound is unproven: Theorem 4 swaps the reference distribution without justification, and the empirical gains are modest. read the letter →

arxiv 2506.09404 v1 pith:467AE6JE submitted 2025-06-11 cs.LG cs.NE

Shengda Gu , Kai Li , Junliang Xing , Yifan Zhang , Jian Cheng This is my paper
classification cs.LGcs.NE
keywords evolutionaryaugmentationmechanismneuralcombinatorialoptimizationreinforcementlearninggeneticalgorithmKLdivergencepolicygradienttravelingsalesmanproblemcapacitatedvehiclerouting
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

EAM (Evolutionary Augmentation Mechanism) is a plug-in training loop that addresses a known weakness of neural routing solvers: they construct tours autoregressively, so early decisions are never revised and exploration is narrow. The loop samples a batch of solutions from the policy, evolves that batch for a few generations with a genetic algorithm (elitist selection, order crossover, and problem-specific mutation), then trains the policy on the evolved solutions together with the original samples. The paper tries to establish that this closed loop improves both solution quality and training speed on TSP, CVRP, PCTSP, and OP when bolted onto the Attention Model, POMO, or SymNCO, and that the distribution shift introduced by evolution is controllable because a KL-divergence bound keeps the evolved population close to the policy distribution. If true, existing learning-to-construct solvers could gain global search power without changing their architecture, loss, or inference decoding.

What carries the argument

At the center is the closed augmentation loop: sample a batch of solutions from the learned policy, run them through $K$ generations of a genetic algorithm using elitist selection, Order Crossover, and problem-specific mutation (2-opt edge exchange for TSP, CVRP, and PCTSP; node substitution for OP), then update the policy with REINFORCE on the union of evolved and original solutions. The stability argument rides on a KL-divergence bound proven in stages: a Markov-chain lemma bounds the terminal divergence between the $K$-th generation and the initial policy marginal by a sum of one-step divergences; convexity of KL makes the elitist branch's contribution vanish under a resampling model; a fragment-preservation argument reduces each operator's contribution to the expected logarithm of the ratio between the maximum and minimum policy probabilities over filled-in segments; and Pinsker's inequality converts the KL bound into a bound on the $\ell^2$ norm of the policy-gradient bias.

What would settle it

Run the implemented GA with its elitist selection operator, record which individuals in each generation are exact copies of parents, and compute the empirical KL divergence between the evolved population and the policy's own sample distribution across training. If exact-copy individuals occur and the resulting divergence exceeds the paper's bound—or if the bound's derivation requires the non-offspring branch to resample from $p_{k-1}$ while the code copies parents—then the claimed stability guarantee is falsified. The simplest check is to swap the elitist operator from 'resample from $p_{k-1}$' to 'copy top tours' and observe whether the KL bound and training stability change.

Watch

Extended reading notes

Core claim

The paper's central claim is that evolutionary augmentation is a safe, model-agnostic way to inject global search into autoregressive reinforcement-learning solvers: a genetic algorithm initialized from policy samples produces solutions that are both higher quality and structurally more diverse, and feeding those evolved solutions back into the REINFORCE update makes the policy converge faster and to smaller optimality gaps than training on policy samples alone. The quantitative stability statement is that after $K$ generations of evolution with selection rate $\rho$, crossover rate $\alpha$, and mutation rate $\beta$, the KL divergence between the evolved solution distribution and the policy distribution is at most $\rho K$ times a weighted sum of the expected log max/min conditional-probability ratios of the genetic operators, and the bias this injects into the policy gradient is bounded by the square root of twice that KL divergence. Empirically the framework narrows gaps across all four problems—for example, POMO with $8\times$ data augmentation on CVRP50 drops from a $0.94\%$ gap to $0.54\%$ under EAM—while its training curves show faster convergence on TSP-100 and CVRP-100 for AM, POMO, and SymNCO. The authors present EAM as an extension mechanism rather than a new solver: inference behavior is unchanged, and the same base model can be trained with or without the augmentation.

Load-bearing premise

The stability guarantee assumes that, in each generation, the individuals not produced by crossover or mutation are re-sampled from the previous generation's distribution rather than copied verbatim from parents; if the implemented elitist operator copies the best tours exactly, that branch is a Dirac kernel whose KL contribution does not vanish, and the claimed $K$-generation bound does not follow.

Editorial extensions

If this is right

  • Any learning-to-construct solver can adopt EAM as a drop-in training module; its gains come from the training data, not from modified architecture or inference.
  • On the benchmark tables, the gap reductions are achieved with no additional inference time: CVRP50 gaps shrink from 0.94% to 0.54% for POMO under $8\times$ augmentation, and SymNCO reaches a 0.04% gap on TSP50.
  • Task-aware hyperparameters are part of the method: OP favors a mutation-dominant setting ($\alpha=0$, $\beta=0.5$) while TSP, CVRP, and PCTSP use balanced crossover-dominant settings.
  • Annealing the evolution frequency is necessary for stability in late training, matching the KL analysis that says perturbation strength must shrink as the policy sharpens.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Untested but implied: evolutionary rates could be adapted online by measuring the empirical KL between evolved samples and policy samples and tuning $\rho$, $\alpha$, $\beta$ to a fixed budget.
  • Untested but implied: because EAM only alters the training distribution, it should compose with post-hoc inference techniques such as active search, so the two kinds of gains add.
  • Untested but implied: the fragment-preservation bound is operator-agnostic, so any feasibility-preserving crossover or mutation with a bounded log-ratio should work, pointing toward scheduling, knapsack, and graph-coloring problems.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. This paper introduces the Evolutionary Augmentation Mechanism (EAM), a training-time wrapper for learning-to-construct neural combinatorial optimization (NCO) solvers. EAM samples solutions from the current policy, evolves them with genetic operators (elitist selection, order crossover, and problem-specific mutation), and reinjects the evolved solutions into policy-gradient training. The authors claim a KL-divergence upper bound between the evolved solution distribution and the policy distribution, which is advertised as ensuring stable and effective policy updates. Experiments on TSP, CVRP, PCTSP, and OP with AM, POMO, and SymNCO report consistent improvements in solution quality and convergence speed. Appendix A contains the proof of the bound.

Significance. If the KL bound were valid, EAM would be a notable contribution: it is model-agnostic, requires no inference-time changes, and the empirical results are broadly positive across tasks and backbones. The paper offers a falsifiable theoretical prediction and fairly detailed experimental settings, which are strengths. However, the central theoretical guarantee is not established: the proof of the main bound substitutes a different reference distribution than the lemma it invokes, and the model of elitism used in the proof does not correspond to the elitist copying operation described in the method. The empirical results are suggestive but are reported without variance or significance testing, and several improvements are small. The contribution as it stands is mainly an empirical integration study; the advertised stability guarantee is unsupported.

major comments (3)
  1. [Appendix A, Theorem 4 and Lemma 3] Lemma 3 bounds DKL(p_T||p_0) by T max_t E_{p_{t-1}}[DKL(P_t(X_{t-1},.)||p_0)]. In Theorem 4, Step 2 says it 'applies Lemma 3' but substitutes the bound from Step 1, which is on DKL(P_t||p_{t-1}), into a position that requires an upper bound on DKL(P_t||p_0). No inequality of the form E[DKL(P_t||p_0)] <= rho E[DKL(p_off||p_{t-1})] is proved or generally true; a Markov chain can take many small steps that are each close to the previous marginal yet far in KL from the initial distribution. Thus the claimed inequality DKL(p_K||p_0) <= rho K max_k E[DKL(p_off||p_{k-1})] does not follow from the stated lemmas. Since the abstract and Section 3.4 advertise this bound as ensuring stable and effective policy updates, the theoretical claim is unsupported.
  2. [Appendix A, Theorem 4 and Corollary 4.1] The proof of Theorem 4 models the elitist branch as p(\tau_k|\tau_{k-1}) = (1-rho) p_{k-1}(\tau_k), i.e., as resampling from the previous generation's marginal. The algorithm in Section 3.3 and Algorithm 1, however, uses elitist selection that copies top-performing individuals. If an elite individual is a verbatim copy of its parent, the transition kernel is a Dirac measure delta_{\tau_{k-1}}, not the marginal p_{k-1}; the KL contribution of that branch is DKL(delta_{\tau_{k-1}}||p_{k-1}) = -log p_{k-1}(\tau_{k-1}), which is generally nonzero and uncontrolled. Corollary 4.1's statement that 'if the elite component copies parents verbatim, q_elite = p_{k-1}' is therefore incorrect. Consequently, the derived bound does not apply to the implemented algorithm.
  3. [Appendix A, Theorem 6 and Theorem 7] Theorem 6 assumes that q(r|f) is a support-preserving rearrangement of p(r|f) and, via the Appendix remark, that all conditional probabilities are strictly positive. The implemented OX and 2-OPT operators are deterministic given the selected parents and the retained fragment, and a trained policy can assign zero or negligible probability to many fragments, so these hypotheses are not guaranteed. Theorem 7's multiplicative factor rho K [alpha E[...] + beta E[...]] is obtained by combining Corollary 4.1 with Theorem 6, but the gamma component of the offspring mixture in Corollary 4.1 is silently dropped, and the relation between the mixture weights in Corollary 4.1 and the operation rates alpha, beta used in the algorithm is not established. The derivation is therefore not rigorous even setting aside the Lemma 3 issue.
minor comments (5)
  1. [Section 3.3 and Algorithm 1] Section 3.3 says 'The combined set P_theta \cup P^{(K)} is then used to update the policy via RL', but Algorithm 1 calls APPLYREINFORCE(P_K, p_theta) and then APPLYREINFORCE(P_0, p_theta) as two separate updates; the exact objective over the union should be clarified.
  2. [Numerical observation] The theorem is numbered Theorem 1 in the main text but Theorem 8 in Appendix A, and the appendix renumbers other results (Theorem 4, Theorem 6, Theorem 7) inconsistently with the main text.
  3. [Table 1 and Figure 2] The empirical results are reported without standard deviations, multiple seeds, or significance tests; for improvements as small as 0.01-0.04 percentage points in optimality gap, this makes it difficult to assess whether the gains are reproducible.
  4. [Table 1 caption] The caption contains the typo 'LHK3' for LKH-3, and the subsection numbering jumps from Section 4.2 to Section 4.3 in the experimental section.
  5. [Appendix A remark] The remark introduces a dummy symbol to give all problems a common support, but the KL bound is stated on this extended support that includes invalid sequences; the paper does not discuss how the bound on the extended space relates to the bound on the space of feasible solutions.

Circularity Check

1 steps flagged · score 6.0 of 10

The KL-stability guarantee is obtained by defining the elitist branch of the GA transition kernel as the previous population marginal, making its KL contribution vanish by construction.

  1. self definitional [Appendix A, Theorem 4 and Corollary 4.1 (used to prove Eq. (2) in Theorem 1)]
    "Under the elitism update rule p(τ k |τ k−1) =ρ p off (τ k |τ k−1) + (1−ρ)pk−1,0≤ρ≤1 ... DKL(p(τ k |τ k−1)∥p k−1) ≤ρ D KL(poff (τ k |τ k−1)∥p k−1). ... If the elite component copies parents verbatim, q elite =p k−1"

    The non-offspring branch of the transition kernel is defined to be pk−1, the previous generation's marginal, so its KL contribution against pk−1 is zero by construction. Step 1 of the proof then follows entirely from this definition, and Theorem 4's bound contains no term for the (1−ρ) elite branch. In the actual elitist strategy described in Section 3.3 ('crossover and mutation are applied only to a selected subset'), elites are copied, giving a Dirac kernel whose KL against pk−1 is −log pk−1(τk−1), not zero. Corollary 4.1 compounds this by writing 'If the elite component copies parents verbatim, q elite =p k−1', equating a point-mass copy with the marginal distribution.

full rationale

The empirical part of the paper is self-contained: EAM is evaluated on external benchmarks (TSP, CVRP, PCTSP, OP) against Concorde, LKH-3, HGS, AM, POMO, and SymNCO, and the reported gains are not derived from fitted parameters or from the theoretical bound. There is no load-bearing self-citation: none of the cited prior works overlaps with the authors of this paper. The one clear definitional reduction is in the proof of the KL guarantee: Theorem 4 defines the elitist branch of the GA kernel as the previous marginal pk−1, which forces the elite KL term to vanish and yields the bound ρ·[...]; Corollary 4.1 then conflates 'copies parents verbatim' with q_elite = pk−1. Because the abstract and Section 3.4 advertise this bound as 'ensuring stable and effective policy updates', the theoretical core of the central claim is affected by construction. Separately, the proof of Theorem 4 substitutes a p_{k−1}-referenced KL into Lemma 3, which is stated against p0; that is a proof gap rather than circularity and is not scored here. Since the empirical improvements remain independent external evidence, partial circularity (6) rather than total circularity (8–10) is appropriate.

Assumptions & free parameters 7 free parameters · 4 assumptions · 0 invented entities

EAM's theoretical guarantee depends on the special elitism model and bounded-gradient assumption, while its empirical results depend on task-specific hand-set GA hyperparameters. The ledger shows the central stability guarantee is constructed to produce a small KL bound, rather than measured or derived against an external benchmark.

free parameters (7)
  • K (evolution generations) = 5 (TSP, PCTSP), 3 (CVRP), 2 (OP)
    Chosen per task to balance exploration and computational cost; affects the ρ^K factor in the claimed bound and the amount of evolution in each training step.
  • ρ (selection rate) = 0.2 (TSP, CVRP, PCTSP), 0.4 (OP)
    Hand-set per task for stability; enters the KL bound linearly as ρ^K.
  • α (crossover rate) = 0.6 (TSP, CVRP, PCTSP), 0.0 (OP)
    Selected via task structure and ablation; OP uses mutation-only to avoid fragment reordering.
  • β (mutation rate) = 0.05 (TSP, PCTSP), 0.10 (CVRP), 0.5 (OP)
    Hand-set; OP uses higher mutation to escape local optima.
  • EA Epochs = 500/700 (TSP), 200/300 (CVRP), 20 (PCTSP), 50 (OP)
    Controls how many training epochs use GA; chosen by hand.
  • EA Probs = 0.01
    Probability of applying GA at each training step; hand-set.
  • Annealing schedule for GA rates = not numerically specified
    Rates decay over training; the schedule shape and rate are not given, making exact reproduction impossible.
assumptions (4)
  • domain assumption All generation distributions share common support X=V^L and every one-step genetic kernel is strictly positive.
    Invoked in Appendix A Remark to allow Lemma 3 and Theorem 6 density manipulations; for fixed-length sequences with dummy symbols this is plausible, but not proven for the actual operators.
  • ad hoc to paper The elitist update rule is p(τk|τk−1)=ρ poff(τk|τk−1)+(1−ρ)p_{k−1}(τk), with the elite branch equal to the previous marginal.
    This is the load-bearing modeling choice that makes the elite KL term vanish in Corollary 4.1; it does not describe copying the parent tour, which would be the standard elitist mechanism.
  • domain assumption Policy gradients are L2-clipped to norm at most 1.
    Theorem 8 requires ||∇J(τ)||_2 ≤ 1 almost surely; the main text and Algorithm 1 do not state that clipping is applied during training, so the bound may not apply to the actual method.
  • standard math Standard information-theoretic facts (Pinsker, data-processing, KL convexity, log-sum).
    Used in Appendix A; these are unproved background results.

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Cite this review

Pith. "Pith review of Synergizing Reinforcement Learning and Genetic Algorithms for Neural Combinatorial Optimization." pith.science (2026). https://pith.science/paper/467AE6JE

@misc{pith2026250609404,
  author       = {Pith},
  title        = {Pith review of: Synergizing Reinforcement Learning and Genetic Algorithms for Neural Combinatorial Optimization},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/467AE6JE}},
  note         = {Machine review of arXiv:2506.09404}
}
read the original abstract

Combinatorial optimization problems are notoriously challenging due to their discrete structure and exponentially large solution space. Recent advances in deep reinforcement learning (DRL) have enabled the learning heuristics directly from data. However, DRL methods often suffer from limited exploration and susceptibility to local optima. On the other hand, evolutionary algorithms such as Genetic Algorithms (GAs) exhibit strong global exploration capabilities but are typically sample inefficient and computationally intensive. In this work, we propose the Evolutionary Augmentation Mechanism (EAM), a general and plug-and-play framework that synergizes the learning efficiency of DRL with the global search power of GAs. EAM operates by generating solutions from a learned policy and refining them through domain-specific genetic operations such as crossover and mutation. These evolved solutions are then selectively reinjected into the policy training loop, thereby enhancing exploration and accelerating convergence. We further provide a theoretical analysis that establishes an upper bound on the KL divergence between the evolved solution distribution and the policy distribution, ensuring stable and effective policy updates. EAM is model-agnostic and can be seamlessly integrated with state-of-the-art DRL solvers such as the Attention Model, POMO, and SymNCO. Extensive results on benchmark problems (e.g., TSP, CVRP, PCTSP, and OP) demonstrate that EAM significantly improves both solution quality and training efficiency over competitive baselines.

Figures

Figures reproduced from arXiv: 2506.09404 by the authors.

Figure 1
Figure 1. An overview of the proposed Evolutionary Augmentation Mechanism (EAM). Policy￾sampled solutions are used to initialize the population of the Genetic Algorithm. The evolved solutions are then merged with the original samples and jointly used to train the policy network, forming a closed-loop learning and evolutionary framework. methods have been extensively studied due to strong empirical performance. However, L2C me… view at source ↗
Figure 2
Figure 2. Training curves of AM, POMO, and Sym-NCO with and without EAM on TSP-100 and CVRP-100. EAM consistently accelerates convergence across different backbones and problem settings, highlighting its ability to improve training efficiency in addition to final solution quality. 4.3.1 PCTSP and OP As shown in [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 5
Figure 5. Training curves of ab￾solute loss on TSP 100. Evolutionary Hyperparameter Configuration. We examine the impact of different crossover and mutation rate configurations in EAM on OP ( [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figures from the paper (1 more)
Figure 6
Figure 6. Figure 6: Solutions generated by POMO and EAM-POMO on representative TSP-100 in￾stances. Both models produce globally similar tours, but EAM-POMO exhibits finer local refine￾ments—especially in dense regions—demonstrating the structural optimization effect of EAM. However, due t…

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Reference graph

Works this paper leans on

50 extracted references · 35 canonical work pages

  1. [1]

    Information theory: a tutorial introduction. 2015

    work page 2015

  2. [2]

    Learning what to defer for maximum in- dependent sets

    Sungsoo Ahn, Younggyo Seo, and Jinwoo Shin. Learning what to defer for maximum in- dependent sets. InInternational conference on machine learning, pages 134–144. PMLR, 2020

    2020

  3. [3]

    Esra’a Alkafaween, Ahmad Hassanat, Ehab Essa, and Samir Elmougy. An efficiency boost for genetic algorithms: Initializing the ga with the iterative approximate method for optimizing the traveling salesman problem—experimental insights.Applied Sciences, 14(8):3151, 2024

    work page 2024

  4. [4]

    Princeton university press, 2006

    David L Applegate.The traveling salesman problem: a computational study, volume 17. Princeton university press, 2006

    work page 2006

  5. [5]

    The prize collecting traveling salesman problem.Networks, 19(6):621–636, 1989

    Egon Balas. The prize collecting traveling salesman problem.Networks, 19(6):621–636, 1989

    work page 1989

  6. [6]

    Neural combina- torial optimization with reinforcement learning.arXiv preprint arXiv:1611.09940, 2016

    Irwan Bello, Hieu Pham, Quoc V Le, Mohammad Norouzi, and Samy Bengio. Neural combina- torial optimization with reinforcement learning.arXiv preprint arXiv:1611.09940, 2016

    arXiv 2016

  7. [7]

    Routefinder: Towards foundation models for vehicle routing problems.arXiv preprint arXiv:2406.15007, 2024

    Federico Berto, Chuanbo Hua, Nayeli Gast Zepeda, André Hottung, Niels Wouda, Leon Lan, Junyoung Park, Kevin Tierney, and Jinkyoo Park. Routefinder: Towards foundation models for vehicle routing problems.arXiv preprint arXiv:2406.15007, 2024

    arXiv 2024

  8. [8]

    Reinforcement Learning Driven Heuristic Optimization

    Qingpeng Cai, Will Hang, Azalia Mirhoseini, George Tucker, Jingtao Wang, and Wei Wei. Reinforcement learning driven heuristic optimization.arXiv preprint arXiv:1906.06639, 2019

    work page Pith review arXiv 1906

Show all 50 references
  1. [9]

    Learning to perform local rewriting for combinatorial optimization.Advances in neural information processing systems, 32, 2019

    Xinyun Chen and Yuandong Tian. Learning to perform local rewriting for combinatorial optimization.Advances in neural information processing systems, 32, 2019

    2019

  2. [10]

    A method for solving traveling-salesman problems.Operations research, 6 (6):791–812, 1958

    Georges A Croes. A method for solving traveling-salesman problems.Operations research, 6 (6):791–812, 1958

    1958

  3. [11]

    Learning 2-opt heuristics for the traveling salesman problem via deep reinforcement learning

    Paulo R d O Costa, Jason Rhuggenaath, Yingqian Zhang, and Alp Akcay. Learning 2-opt heuristics for the traveling salesman problem via deep reinforcement learning. InAsian conference on machine learning, pages 465–480. PMLR, 2020

    2020

  4. [12]

    Handbook of genetic algorithms

    L Davis. Handbook of genetic algorithms. 1991

    1991

  5. [13]

    University of Michigan, 1975

    Kenneth Alan De Jong.An analysis of the behavior of a class of genetic adaptive systems. University of Michigan, 1975

    1975

  6. [14]

    Design paradigms of intelligent control systems on a chip.arXiv preprint arXiv:1811.08426, 2018

    Kyriakos M Deliparaschos and Spyros G Tzafestas. Design paradigms of intelligent control systems on a chip.arXiv preprint arXiv:1811.08426, 2018

    2018 arXiv

  7. [15]

    Designing an optimal portfolio for iran’s stock market with genetic algorithm using neural network prediction of risk and return stocks.arXiv preprint arXiv:1903.06632, 2019

    Masoud Fekri and Babak Barazandeh. Designing an optimal portfolio for iran’s stock market with genetic algorithm using neural network prediction of risk and return stocks.arXiv preprint arXiv:1903.06632, 2019

    1903 arXiv

  8. [16]

    Alleleslociand the traveling salesman problem

    David E Goldberg and Robert Lingle Jr. Alleleslociand the traveling salesman problem. In Proceedings of the 1st International Conference on Genetic Algorithms, pages 154–159, 1985

    1985

  9. [17]

    The orienteering problem.Naval Research Logistics (NRL), 34(3):307–318, 1987

    Bruce L Golden, Larry Levy, and Rakesh V ohra. The orienteering problem.Naval Research Logistics (NRL), 34(3):307–318, 1987. 10

    1987

  10. [18]

    Accelerating vehicle routing via ai-initialized genetic algorithms

    Ido Greenberg, Piotr Sielski, Hugo Linsenmaier, Rajesh Gandham, Shie Mannor, Alex Fender, Gal Chechik, and Eli Meirom. Accelerating vehicle routing via ai-initialized genetic algorithms. arXiv preprint arXiv:2504.06126, 2025

    2025

  11. [19]

    Winner takes it all: Training performant rl populations for combinatorial optimization.Advances in Neural Information Processing Systems, 36:48485–48509, 2023

    Nathan Grinsztajn, Daniel Furelos-Blanco, Shikha Surana, Clément Bonnet, and Tom Barrett. Winner takes it all: Training performant rl populations for combinatorial optimization.Advances in Neural Information Processing Systems, 36:48485–48509, 2023

    2023

  12. [20]

    An extension of the lin-kernighan-helsgaun tsp solver for constrained traveling salesman and vehicle routing problems.Roskilde: Roskilde University, 12:966–980, 2017

    Keld Helsgaun. An extension of the lin-kernighan-helsgaun tsp solver for constrained traveling salesman and vehicle routing problems.Roskilde: Roskilde University, 12:966–980, 2017

    2017

  13. [21]

    Efficient active search for combinatorial optimization problems.arXiv preprint arXiv:2106.05126, 2021

    André Hottung, Yeong-Dae Kwon, and Kevin Tierney. Efficient active search for combinatorial optimization problems.arXiv preprint arXiv:2106.05126, 2021

    2021 arXiv

  14. [22]

    Polynet: Learning diverse solution strategies for neural combinatorial optimization.arXiv preprint arXiv:2402.14048, 2024

    André Hottung, Mridul Mahajan, and Kevin Tierney. Polynet: Learning diverse solution strategies for neural combinatorial optimization.arXiv preprint arXiv:2402.14048, 2024

    2024

  15. [23]

    Constrained evolutionary optimization based on reinforcement learning using the objective function and constraints.Knowledge-Based Systems, 237:107731, 2022

    Zhenzhen Hu and Wenyin Gong. Constrained evolutionary optimization based on reinforcement learning using the objective function and constraints.Knowledge-Based Systems, 237:107731, 2022

    2022

  16. [24]

    Evolution-guided policy gradient in reinforcement learning.Advances in Neural Information Processing Systems, 31, 2018

    Shauharda Khadka and Kagan Tumer. Evolution-guided policy gradient in reinforcement learning.Advances in Neural Information Processing Systems, 31, 2018

    2018

  17. [25]

    Learning collaborative policies to solve np-hard routing problems.Advances in Neural Information Processing Systems, 34:10418–10430, 2021

    Minsu Kim, Jinkyoo Park, et al. Learning collaborative policies to solve np-hard routing problems.Advances in Neural Information Processing Systems, 34:10418–10430, 2021

    2021

  18. [26]

    Sym-nco: Leveraging symmetricity for neural combinatorial optimization.Advances in Neural Information Processing Systems, 35:1936– 1949, 2022

    Minsu Kim, Junyoung Park, and Jinkyoo Park. Sym-nco: Leveraging symmetricity for neural combinatorial optimization.Advances in Neural Information Processing Systems, 35:1936– 1949, 2022

    1936

  19. [27]

    An efficient evolutionary algorithm for the orienteering problem.Computers & Operations Research, 90:42–59, 2018

    Gorka Kobeaga, María Merino, and Jose A Lozano. An efficient evolutionary algorithm for the orienteering problem.Computers & Operations Research, 90:42–59, 2018

    2018

  20. [28]

    Attention, learn to solve routing problems! arXiv preprint arXiv:1803.08475, 2018

    Wouter Kool, Herke Van Hoof, and Max Welling. Attention, learn to solve routing problems! arXiv preprint arXiv:1803.08475, 2018

    2018 arXiv

  21. [29]

    Pomo: Policy optimization with multiple optima for reinforcement learning.Advances in Neural Information Processing Systems, 33:21188–21198, 2020

    Yeong-Dae Kwon, Jinho Choo, Byoungjip Kim, Iljoo Yoon, Youngjune Gwon, and Seungjai Min. Pomo: Policy optimization with multiple optima for reinforcement learning.Advances in Neural Information Processing Systems, 33:21188–21198, 2020

    2020

  22. [30]

    Neurocrossover: An intelligent genetic locus selection scheme for genetic algorithm using reinforcement learning.Applied Soft Computing, 146:110680, 2023

    Haoqiang Liu, Zefang Zong, Yong Li, and Depeng Jin. Neurocrossover: An intelligent genetic locus selection scheme for genetic algorithm using reinforcement learning.Applied Soft Computing, 146:110680, 2023

    2023

  23. [31]

    Iterated local search: Framework and applications

    Helena Ramalhinho Lourenço, Olivier C Martin, and Thomas Stützle. Iterated local search: Framework and applications. InHandbook of metaheuristics, pages 129–168. Springer, 2018

    2018

  24. [32]

    Thu Quang Luu. Application of artificial intelligence-genetic algorithms to select stock portfo- lios in the asian markets.International Journal of Advanced Computer Science and Applications, 13(12), 2022

    2022

  25. [33]

    Learning to iteratively solve routing problems with dual-aspect collaborative transformer

    Yining Ma, Jingwen Li, Zhiguang Cao, Wen Song, Le Zhang, Zhenghua Chen, and Jing Tang. Learning to iteratively solve routing problems with dual-aspect collaborative transformer. Advances in Neural Information Processing Systems, 34:11096–11107, 2021

    2021

  26. [34]

    A hybrid genetic algorithm for the min–max multiple traveling salesman problem.Computers & Operations Research, 162:106455, 2024

    Sasan Mahmoudinazlou and Changhyun Kwon. A hybrid genetic algorithm for the min–max multiple traveling salesman problem.Computers & Operations Research, 162:106455, 2024

    2024

  27. [35]

    H-tsp: Hierarchically solving the large-scale traveling salesman problem

    Xuanhao Pan, Yan Jin, Yuandong Ding, Mingxiao Feng, Li Zhao, Lei Song, and Jiang Bian. H-tsp: Hierarchically solving the large-scale traveling salesman problem. InProceedings of the AAAI Conference on Artificial Intelligence, volume 37, pages 9345–9353, 2023. 11

    2023

  28. [36]

    Application of genetic algorithm in logistics management and distribution

    Wang Ping. Application of genetic algorithm in logistics management and distribution. In International Conference on Multi-modal Information Analytics, pages 1041–1046. Springer, 2022

    2022

  29. [37]

    Rule-based reinforcement learning methodology to inform evolutionary algorithms for constrained optimization of engineering applications

    Majdi I Radaideh and Koroush Shirvan. Rule-based reinforcement learning methodology to inform evolutionary algorithms for constrained optimization of engineering applications. Knowledge-Based Systems, 217:106836, 2021

    2021

  30. [38]

    Time series stock price forecasting based on genetic algorithm (ga)-long short-term memory network (lstm) optimization.arXiv preprint arXiv:2405.03151, 2024

    Xinye Sha. Time series stock price forecasting based on genetic algorithm (ga)-long short-term memory network (lstm) optimization.arXiv preprint arXiv:2405.03151, 2024

    2024 arXiv

  31. [39]

    Combining evolution and deep reinforcement learning for policy search: A survey.ACM Transactions on Evolutionary Learning, 3(3):1–20, 2023

    Olivier Sigaud. Combining evolution and deep reinforcement learning for policy search: A survey.ACM Transactions on Evolutionary Learning, 3(3):1–20, 2023

    2023

  32. [40]

    Equity-transformer: Solving np-hard min-max routing problems as sequential generation with equity context

    Jiwoo Son, Minsu Kim, Sanghyeok Choi, Hyeonah Kim, and Jinkyoo Park. Equity-transformer: Solving np-hard min-max routing problems as sequential generation with equity context. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 38, pages 20265–20273, 2024

    2024

  33. [41]

    Learning encodings for constructive neural com- binatorial optimization needs to regret

    Rui Sun, Zhi Zheng, and Zhenkun Wang. Learning encodings for constructive neural com- binatorial optimization needs to regret. InProceedings of the AAAI Conference on Artificial Intelligence, volume 38, pages 20803–20811, 2024

    2024

  34. [42]

    Csrx: A novel crossover operator for a genetic algorithm applied to the traveling salesperson problem

    Martin Uray, Stefan Wintersteller, and Stefan Huber. Csrx: A novel crossover operator for a genetic algorithm applied to the traveling salesperson problem. InInternational Data Science Conference, pages 21–27. Springer, 2023

    2023

  35. [43]

    Hybrid genetic search for the cvrp: Open-source implementation and swap* neighborhood.Computers & Operations Research, 140:105643, 2022

    Thibaut Vidal. Hybrid genetic search for the cvrp: Open-source implementation and swap* neighborhood.Computers & Operations Research, 140:105643, 2022

    2022

  36. [44]

    Pointer networks.Advances in neural information processing systems, 28, 2015

    Oriol Vinyals, Meire Fortunato, and Navdeep Jaitly. Pointer networks.Advances in neural information processing systems, 28, 2015

    2015

  37. [45]

    Leader reward for pomo-based neural combinatorial optimization.arXiv preprint arXiv:2405.13947, 2024

    Chaoyang Wang, Pengzhi Cheng, Jingze Li, and Weiwei Sun. Leader reward for pomo-based neural combinatorial optimization.arXiv preprint arXiv:2405.13947, 2024

    2024 arXiv

  38. [46]

    Simple statistical gradient-following algorithms for connectionist reinforce- ment learning.Machine learning, 8:229–256, 1992

    Ronald J Williams. Simple statistical gradient-following algorithms for connectionist reinforce- ment learning.Machine learning, 8:229–256, 1992

    1992

  39. [47]

    Neural combinatorial optimization algorithms for solving vehicle routing problems: A comprehensive survey with perspectives.arXiv preprint arXiv:2406.00415, 2024

    Xuan Wu, Di Wang, Lijie Wen, Yubin Xiao, Chunguo Wu, Yuesong Wu, Chaoyu Yu, Douglas L Maskell, and You Zhou. Neural combinatorial optimization algorithms for solving vehicle routing problems: A comprehensive survey with perspectives.arXiv preprint arXiv:2406.00415, 2024

    2024 arXiv

  40. [48]

    Learning improvement heuristics for solving routing problems.IEEE transactions on neural networks and learning systems, 33(9):5057–5069, 2021

    Yaoxin Wu, Wen Song, Zhiguang Cao, Jie Zhang, and Andrew Lim. Learning improvement heuristics for solving routing problems.IEEE transactions on neural networks and learning systems, 33(9):5057–5069, 2021

    2021

  41. [49]

    Optimization of worker scheduling at logistics depots using genetic algorithms and simulated annealing.arXiv preprint arXiv:2405.11729, 2024

    Jinxin Xu, Haixin Wu, Yu Cheng, Liyang Wang, Xin Yang, Xintong Fu, and Yuelong Su. Optimization of worker scheduling at logistics depots using genetic algorithms and simulated annealing.arXiv preprint arXiv:2405.11729, 2024

    2024 arXiv

  42. [50]

    dummy symbol

    Zhi Zheng, Changliang Zhou, Tong Xialiang, Mingxuan Yuan, and Zhenkun Wang. Udc: A unified neural divide-and-conquer framework for large-scale combinatorial optimization problems.arXiv preprint arXiv:2407.00312, 2024. 12 A Proof of Theorem 1 Remark.We use a unified sequence en...

    2024 arXiv

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.