Combinatorial Optimization

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33 papers in the last four weeks, up 83% on the four weeks before. 0.3% of all new papers.

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Latest papers 277

Jul 22, 2026quant-ph

DQAOA-GPT: AI-Accelerated Distributed Quantum Optimization for Combinatorial Problems

While combinatorial optimization problems are central to many scientific and engineering applications, their solution remains challenging due to exponentially large search spaces. Variational quantum algorithms offer a promising route for tackling such problems, yet their practical performance is limited by repeated quantum circuit evaluations and classical parameter updates. In this work, we introduce DQAOA-GPT, a hybrid framework that integrates the distributed quantum approximate optimization algorithm (DQAOA), which decomposes a large optimization problem into smaller sub-problems, with GPT-based quantum circuit generation for solving those sub-problems. Rather than relying on iterative variational optimization, the proposed approach uses a trained generative model to directly generate high-quality quantum circuits for the decomposed sub-problems. As a benchmark, we evaluate DQAOA-GPT against conventional DQAOA on dense HUBO optimization problems with up to 100 decision variables. The results demonstrate that DQAOA-GPT significantly reduces computational cost while maintaining competitive solution quality, with larger acceleration observed for larger sub-problem sizes. Although this work focuses on benchmark-scale validation, the framework provides a promising foundation for larger-scale combinatorial optimization in hybrid HPC-QC environments through increased GPU resources and parallel computing capability.

Seongmin Kim, Abhinav Rijal, Yuri Alexeev +5

National Center for Computational Sciences, Oak Ridge National Laboratory, Oak Ridge, TN, USA · Department of Physics & Astronomy, University of Tennessee, Knoxville, TN, USA · NVIDIA Corporation, Santa Clara, CA, USA +3

Distributed Optimization Combinatorial Optimization Quantum Approximate Optimization Algorithm

Jul 22, 2026cs.AI

Coordinating from Memory: Graph-Structured Experience Reuse for Multi-Agent Adaptation in Dynamic Manufacturing

Dynamic manufacturing environments require multi-agent systems to coordinate effectively under frequent operational disturbances such as machine failures, urgent job arrivals, and processing time variations. Existing multi-agent reinforcement learning approaches treat each disturbance episode independently, discarding valuable coordination experience that could accelerate future adaptation. In this paper, we propose a Graph-Structured Experiential Memory (GSEM) framework for multi-agent coordination in dynamic manufacturing. The framework encodes historical coordination episodes as heterogeneous relational graphs that capture task dependencies, machine states, and inter-agent collaboration patterns. When a new disturbance occurs, a graph neural network-based retrieval mechanism identifies structurally similar past episodes, enabling experience-guided policy adaptation rather than learning from scratch. Experiments on dynamic flexible job-shop scheduling benchmarks with three disturbance types show that GSEM reduces makespan by 4.1%-10.0% and adaptation time by 33%-38% compared to the strongest memory-augmented baseline, with the advantage increasing under higher disturbance frequency. Ablation studies and cross-disturbance transfer experiments further validate the necessity of graph-structured encoding and similarity-based retrieval and demonstrate the cross-disturbance generalizability of learned coordination patterns.

Chengxiao Dai, Zhanhui Lin, Zhaokun Yan +3

School of Computer Science, University of Sydney, Sydney, Australia. · School of Computation, Information and Technology, Technical University of Munich, Munich, Germany. · School of Life and Environmental Sciences, University of Sydney, Sydney, Australia. +2

Multi-Agent Coordination Combinatorial Optimization Memory-Augmented Agents Multi-Agent Reinforcement Learning

Jul 22, 2026math.OC

Optimal Placement of Docking Stations and Resident AUVs for Subsea Pipeline Inspection

A two-stage mixed-integer linear programming framework is introduced for subsea pipeline incident response planning, jointly optimizing Subsea Docking Plate (SDP) placement and resident autonomous underwater vehicle allocation to minimize both maximum and average response times under spatial uncertainty. Phase 1 minimizes the maximum response time across all potential leak locations. Phase 2 reduces the average response time subject to the maximum bound. A case study based on the Johan Sverdrup oil and gas field in Norway, with 9 SDP options and 33 pipelines, shows that just a few well-placed SDPs are enough to achieve top performance. A cost versus time Pareto analysis reveals the trade-off between deployment expenditure and response efficiency, providing actionable guidance for designing resilient and cost-effective subsea inspection networks.

Gabrielė Kasparavičiūtė, Pasquale Grippa, Kjetil Skaugset +2

Department of Marine Technology, Norwegian University of Science and Technology (NTNU), Trondheim, Norway · Lakeside Labs GmbH, Klagenfurt, Austria · Equinor ASA, Norway

Industrial Inspection Combinatorial Optimization Underwater Robotics

Jul 22, 2026cs.LG

AlphaRoute: Large Language Models as Semantic Optimizers for Multi-Objective Routing

Very Large Scale Integration (VLSI) global routing is an NP-hard combinatorial optimization problem requiring signal net assignment across capacity-constrained 3D grids while minimizing congestion, wirelength, and via transitions. Because traditional heuristics rely on static penalty schedules that fail on complex congestion topologies, we present AlphaRoute: a multi-objective adaptive search framework reformulating rip-up and reroute (R&R) into a dynamic optimization system. We introduce SHAP-based overflow decomposition to isolate per-net congestion, driving targeted subgraph extraction via 3D Dijkstra maze routing and an adaptive PathFinder policy. Crucially, AlphaRoute employs Large Language Models (LLMs) as semantic policy optimizers. Bounded by a deterministic knowledge graph, the LLMs interpret congestion metrics to dynamically adjust penalty parameters. Evaluated on ISPD 2025 benchmarks, AlphaRoute reduces overflow by 98.6% on MEMPOOL. On the constrained ARIANE design, we achieve an overflow of 146,109 (a 29.8x reduction in overflow over the state of the art), yielding a penalized score of S_orig = 0.0538 versus the State-of-the-art (SOTA) 1.780. These results demonstrate that superior algorithmic search geometry can overcome the latency of interpreted Python implementations.

Kabir Murjani, Mishri Bhavsar, Manish I. Patel +1

Department of Electrical Engineering, Institute of Technology, Nirma University, Ahmedabad, India · Department of Electronics and Communication Engineering, Institute of Technology, Nirma University, Ahmedabad, India · Center for Semiconductor Microelectronics, Arizona State University, Tempe, Arizona, USA

Automated Heuristic Design Large Language Model-Guided Optimization Electronic Design Automation Combinatorial Optimization Multi-Objective Optimization

Jul 21, 2026cs.AI

On the Effectiveness of Pretraining for Graph Combinatorial Optimization

This paper introduces a self-supervised pretraining framework for graph combinatorial optimization specifically designed to address the nature of routing problems like the Traveling Salesman Problem. By utilizing graph contrastive learning with geometric augmentations (specifically, rotations and axial reflections) the model is forced to learn invariant structural representations and global relative distance distributions. Results demonstrate that this pretraining strategy outperforms non-pretrained models across various problem scales. Notably, the hybrid strategy (combining rotation and reflection) achieved a 6.57% improvement in tour length for TSP1000, proving that geometric pretraining is an important inductive bias for effectively scaling neural solvers to high-dimensional instances.

David Aguado, Daniel Fuertes, Carlos R. del-Blanco +1

Grupo de Tratamiento de Imágenes, Information Processing and Telecomunications Center, ETSI Telecomunicación, Universidad Politécnica de Madrid, 28040, Madrid, Spain

Traveling Salesperson Problem Self-Supervised Pre-Training Combinatorial Optimization Graph Contrastive Learning Neural Combinatorial Optimization

Jul 21, 2026cs.AI

Enhancing Transformer-based Routing by Encoding Distance via Relative Positional Encoding

This paper explores Relative Positional Encoding (RPE) as an additive bias in Transformer architectures to solve the Team Orienteering Problem. By embedding in the attention mechanism pairwise spatial relationships among nodes of the graph that represents the routing problem, the transformer encoder can compute a richer spatial-aware graph embedding that allows the decoder to estimate better routes. Experimental results involving instances up to 100 nodes demonstrate consistent improvements in collected rewards and optimality gaps over vanilla Transformer architectures used by other state-of-the-art works. These findings highlight that explicit relational modeling significantly enhances scalability and generalization for complex combinatorial optimization.

Leyre Encío, Daniel Fuertes, Carlos R. del-Blanco +1

Grupo de Tratamiento de Imágenes, Information Processing and Telecomunications Center, ETSI Telecomunicación, Universidad Politécnica de Madrid, 28040, Madrid, Spain

Combinatorial Optimization Positional Encoding Graph Transformer Neural Combinatorial Optimization

Jul 21, 2026cs.LG

Graph Neural Network-based Algorithm Selection for the Traveling Salesman Problem: A Systematic Study of Cost and Rank Losses under Distinct Budget Regimes

Automated Algorithm Selection (AS) aims to improve problem-solving performance by selecting, for each problem instance, the most suitable algorithm from a predefined portfolio. This is particularly relevant to the Traveling Salesman Problem (TSP), where solver performance is strongly instance-dependent. We introduce GNNAS-TSP, a Graph Neural Network (GNN)-based AS framework that learns TSP instance representations directly from raw graph data, avoiding manual feature engineering. GNNAS-TSP formulates AS as a joint cost-prediction and ranking task. We evaluate cost-based (mean squared error (MSE), mean absolute error (MAE), and Huber), rank-based (RankNet, ListNet, and LambdaRank), and hybrid learning objectives for a portfolio comprising Chained Lin-Kernighan, Edge Assembly Crossover, Lin-Kernighan-Helsgaun, Multiagent Optimization System, and Concorde. Experiments use fixed computational budgets of 10 and 60 seconds. On the held-out test set, the selected configurations improve on the Single Best Solver (SBS) in normalized solution cost at both budgets. For the 10s budget, AS achieves substantial and statistically significant cost improvement over SBS. Overall, the results suggest that GNNAS-TSP is a useful meta-solving strategy when exploitable variation exists across solver performance.

Zhaoxuan Li, Jiale Yang, Yifei Lu +1

Duke Kunshan University, 8 Duke Avenue, Kunshan, 215316, China

Traveling Salesperson Problem Algorithm Selection Learning to Rank Combinatorial Optimization

Jul 18, 2026cs.LG

On the Potential of Graph Neural Networks as Metamodels for Supply Chain Optimization: Dataset, Architectures, and Directions

Graph Neural Networks (GNNs) have emerged as a powerful, differentiable class of learning models for graph-structured systems. Their ability to generalize across topologies opens the prospect of a surrogate for combined structural and parametric optimization, which classical metamodels cannot offer. Supply chains are a natural target, yet the use of GNN surrogates for supply chain problems is largely unexplored. This paper lays the foundation, presents initial steps, and discusses key research directions. As a foundation, we formulate the problem and create a large public training dataset of programmatically generated supply chain graphs with input parameters and steady-state performance metrics obtained using our SupplyNetPy simulation library. As initial steps, we explore GNN architectures that work well as surrogates for node- and network-level predictions, and analyze their accuracy-compute trade-off against simulation. Most importantly, we outline the exciting directions this opens, namely gradient-based optimization over topology, fast design-space exploration, and sensitivity analysis.

Tushar Lone, Neha Karanjkar

School of Mathematics and Computer Science, Indian Institute of Technology Goa, Ponda, Goa, INDIA

Neural Surrogate Modeling Topology Optimization Combinatorial Optimization Supply Chain Management

Jul 18, 2026cs.MA

When Is Heterogeneous Distance-Decay Facility Location Tractable? A Structural Classification, Exact Methods, and a Real-World Study

We study continuous planar facility location in which a demand point's captured value decays with distance, with the per-point decay scale varying across points. This heterogeneity is ubiquitous yet underexploited, and one nearest-facility objective unifies decay, clustering, and median goals, containing k-means, the Weber/p-median problem, and maximum covering as special cases. We make four contributions. (i) A tractability classification: the discrete objective is always monotone submodular, so the (1-1/e) greedy guarantee holds regardless of decay shape or heterogeneity, and the continuous cooperative objective is concave if and only if the decay is concave in distance; the clip max(0,d) in common coverage specifications is what destroys concavity, and the classification is tight. (ii) An exact discrete method: the candidate-discretized maximum-cover MIP has an empirically tight LP relaxation (~0% gap) and is solved by branch-and-bound in seconds for n <= 500. (iii) A force-as-gradient / large-neighborhood-search heuristic, within 0.5% of the discrete optimum, that outperforms the (1-1/e) greedy, Cooper-style alternating location-allocation, particle swarm optimization, and weighted k-means (30/30 per-instance wins at K=30, p<10^-9) and is competitive with bespoke solvers on k-means, Weber/p-median, and shape-demand instances. (iv) A real-world study: on 592,667 urban-delivery orders, ignoring the calibrated decay variation loses up to 9.7% of captured demand and relocates facilities by up to 37% of the map; a retail dataset calibrates the decay as exponential with scale R ~ 1.4 km.

Zhou He, T. C. E. Cheng, Jichang Dong

School of Economics and Management, University of Chinese Academy of Sciences, N606-3, #3 Zhongguancun Nanyitiao, Haidian District, Beijing 100190, China · Department of Logistics and Maritime Studies, The Hong Kong Polytechnic University, 11 Yuk Choi Rd, Hung Hom, Hong Kong, China

Metaheuristic Optimization Combinatorial Optimization Approximation Algorithms Large Neighborhood Search

Jul 17, 2026cs.LG

Graph Coloring Approach to Solving Sudoku with Oscillatory Neural Networks

Oscillatory Neural Networks (ONNs) present an attractive physics-based computing paradigm rooted in the dynamics of a network of typically fully coupled oscillators aiming to minimize an underlying energy function. In this paper, we propose an ONN-based solver for one well-known constrained combinatorial optimization problem, namely a Sudoku, by formulating the problem as a Graph Coloring problem. By modifying the already existing Graph Coloring solver to a computationally cheaper version and introducing an additional term ensuring the fulfillment of the Sudoku constraints, our solver is shown to significantly outperform the existing HNN- and ONN solvers in terms of accuracy. In particular, we are able to achieve nearly flawless accuracies on

4 \times 4

as well as rather high accuracies on

9 \times 9

Sudoku puzzles for different numbers of unknown digits.

Filip Sabo, Aida Todri-Sanial

NanoComputing Research Lab, Electrical Engineering Department Eindhoven University of Technology Eindhoven, the Netherlands

Oscillatory Neural Networks Combinatorial Optimization Constraint Satisfaction Neural Combinatorial Optimization

Jul 16, 2026cs.DM

New Snake-in-the-Box Records via Snakepit Surgery and Learned Construction

The snake-in-the-box problem asks for a longest induced path in the hypercube graph

Q_n

. We find a length-191 snake in dimension

n=9

, the lowest dimension where the maximum is unknown, improving the previous record of 190 that had stood for 14 years. We also establish new lower bounds in dimensions 10-13. To find these records, we introduce snakepits, collections of disjoint snakes, to expand the search space and open new routes between snakes. This motivates our new Snakepit-in-the-Box benchmark, which seeks maximal edge counts when allowing multiple components. Finally, we introduce Beam Anchor, a search-supervised learned constructor algorithm that finds 100 inequivalent length-190 snakes in dimension 9.

Paul Orland, Lucas Fagan, Michele Tarquini +7

Combinatorial Optimization

Jul 16, 2026cs.LO

Can LLMs Build a MaxSAT Solver from Papers? The CoreForge Experience

We report on CoreForge, an experience in using large language models (LLMs) to build an unweighted MaxSAT solver from research papers rather than from an existing solver codebase. The project focuses on unsatisfiability-based MaxSAT algorithms and follows an iterative workflow that combines paper discussions with ChatGPT, implementation through Codex prompts, and repeated LLM-assisted code audits and revisions. Although the codebase implements several algorithms and solver components, our evaluation focuses on configurations that combine core-guided optimization, lightweight preprocessing, core minimization, integration with integer linear optimization backends, and a new core-sequence lookahead approach. Our experience suggests that LLMs can support solver implementation from papers, while requiring external validation, benchmarking, and human guidance. In our experiments, fuzzing and MaxSAT Evaluation instances did not reveal wrong answers in the tested configurations, although performance remains below the best hand-engineered MaxSAT solvers. We summarize what worked, what remained difficult, and the lessons for future LLM-assisted solver development.

Ruben Martins

Carnegie Mellon University

LLM-Based Program Synthesis Combinatorial Optimization Maximum Satisfiability LLM Code Generation

Jul 16, 2026cs.LG

CASP: Learning-Augmented Offline Approximation with Verifiable Certificates and Bounded-Loss PAC Guarantees

Machine-learned predictions can speed up offline NP-hard optimization, but asking a predictor what to do amounts to asking it to solve the problem, and committing an unchecked prediction forfeits every worst-case guarantee. CASP (Certificate-Augmented Solution Pruning) instead asks which parts of the search space may be ignored, and accepts each answer only after a sound polynomial-time verifier has checked it, so correctness never depends on prediction quality. We develop the learning theory of this design. The verifier makes the induced loss class uniformly bounded, so certificate parameters are learnable from

\tilde O(\varepsilon^{-2}\log K)

samples (

K

the maximum instance size), whereas the unverified commitment class admits no distribution-free rate and, under cost spread

R

, none below

Ω(R/\varepsilon^2)

. Filtering noisy predictions by verifiable confidence dominates the standard min-combiner, with a margin we compute in closed form, and the prediction stays useful even given the LP, because it breaks ties on degenerate optimal faces, where every symmetric LP policy, meaning one whose commitments depend on the instance only through the verifiable confidence values, provably stalls. Experiments on five problems test the theory's quantitative predictions. With trained predictors, unverified pruning loses up to

26%

of the optimum under distribution shift, while the verified deployment of the same predictions loses nothing.

Haifeng Li, Mo Hai

School of Information, Central University of Finance and Economics Beijing 102206, China

Combinatorial Optimization Learning-Augmented Algorithms PAC Learning Approximation Algorithms Statistical Learning Theory

Jul 15, 2026cs.LG

Low-Latency Relay Selection in NR-V2X Vehicular Communications via Graph Isomorphism Networks with Edge Features

Reliable, low-latency uplink connectivity is a key requirement for C-V2X networks in dense urban environments, where fast channel variations and blockages often degrade direct vehicle-to-infrastructure links. Multi-hop relaying can restore coverage, but relay-link activation under radio, capacity, and routing constraints results in an NP-hard optimisation problem, typically solved via Mixed-Integer Linear Programming (MILP), whose runtime scales poorly with graph size. This paper introduces an edge-aware Learning-to-Optimise framework for real-time relay selection. Each V2X snapshot is modelled as a directed graph: node features encode vehicle state and traffic demand, while edge features capture radio-link capacity. An offline MILP oracle generates optimal relay configurations that supervise a Graph Isomorphism Network with Edge Features (GINE), enabling edge-level relay activation through a single forward pass, with tightly bounded inference latency. To bridge learning and exact optimisation, we also propose a hybrid GINE-Pruned MILP (GP-MILP) strategy in which GINE predictions prune the MILP search space. Experiments on a large-scale dataset generated via an OSM-SUMO-GEMV

^2

pipeline show that GINE closely matches MILP decisions at the link level (accuracy 0.9589), F1-score (0.9544) on validation) and yields consistent end-to-end connectivity gains over a 1-hop MILP baseline (up to 9.2% with four RSUs and 12% with two RSUs). Inference latency remains tightly bounded, with all evaluated instances completing within 5~~ms. Moreover, GP-MILP preserves MILP-equivalent solutions (same objective value) while achieving solver runtimes below 30~~ms for more than 98%) of the graph instances, making MILP-grade optimisation compatible with stringent NR-V2X latency budgets.

Giambattista Amati, Federica Mangiatordi, Emiliano Pallotti +3

Fondazione Ugo Bordoni (FUB) Rome, Italy · University of Rome Tor Vergata (UniRoma2) Rome, Italy

Mixed-Integer Linear Programming Learning to Optimize Combinatorial Optimization V2X Communication

Jul 15, 2026cs.RO

Dynamical Vehicle Orienteering Problem for Multi-Rotor Unmanned Aerial Vehicles

This paper introduces the Dynamical Vehicle Orienteering Problem (DVOP), a generalization of the Orienteering Problem (OP). The OP maximizes the reward collected from spatial targets under a limited travel budget; the DVOP extends it by accounting for both external and vehicle-actuated forces. We study the DVOP in the context of multi-rotor Unmanned Aerial Vehicle (UAV) flight planning, using a three-dimensional Point-Mass Model (PMM) constrained by maximum velocity and acceleration magnitudes and subject to gravitational acceleration, with the travel budget expressed as a maximum flight time. Because the DVOP couples reward maximization with time-optimal trajectory planning, it cannot be formulated as a simple graph problem and solved exactly without relaxing or under-actuating the vehicle dynamics. We therefore propose two solution approaches: a Branch-and-Bound (BnB) procedure that combines Non-Linear Programming (NLP) and Mixed-Integer Linear Programming (MILP) to provide high-quality solutions, and a Large Neighborhood Search (LNS) metaheuristic that supplies an initial reward bound and scales to instances intractable for the BnB. The BnB relies on a novel MILP formulation of travel costs based on minimum-time trajectory primitives through target triplets, yielding a tight reward upper bound, while the LNS uses limited thrust decomposition to compute fast, high-quality PMM trajectories. Experiments on benchmark instances show improvements of up to 37 % over state-of-the-art solutions for the Kinematic Orienteering Problem, and a real-world deployment on a multi-rotor UAV verifies the proposed PMM solution trajectories.

František Nekovář, Matej Novosad, Martin Saska +1

Faculty of Electrical Engineering, Czech Technical University, Technicka 2, 166 27, Prague, Czech Republic

Trajectory Optimization Branch and Bound UAV Navigation Combinatorial Optimization Vehicle Routing UAV Trajectory Optimization+1

Jul 15, 2026math.OC

Learned Pairwise Deep Dual-Optimal Inequalities for Stabilizing Column Generation

Column generation (CG) is central to many large-scale optimization algorithms, including branch-price-and-cut methods for vehicle routing problems, but unstable dual solutions can substantially slow its convergence. Existing deep dual-optimal inequalities can reduce this instability by restricting the dual space. Their construction, however, typically relies on problem-specific exchange arguments that are difficult to establish for routing problems with capacity limits, time windows, and other resource constraints. We introduce learned pairwise deep dual-optimal inequalities (L-PDDOIs), a learning framework that predicts pairwise orderings between dual variables and incorporates their primal counterparts directly into the master problem. To construct training labels, the framework samples optimal dual solutions and selects pairwise order relations that hold simultaneously on a sufficiently large common subset of the samples. A classifier then assigns a score to each candidate relation. Because conflicts and redundancies among the predicted relations can impair performance, graph-based postprocessing filters and compresses the candidate set before deployment. We further introduce a recovery procedure that selectively relaxes learned inequalities and provides a certificate when the baseline CG bound has been restored. On the main test sets for the capacitated vehicle routing problem and the vehicle routing problem with time windows, direct deployment of L-PDDOIs reduces the geometric mean root CG time by 89.7% and 93.9%, respectively, while incurring mean bound losses of only 1.3% and 0.5%. The recovery procedure retains corresponding time reductions of 54.8% and 83.1%, respectively, while guaranteeing no loss in the CG bound.

Zhengzhong Ricky You, Bo Tang, Haoran Liu +1

Department of Civil Engineering, Tsinghua University, Beijing 100084, China · MIT Sloan School of Management, Massachusetts Institute of Technology, 100 Main Street, Cambridge, MA 02142, USA · Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL 32611, USA

Primal-Dual Optimization Combinatorial Optimization Vehicle Routing

Jul 13, 2026cs.AI

Connected by Construction: Learning Tractable Near-Tour Marginals for Traveling Salesman Problems

Learning-based methods for the traveling salesman problem (TSP) are often evaluated through the tours produced after decoding or search, but the learned object itself frequently lives in a surrogate space such as heatmaps, assignments, construction policies, or search-guidance scores. This hides the fundamental question: what Hamiltonian structure has actually been learned before decoding? In this study, we directly answer this question by learning TSP through a structurally meaningful latent object, rather than leaving most of the Hamiltonian structure to the final decoding stage. Based on a connected-by-construction rooted

1

-tree Gibbs family, we propose an end-to-end unsupervised learning pipeline called \emph{C2TSP}. The pipeline learns residual edge perturbations from unbiased TSP cost through implicit differentiation. For structural correction, a smoothed Held--Karp layer restores expected degree balance, while certificate-guided sharpening further pushes the connected distribution toward more tour-like structures. Experiments show that C2TSP yields strong decoding performance while preserving interpretable structural information. Ablations further verify that edge perturbation and certificate-guided sharpening jointly improve both tour cost and tour-like structure.

Ke Sun, Xinyuan Zhang, Xinwu Qian

Department of Civil and Environmental Engineering, Rice University, Houston, TX

Traveling Salesperson Problem Combinatorial Optimization Neural Combinatorial Optimization

Jul 13, 2026cs.DM

Representing the Non-dominated Set of Multi-objective Network Problems by Supported Non-dominated Points

In multi-objective combinatorial optimization, unsupported non-dominated points typically outnumber supported points and are often significantly more challenging to compute. Recent studies show that extreme supported non-dominated points provide high-quality representations of the non-dominated set for certain binary problems. We demonstrate that this observation does not generalize to capacitated network optimization problems: representation quality decreases with increasing arc capacities, whereas supported non-dominated points consistently provide high-quality representations with respect to several quality indicators. However, supported point sets may still be too large in practical applications, where only a small, fixed number of alternatives is typically desired. Selecting fixed-size representations from the non-dominated set requires its computationally expensive generation and thus diminishes the computational advantages that representations are intended to provide. We therefore suggest the (extreme) supported points as alternative candidate sets in subset selection problems. Our numerical results show that restricting the candidate set to supported non-dominated points yields fixed-size representations of nearly the same quality as those selected from the complete non-dominated set. Overall, supported non-dominated points serve both as high-quality representations and as reasonable candidate sets for subset selection.

David Könen, Lara Löhken, Michael Stiglmayr

University of Wuppertal, School of Mathematics and Natural Sciences, Optimization Group, Gaußstraße 20, 42103 Wuppertal, Germany · Corresponding author

Combinatorial Optimization Multi-Objective Optimization Pareto Optimization

Jul 13, 2026cs.LG

Time-Lag-Aware Deep Reinforcement Learning for Flexible Job-Shop Scheduling in PPVC Module Factories

Prefabricated prefinished volumetric construction moves most building work into module factories, whose production floor operates as a flexible job shop. A major complication is decisive: long post-operation time-lags caused by concrete curing, watertightness ponding tests, and paint drying, during which a module is blocked while its workstation stays free. On benchmark instances grounded in an official national prefabrication guidebook, these lags inflate even the optimal reference makespan by about 67% on average, and ignoring them at decision time, then repairing to feasibility, is worse than every dispatching rule. We adapt a state-of-the-art dual-attention deep reinforcement learning solver through three minimally invasive, individually ablatable extensions: lag-aware dynamics with an admissible reward bound, two anticipatory lag feature channels, and liveness-masked operation- and station-type embeddings. With every extension disabled the implementation reproduces the original solver exactly, so all gains are attributable to the adaptations. We release a public, guidebook-grounded benchmark generator. On held-out instances the learned policy is the strongest solver-free scheduler: it reaches within about 4% of a constraint-programming reference and beats every dispatching rule and a genetic-algorithm metaheuristic, with its advantage widening under capacity contention, and a single size-mixed policy carries this lead across the trained range of factory sizes. It needs no solver, model, or license in the loop and re-plans within seconds of a disruption; where an exact solver can be deployed, that solver remains the quality ceiling, a boundary we map explicitly.

Ziheng Zhang, Wei Zhang

Singapore Institute of Technology, Singapore

Manufacturing Reinforcement Learning Combinatorial Optimization RL for Combinatorial Optimization Job Shop Scheduling

Jul 13, 2026cs.CL

RefineEvo: Planning-Guided Heuristic Evolution with Bidirectional Experience

Automatic Heuristic Design (AHD) has emerged as a transformative approach for solving combinatorial optimization problems. While recent Large Language Model (LLM)-based methods have shown promise, they predominantly rely on fixed evolutionary operators and struggle to effectively accumulate and reuse historical search experience. This paper proposes RefineEvo, a novel evolutionary framework that transforms AHD from a static trial-and-error process into a planning-guided, experience-driven system. RefineEvo introduces a Planner to dynamically schedule evolutionary operators and trigger refinement based on the current search state, and a Reflector to distill valuable lessons into a Bidirectional Experience Pool containing both positive insights and negative pitfalls. This synergistic framework enables the system to adapt its search tools to the evolving complexity of the problem and leverage trajectory-aware, situation-conditioned insights to guide generation. Experiments on several classic combinatorial optimization benchmarks demonstrate that RefineEvo consistently outperforms strong baselines. In particular, RefineEvo delivers superior solution quality while improving token efficiency, enabling more efficient and autonomous heuristic design.

Yang Wu, Junran Pan, Yifan Zhang +3

C2DL, Institute of Automation, Chinese Academy of Sciences · School of Artificial Intelligence, University of Chinese Academy of Sciences, Beijing · University of Chinese Academy of Sciences, Nanjing +1

Automated Heuristic Design Evolutionary Optimization Large Language Model-Guided Optimization Combinatorial Optimization

Jul 13, 2026cs.LG

A Multi-Agent Framework for Zero-Dimensional Reduced-Order Model Planning

Zero-dimensional reduced-order models (0D ROMs) are central to multi-dimensional design workflows for high-end complex equipment. However, the planning process currently relies on manual expertise, limiting topological exploration and prolonging iterations. Even traditional optimization methods such as Genetic Algorithms (GA) are typically confined to local parameter tuning. Although Large Language Model (LLM) agents have shown promise in exploring large sample spaces, and frameworks such as Chain of Thought (CoT) and Reason and Act (ReAct) improve reasoning reliability, while Retrieval-Augmented Generation (RAG) overcomes domain knowledge barriers, a single agent still falls short for the long-horizon and highly coupled nature of complex 0D ROM planning. This paper proposes the Zero-dimensional reduced-order model CO-Planning framework (Z-COPA), a multi-agent architecture featuring a Symbolic Action Graph Engine (SAGE) and a MILP-Guided Navigation (MGN) optimizer. Its core innovation is a dedicated graph representation method that accurately encodes the 0D flow network topology, converting the empirical planning process into a rigorous graph structure optimization problem. We validate the forward and inverse design capabilities and generalization performance of Z-COPA on two real aircraft engine secondary-air systems, two IEEE power-distribution reconfiguration benchmarks, and two water-distribution network benchmarks. The results show superior task completion quality, obtaining the best performance in both forward and reverse design of air systems. Z-COPA disrupts the traditional 0D model planning paradigm, providing a new technical approach for exploring broader topological space and achieving highly automated, globally optimal air system architectures.

Bingteng Sun, Hao Yin, Yiling Chen +9

Advanced Gas Turbine Laboratory, Institute of Engineering Thermophysics, Chinese Academy of Sciences, Beijing, 100190, China. · National Key Laboratory of Science and Technology on Advanced Light-duty Gas-turbine, Beijing, 100190, China. · School of Computer Science and Technology, Shandong University, 72 Binhai Road, Qingdao, 266237, Shandong Province, China. +3

Combinatorial Optimization Reduced-Order Modeling Graph-Based Planning Multi-Agent Planning LLM Agent Planning

Jul 9, 2026cs.LG

MPFlow: Learning Budgeted Max-Flow Optimization on the Lightning Network with Deep Graph Reinforcement Learning

We address liquidity placement in the Bitcoin Lightning Network (LN): given a fixed budget, which channels should a node open to maximize its routing capacity? We cast this as a budget-constrained combinatorial optimization problem on graphs, selecting

k

edge additions that maximize

s

--

t

max-flow, a theory-grounded measure of routing capacity, and solve it with graph reinforcement learning. Our lightweight agent combines a message-passing policy network with proximal policy optimization (PPO) and action masking, and is trained under a hub-exclusion curriculum: the network's top hubs are removed from training subgraphs, forcing the policy to learn capacity-aware placement rather than hub attachment. In extensive experiments on real Lightning Network snapshots, our method consistently outperforms strong heuristic baselines on the max-flow objective across multiple seeds and unseen graphs. The agent has been deployed in production for peer recommendations, executing 4640 channel-open decisions that cumulatively allocate 267.3 BTC over $16 million across 30 managed nodes.

Harrison Rush, Vincent Davis, Simone Antonelli +3

Amboss Technologies, Green Cove Springs, USA · CISPA Helmholtz Center for Information Security · Stillmark, San Francisco, USA +1

Combinatorial Optimization Decentralized Finance RL for Combinatorial Optimization

Jul 6, 2026cs.NE

QDEvo: A Multi-Objective Quality-Diversity Framework for Automated Heuristic Design

The integration of Large Language Models (LLMs) with evolutionary computation has emerged as a powerful paradigm for automated heuristic design in combinatorial optimization. However, existing approaches suffer from mode collapse, converging to homogeneous populations that lack semantic diversity and fail to explore the full algorithmic space. We propose Quality-Diversity Evolution (QDEvo), a multi-objective framework that integrates Quality-Diversity optimization with LLM-driven heuristic search, maintaining an unbounded archive of semantically diverse algorithms using pre-trained code embeddings and incorporating hierarchical self-reflection to guide the evolutionary process. Extensive experiments across standard benchmarks and real-world industrial applications demonstrate that QDEvo significantly outperforms state-of-the-art methods in both Hypervolume and Inverted Generational Distance metrics. Our framework enables the discovery of heuristics that are simultaneously high-performing, computationally efficient, and semantically diverse, providing practitioners with a rich portfolio of solutions for complex optimization problems.

Nam Do Khanh, Nhat Nguyen Tran Minh, Dat Pham Vu Tuan +2

Hanoi University of Science and Technology Hanoi, Vietnam · George Mason University Fairfax, Virginia, USA

Automated Algorithm Discovery Automated Heuristic Design Metaheuristic Optimization Large Language Model-Guided Optimization Combinatorial Optimization Quality-Diversity Optimization+1

Jul 4, 2026cs.DS

TSP with Predictions: Heatmap to Tour with Provable Guarantees

The Traveling Salesperson Problem (TSP) has long served as a benchmark for evaluating the strength of optimization techniques in the classical theory of algorithms. In recent efforts to apply ML to algorithmic problems, TSP has also become a natural testbed for the development of ML-based techniques. A common approach is to train a neural network to output a heatmap estimating the likelihood of each edge to be part of the optimal tour; however, converting such a heatmap into an actual tour remains a non-trivial and often computationally intensive step. In this work, we propose algorithms for transforming heatmaps into tours with theoretical guarantees linking the achieved approximation ratio to the quality of the provided heatmap. In the spirit of algorithms with predictions, our results can be described as

(1+2\fracη{\mathrm{OPT}})

-approximation algorithms, where

η

denotes the L1 distance between the prediction (heatmap) and an optimal solution (tour). Since the previous works lack such explicit guarantees, we compare our approach against them experimentally.

Marek Eliáš, Fabrizio Grandoni, Adam Polak +1

Traveling Salesperson Problem Combinatorial Optimization Learning-Augmented Algorithms Approximation Algorithms Neural Combinatorial Optimization

Jul 3, 2026cs.AI

A Sliding-Window-Based Reinforcement Learning for Dynamic Assembly Flow Shop Scheduling with Multi-Product Delivery

Multi-product kitting delivery imposes significant challenges for real-time scheduling in hybrid manufacturing systems that integrate processing and assembly, as dynamic order arrivals simultaneously alter supply dependencies and the set of feasible job-machine assignments. This paper proposes a sliding-window-based reinforcement learning (SWRL) framework for end-to-end online scheduling in the flexible assembly flow shop scheduling problem with complex kitting constraints. The problem is formulated as a heterogeneous graph-based Markov decision process that captures the dual-layer kitting structure and the tail-product bottleneck dynamics that produce a sparse reward landscape. To address the resulting challenges, SWRL integrates a sliding-window filtering mechanism that filters inactive nodes and prioritizes kitting-critical operations, a spatiotemporal graph encoding network that tracks bottleneck shifts across consecutive decision states, and a dynamic action mapping module with a constrained waiting strategy that adapts to the changing action space under variable topologies. Experiments on real-world instances from a home appliance manufacturer demonstrate that SWRL achieves consistent tardiness reductions over classical dispatching rules and existing deep reinforcement learning methods, and exhibits robust performance across varying resource configurations, order loads, and arrival concentrations.

Junhao Qiu, Jianjun Liu, Ting Liu +3

School of Electromechanical Engineering, Guangdong University of Technology, Guangzhou, China · Department of Computer Science, City University of Hong Kong, Hong Kong

Combinatorial Optimization RL for Combinatorial Optimization

Jul 2, 2026cs.NE

Hybridizing a Grouping Metaheuristic with Reinforcement Learning for the One-Dimensional Bin Packing Problem

The one-dimensional bin packing problem (1D-BPP) is a canonical NP-hard combinatorial optimization problem with broad industrial applications. We propose RL-HGGA, a hybrid algorithm that integrates Falkenauer's Hybrid Grouping Genetic Algorithm (HGGA) with a tabular Q-learning controller. Rather than applying genetic operators at fixed probabilities, a Q-learning agent dynamically selects among eight macro-actions -- including BPCX crossover, light and heavy mutation, Martello-Toth local search, and population restart -- based on an eight-dimensional state representation encoding generation progress, stagnation level, optimality gap, average fitness, population variance, and average bin fill rate. The agent is trained with an epsilon-greedy policy over 400 episodes, with epsilon decaying to 0.05. Experiments on standard benchmark families (Falkenauer T/U, Scholl 1-3, Hard28) show that RL-HGGA achieves an average optimality gap of 0.95% -- competitive with HGGA (0.75%) and well below FFD (2.47%) -- while reducing mean computation time from 64.22 s to 1.29 s, a 50x speedup. These results demonstrate that learned adaptive operator selection can achieve near-HGGA solution quality at a fraction of the computational cost.

Zitouni Rania, Mostefai Mounir Sofiane, Tati Youcef +3

Square Two Team – Optimization Module, École Nationale Supérieure d’Informatique (ESI), Algiers, Algeria

Metaheuristic Optimization Combinatorial Optimization RL for Combinatorial Optimization Genetic Algorithms

Jul 1, 2026cs.LG

Neural Certificate Pricing for Combinatorial Optimization Problems

Combinatorial optimization (CO) problems are difficult because certifiable discrete structure induces exponential search. One needs to search over the set exponentially many candidates to certify optimality, however, the structural feasibility of a path, packing, or cover can be verified in polynomial time once supplied. In this study, we introduce Neural Certificate Pricing (NCP) that exploits this asymmetry under an unsupervised learning framework. A neural network is trained to predict certificate-level dual prices, while a structured recovery layer constructs the induced primal marginal. NCP can be viewed as amortized separation: instead of enumerating violated inequalities, it learns the residual prices through which their aggregate effect enters recovery. When the certificate-consistency condition holds, the recovered marginal is globally feasible, and a local theory shows that first-order errors in the predicted price induce only second-order loss in objective value. Across three classes of CO problems, NCP either outperforms state-of-the-art neural baselines by large margins or matches them at a fraction of the computation time, and shows stronger out-of-distribution generalization.

Jingyi Chen, Xinyuan Zhang, Xinwu Qian

Department of Civil and Environmental Engineering, Rice University, Houston, TX

Primal-Dual Optimization Unsupervised Learning Combinatorial Optimization Neural Combinatorial Optimization

Jun 30, 2026cs.RO

Dual-Informed Vertical Expansion for Multi-Objective Node Selection in Anytime Conflict-Based Search

Conflict-Based Search (CBS) is a leading exact algorithm for Multi-Agent Path Finding (MAPF), but its high-level node-selection rule is usually treated as a fixed implementation detail. Standard best-first selection is strong for minimizing expanded nodes and closing the optimality certificate, yet it can maintain a large frontier, interrupt parent-child expansion sequences, and provide no feasible incumbent until termination. This paper studies node selection as a first-class design choice for exact CBS. We introduce Dual-Informed Vertical Expansion (DIVE), a policy that is best-bound between dives and depth-oriented within a dive. DIVE starts each dive from the current best-bound frontier, follows promising children to exploit parent-child locality, and uses incumbent pruning to limit unproductive excursions. We formalize CBS node selection through a branch-and-bound view, prove that the traversal policy can be changed without affecting exactness, and analyze the resulting trade-offs among expanded nodes, dive breaks, queue size, and primal-dual bound progress. The analysis predicts three complementary extremes. Best-first search is node efficient, iterative deepening is memory efficient, and DIVE is dive efficient while retaining regular best-bound reanchoring. Experiments on standard MAPF benchmarks support this trade-off map. DIVE consistently reduces dive breaks, provides early incumbents with certified gaps, uses substantially less queue memory than best-first search, and benefits from warm starts and simple responsive variants in dense or memory-limited regimes.

Willem van Osselaer, Jiarui Li, Meshal Alharbi +1

Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, Cambridge, MA, USA

Branch and Bound Tree Search Combinatorial Optimization Conflict-Based Search Multi-Agent Path Finding

Jun 30, 2026cs.AI

Adaptive Cluster-First Route-Second Decomposition for Industrial-Scale Vehicle Routing

Large-scale capacitated vehicle routing problems (CVRPs) are commonly addressed using cluster-first route-second (CFRS) approaches that split a routing instance into smaller, computationally tractable subproblems. Existing splitting methods typically rely on fixed partitioning rules, predefined optimization objectives, or learned policies, which may perform inconsistently across instances exhibiting different spatial, demand, and operational characteristics. In this work, we propose an adaptive CFRS system that formulates a decomposition procedure as an iterative decision-making process. Motivated by the recent success of large language models (LLMs) in reasoning and tool selection, the system employs an LLM as a high-level decision maker that analyzes the evolving decomposition state and selectively applies further clustering, balancing, and refinement operators. The proposed algorithm jointly partitions customers and vehicles, enabling capacity-aware clustering while adapting partitioning decisions to the characteristics of each problem. We evaluate the approach on synthetic and benchmark-derived CVRP instances containing up to 500,000 customers. Experimental results demonstrate competitive performance on benchmark-scale instances while exhibiting improved scalability and robust routing quality on substantially larger problems. These results highlight the potential of adaptive, LLM-guided decision support as a practical approach for industrial-scale vehicle routing and large-scale logistics planning.

Oguzhan Karaahmetoglu, Hyong Kim

Carnegie Mellon University · Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA, 15213 USA

Large Language Model-Guided Optimization Combinatorial Optimization Vehicle Routing

Jun 30, 2026cs.NE

A Large-Scale Empirical Evaluation of MMAO Under Fair-Budget Continuous and Discrete Benchmarks

This paper evaluates the Metabolic Multi-Agent Optimizer (MMAO) under a stricter empirical protocol rather than reintroducing the framework itself. The study asks whether MMAO's closed-loop resource-allocation principle remains credible under broader, more standard, and more explicitly budget-controlled continuous and discrete benchmarks. The main completed matrix covers eight CEC2017 functions at 10D and 30D with 20 seeds each, and five TSPLIB instances with 20 seeds each, together with stronger reproducible baselines including PSO-lite, ES-lite, and an iterated-greedy 2-opt route baseline. We further add trajectory-level diagnostics for communal budget, success rate, role evolution, and population turnover, plus an auxiliary OR-Library multiple-knapsack slice to extend the discrete evidence beyond routing. Under this protocol, MMAO clearly outperforms the external baseline set on the continuous side and on the TSPLIB side, while the ablation variants remain much closer to the full method than the external baselines are. We therefore position MMAO as a benchmark-backed cross-domain adaptive framework whose most clearly validated value is endogenous resource redistribution under evidence pressure, while also noting that the strongest remaining gap is not basic workability but sharper mechanism isolation and broader competition-grade comparison.

Jinliang Xu, Liping Ma

Jinliang Xu is with the current study team · Department of Disease Control and Prevention, The Seventh Medical Center of Chinese PLA General Hospital, Beijing, China

Multi-Agent System Optimization Metaheuristic Optimization Combinatorial Optimization Ising Optimization Multi-Agent Systems