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

Jun 29, 2026math.OC

Local-Minima-Preserving Continuous Relaxation of Ising Problems

The generalized Ising problem captures a broad spectrum of hard combinatorial problems, including MAX-CUT, Number Partitioning (NPP), and Maximum Independent Set. In this work, we consider the notion of one-flip local minima for this problem. We construct a polynomial relaxation and prove the landscape equivalence theorem: there exists a one-to-one correspondence between the local minima of the relaxation and the one-flip minima of the original Ising problem. This guarantee reduces the Ising problem to finding the local minima of a smooth function, allowing us to leverage gradient-based optimizers such as ADAM. We demonstrate that our method is scalable and it achieves strong performance across challenging benchmarks, including spin-glass models, MAX-CUT, and NPP.

Debraj Banerjee, Santanu Mahapatra, Kunal N. Chaudhury

Department of Electrical Engineering, Indian Institute of Science, Bangalore, India · Department of Electronic Systems Engineering, Indian Institute of Science, Bangalore, India

Combinatorial Optimization Ising Optimization

Jun 27, 2026cs.NE

Road to scalability for efficient graph search on massively parallel neuromorphic hardware

Efficient computation of shortest paths in weighted graphs is a fundamental problem with many applications. Neuromorphic hardware platforms promise massively parallel, efficient computation, changing parallelism tradeoffs. In this work, we introduce NEURO-MAPP (Neuromorphic-based Min-Add Parallel Propagation), a distributed shortest path algorithm designed to use the local computation and network communication available in neuromorphic systems. We provide an optimized implementation of the algorithm on the SpiNNaker 2 platform and evaluate its performance on a selection of synthetic and real-world graphs. These results are compared to Dijkstra's algorithm on a modern CPU. We find that the NEURO-MAPP implementation scales favorably in terms of runtime for many graph types while consuming less energy per shortest-path query than the CPU implementation in almost all cases. These findings highlight the potential of neuromorphic hardware featuring sparse, spike-based communication as a scalable and energy-efficient platform for computation in graph search and related tasks.

Oskar von Seeler, Elena C. Offenberg, Carlo Michaelis +4

Department of Neuro- and Sensory Physiology, University Medical Center Göttingen, Germany · Campus Institute Data Science, University of Göttingen, Germany · Third Institute of Physics – Biophysics, University of Göttingen, Germany +2

Combinatorial Optimization Neuromorphic Computing

Jun 26, 2026cs.RO

Locker-based Truck-Drone Routing with Integrated Considerations of Pickups, Deliveries, and No-Fly Zones

Truck-drone delivery is an emerging last-mile logistics mode combining the long-haul capacity of trucks with the flexible service capability of drones. In locker-based operations, smart lockers serve not only as temporary parcel storage facilities but also as automated drone docking and service nodes. These automated nodes support drone takeoff, landing, parcel handover, and battery replacement, thereby significantly extending the service range and operational flexibility of drone-assisted delivery networks. However, practical locker-based delivery systems face complex real-world challenges, requiring the integrated coordination of not only parcel delivery, return pickup, battery-constrained and load-dependent drone flights, but also necessary detours around restricted airspace. To address this practical and multifaceted challenge, this paper introduces a locker-based truck-drone routing problem with integrated considerations of pickups, deliveries, and no-fly zones (LTDRP-PDNF), with the objective of minimizing the total operational cost of a fleet of drone-equipped trucks. We formulate the route construction process as a Markov Decision Process and develop a two-stage deep reinforcement learning-based neural heuristic. The first stage utilizes an attention-based encoder and a Bidirectional Gated Recurrent Unit decoder to solve the truck-only routing problem, formulated as a capacitated vehicle routing problem. The second stage combines a policy-transfer strategy with a hybrid dispatch assignment heuristic to construct fully coordinated truck and drone routes for LTDRP-PDNF. Experiments on instances of different scales demonstrate that the proposed method outperforms metaheuristic and neural heuristic baselines in most cases while maintaining exceptionally short computation times, offering an effective, scalable solution framework under practical operational constraints.

Xuanyu Liu, Hui Hu, Jiao Zhao +2

College of Transportation Engineering, Chang’an University, China · Faculty of Science and Technology, University of Nottingham Ningbo China

Combinatorial Optimization Vehicle Routing RL for Combinatorial Optimization

Jun 26, 2026cs.NE

MMAO: A Metabolic Multi-Agent Optimizer with Endogenous Resource Allocation for Continuous and Discrete Optimization

Traditional meta-heuristics often rely on fixed population sizes, manually chosen search scales, and externally attached parameter-control modules. This paper presents the \textit{Metabolic Multi-Agent Optimizer} (MMAO), a cross-domain optimization framework in which adaptation is derived endogenously from a private-public metabolic resource loop. Each agent carries internal energy, a continuous role state, motion or structural memory, and local search history, while the population shares a communal resource pool. Fitness improvements are converted into normalized metabolic gains through a robust progress scale and a recent success statistic; the same closed loop then regulates sensing intensity, search amplitude, role drift, branching, pruning, respawning, and elite reinvestment. In the continuous setting, MMAO uses energy-regulated symmetric zero-order probing and role-interpolated motion. In the discrete setting, the same control law is instantiated through structural sensing, local route improvement, guided perturbation, and energy-weighted edge reuse. The paper combines an implementation-faithful formulation with a reproducible experimental study on a CEC2017 subset (10D/30D, 20 seeds) and five TSPLIB instances (100 discrete runs in total). The current evidence supports MMAO primarily as a parameter-light, self-calibrating optimization framework whose main validated originality lies in metabolically endogenous resource allocation across heterogeneous search behaviors, rather than as a universally superior optimizer.

Jinliang Xu, Liping Ma

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

Jun 25, 2026cs.AI

Context-Aware Synthesis of Optimization Pipelines for Warehouse Optimization

Order fulfillment in manual picker-to-goods warehouses involves interconnected decisions such as item assignment, order batching, and picker routing. While integrated models capture interactions between these decisions, practical warehouse systems often require decomposed approaches due to organizational boundaries, differing responsibilities, or limited data availability. Existing studies primarily evaluate algorithms for isolated subproblems or fixed subproblem combinations for specific warehouse settings, but lack a general mechanism to determine applicable algorithm configurations, compose them into valid solution pipelines, and assess their performance. With Context-Aware Synthesis of Optimization Pipelines (CASOP), we propose a framework for constructing and evaluating context-specific optimization pipelines and apply these to order fulfillment. The framework comprises: (1) a modular repository of algorithms for common order fulfillment problems; (2) semantic data and algorithm cards to describe warehouse context and algorithm requirements; (3) a taxonomy that structures order fulfillment problems into relevant subproblems; (4) a pipeline synthesizer that identifies applicable algorithms for a given warehouse context and composes all valid optimization pipelines; and (5) a pipeline evaluator that assesses all resulting pipelines. We demonstrate the framework on 7 benchmark instance sets covering four problem classes, resulting in 1,063,044 valid pipelines. The framework supports researchers and practitioners in designing, automatically synthesizing, and selecting valid, high-performing algorithmic pipelines for warehouse operations. The software is open-source and available at https://github.com/kit-dsm/ware_ops_pipes and https://github.com/kit-dsm/ware_ops_algos. Keywords: Warehouse optimization, Algorithm selection, Pipeline synthesis, Order fulfillment

Janik Bischoff, Anne Meyer, Uta Mohring +6

Institute for Information Management in Engineering, Karlsruhe Institute of Technology, Germany · Department of Business Administration, University of Zurich, Switzerland · Institute for Operations Research, Karlsruhe Institute of Technology, Germany +1

Algorithm Selection Automated Algorithm Discovery Combinatorial Optimization Program Synthesis

Jun 25, 2026cs.AI

Scientific discovery as meta-optimization: a combinatorial optimization case study

Scientific discovery is fundamentally an optimization problem, defined by a vast "state space" of theories and experiments, and an evaluation criterion based on quality, novelty, and validity. Large language models (LLMs) have enabled automated exploration of this space, but we argue that simultaneous modification of the evaluation criteria is equally important. Here, we propose formalizing research as meta-optimization, where the optimization objective itself is also being optimized. Our key contribution is "consensus objective aggregation," where LLM-generated objective functions are combined via correlation-weighted voting, yielding a stable, self-correcting evaluation criterion that evolves as understanding deepens. We apply this framework to algorithm discovery for 3-SAT problems based on digital MemComputing machines, reducing the baseline scaling with problem size

N

from

\sim N^{2.51}

to

\sim N^{1.33}

and delivering a

\sim 67\times

speedup on the largest instances tested. As a problem-agnostic framework, we hope this approach will considerably aid scientific discovery.

Yuan-Hang Zhang, Chesson Sipling, Massimiliano Di Ventra

Automated Algorithm Discovery Combinatorial Optimization Large Language Model-Guided Scientific Discovery

Jun 24, 2026cs.AI

Geometry-Aware MCTS for Extremal Problems in Combinatorial Geometry

We study certain extremal problems in combinatorial geometry that ask about configurations of points in an

n \times n

grid that satisfy strict, global geometric constraints. Classical exact solvers suffer from combinatorial explosion for these types of problems, and standard reinforcement learning and transformer-based models struggle with the sparse reward "validity cliff" and quadratic token-consumption limits. To overcome these bottlenecks, we propose a Geometry-Aware Monte Carlo Tree Search (MCTS) framework. Our approach strictly enforces geometric constraints through incremental updates to the feasible action space. For constraints about collections of collinear points, like those that occur in the classic No-Three-in-Line problem (Max-N3IL), this mechanism reduces the constraint checking complexity from

O(n^3)

to

O(n^2)

. To improve search efficiency, we exploit geometric symmetries in two ways: canonical pruning during node expansion to reduce the branching factor, and symmetric batch transitions to accelerate the discovery of promising configurations. We perform extensive experiments and establish new best-known computational results on five out of six of the problems that we considered. Notably, for Max-N3IL we find configurations of size roughly

1.8 n

for grids of size

82 \le n \le 119

. For the Smallest Complete Set problem, we find configurations of size roughly

0.95 n

, providing new upper bounds within the tested grids. This work establishes Geometry-Aware MCTS as a highly adaptable framework for discovering novel configurations in combinatorial geometry.

Luoning Zhang, Xu Zhuang, Tianhao Wang +1

Department of Mathematics, University of California, Irvine

Symmetry Breaking Combinatorial Optimization Monte Carlo Tree Search

Jun 23, 2026cs.AI

Cost-Optimal Decision Diagrams for Stochastic Boolean Function Evaluation

In many decision-making scenarios, acquiring information incurs different costs. We consider the problem of constructing a deterministic evaluation strategy that minimizes the expected cost of evaluating a propositional formula under variable costs and a probability distribution over truth assignments. We present a branch-and-bound algorithm with variable-selection heuristics, pruning, and caching. To the best of our knowledge, it is the first practical exact algorithm for this level of generality. Experiments on random instances demonstrate scalability and quantify the efficiency-quality trade-off of a greedy beam-search variant. We additionally evaluate a structured heart-disease diagnosis instance. Finally, we prove that the problem is

\#P

-hard and contained in

\mathrm{PSPACE}

.

Xia Zong, Tuomo Lehtonen, Jussi Rintanen

Department of Computer Science, Aalto University

Branch and Bound Cost-Aware Inference Combinatorial Optimization

Jun 23, 2026cs.AI

GES-TSP: Graph Edge Sparsification for TSP

Solving large-scale instances of the Traveling Salesman Problem (TSP) exactly is computationally expensive. Researchers often employ graph sparsification methods to improve computational efficiency. Traditional sparsification methods typically rely on fixed heuristics and fail to fully exploit instance-specific structural information. In this paper, we propose Graph Edge Sparsification (GES), a learning-based sparsification approach for Euclidean TSP. By incorporating geometric structural information and combinatorial optimization technology, our proposed method adaptively generates a sparsification graph for different instances, significantly reducing the graph size and accelerating the solving process. Experimental results demonstrate that our sparsification method can prune up to 95% of edges on the MATILDA dataset, while keeping the solution gap within 1% of the optimal value. Moreover, our approach exhibits strong generalization capability on the TSPLIB benchmark.In some large-scale instances, the pruning rate exceeds 99%, while the optimality gap remains below 1%.

Tianfeng Chen, Xianyue Li

School of Mathematics and Statistics Lanzhou Universtiy

Traveling Salesperson Problem Graph Structure Learning Graph Sparsification Combinatorial Optimization

Jun 23, 2026cs.NE

Adaptive Enhanced Quantum-inspired Simulated Bifurcation Algorithm for Population State Perception

Existing quantum-inspired simulated bifurcation algorithms rely on dynamic scheduling methods but lack the ability to adapt effectively to different problem instances. Additionally, during the evolutionary stage, balancing exploration and exploitation remains challenging. The fundamental issue stems from the widespread use of static preset parameters and globally uniform strategies, which can diminish algorithm effectiveness and lead to result homogenization. This article proposes an Adaptive Enhanced Quantum-inspired Simulated Bifurcation (AE-QSB) framework driven by population states. By leveraging perception indicators of four distinct population states, the QSB algorithm establishes a closed-loop strategy encompassing perception, decision-making, and execution. Within this framework, we introduce three complementary algorithms spanning a spectrum from efficient extremum seeking (ME-BSB), through population-level uniform refinement (SE-DSB), to density-aware adaptive scheduling (SG-DSB). On the medium-sized graph G22, both SE-DSB and SG-DSB achieve a mean gap below 0.05%, while ME-BSB attains the optimal trade-off between runtime and solution quality with a gap of 0.26% and the shortest single-run time. We compared AE-QSB variants with other algorithms across all benchmark graphs from G1 to G81. The results demonstrate that AE-QSB achieved the lowest mean gap on 74.6% of the graphs and the highest average approximation rate on 84.5% of the graphs. Ablation experiments further revealed that subgroup exploration and rescue mechanisms play crucial roles in both multifactor and single-factor components. This study demonstrates that population statistical information during dynamic evolution provides a computable and effective foundation for adaptive control, enabling quantum-inspired optimization methods to transition from fixed scheduling to data-driven closed-loop control.

Dongmei Liu, Jian Li, Xiubo Chen +1

State Key Laboratory of Networking and Switching Technology, Cyber Security Center, School of Cyberspace Security, Beijing University of Posts and Telecommunications, Beijing 100876, China

Combinatorial Optimization Quadratic Unconstrained Binary Optimization

Jun 22, 2026cs.AI

Joint Air Traffic Flow and Capacity Management via Answer Set Programming

Operational Air Traffic Flow and Capacity Management (ATFCM) balances flight demand with available sector capacity, to ensure safe and efficient operations. Mathematical models enhance operational ATFCM performance by framing demand-capacity balancing as an optimization problem, maximizing efficiency while adhering to safety constraints. However, SOTA research optimizes the aircraft trajectories (called ATFM) or the sector configuration (called DAC) separately. This leaves a research gap of whether joint optimization of ATFM and DAC can bring benefits. We partially address this limitation by introducing a joint ATFCM model with an encoding in Answer Set Programming (ASP). The ASP implementation is evaluated against two baselines applied to our joint model: a SOTA Mixed Integer Programming (MIP) model and an iterative CASA-based heuristic. Computational experiments utilize an instance generator fitted to historical OpenSky Network flight data. Our results indicate that the ASP model outperforms the MIP model, while ASP remains competitive against heuristics on small instances. Furthermore, while DAC has the largest improvement on solving performance compared to rerouting and delaying, unrestricted variants of DAC or rerouting lead to search space thrashing.

Alexander Beiser, Markus Hecher, Nysret Musliu +1

TU Wien, Vienna, Austria · University of Potsdam, Germany & CNRS, France

Air Traffic Management Intelligent Transportation Systems Combinatorial Optimization

Jun 22, 2026cs.CC

Learning-Augmented Algorithms for Online Vertex Cover

This paper studies learning-augmented online weighted vertex cover with advice and a parameter

λ\in (0,1)

. We consider two graph cases: bipartite graphs and general graphs. In both settings, the online algorithm must maintain a feasible vertex cover under irrevocable decisions. We show that these problems admit the same robustness--consistency tradeoffs as learning-augmented ski rental. For the bipartite graph model, we give a randomized algorithm that is

\frac{1}{1-e^{-λ}}

-robust and

\fracλ{1-e^{-λ}}

-consistent. For the general graph model, we give a deterministic algorithm that is

(1+\frac{1}λ)

-robust and

(1+λ)

-consistent. We prove that the tradeoffs above are optimal in both settings. We also validate the proposed algorithms through experiments on synthetic and real-world datasets.

Tianhang Lu, Runtian Ren, Shengcai Liu

Guangdong Provincial Key Laboratory of Brain-Inspired Intelligent Computation, Department of Computer Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China

Competitive Analysis Combinatorial Optimization Learning-Augmented Algorithms

Jun 22, 2026cs.LG

GeoRouteNet: Geometry-Enhanced Non-Autoregressive Neural Solver for the Traveling Salesman Problem

The traveling salesman problem (TSP) is a canonical NP-hard combinatorial optimization benchmark that tests the representational capacity and generalization of neural solvers. While non-autoregressive (NAR) approaches offer parallel inference, they often lack sufficient geometric inductive bias and stable training signals, leading to degraded performance under cross-scale and cross-distribution shifts. We propose GeoRouteNet, a geometry-enhanced NAR neural solver for Euclidean TSP. On the model side, GeoRouteNet incorporates centered node features, learnable radial distance basis functions, distance-aware graph attention with explicit edge messaging, LayerNorm-SwiGLU feed-forward blocks, and cross-layer attentive residual mixing. On the training side, we design multi-candidate self-comparison reinforcement learning (MCS-RL), which samples multiple candidate tours per instance, constructs adaptive baselines from greedy and peer candidates, and adds winner-candidate guidance with annealed entropy regularization. On 10,000 random TSP50 instances, GeoRouteNet achieves a 0.32% optimality gap under Beam-1000 decoding. On TSP100, the gap is 1.26%. On 27 stratified TSPLIB EUC_2D instances, the overall gap drops from 17.12% (NAR4TSP reproduction) to 3.60%, while batch inference throughput substantially exceeds that of Concorde and LKH3. Ablation studies confirm that geometric structure enhancement and multi-candidate training are complementary: structure improvements dominate cross-distribution gains, while MCS-RL further stabilizes solution quality when paired with a strong geometric encoder.

Xiang Li

College of Computer Science, Yangtze University, Jingzhou, China

Traveling Salesperson Problem Graph Neural Networks Reinforcement Learning Combinatorial Optimization RL for Combinatorial Optimization Neural Combinatorial Optimization

Jun 20, 2026cs.LG

Meta-Reinforcement Learning via Evolution for Multi-Objective Combinatorial Supply Chain Optimisation

Meta-reinforcement learning is a promising approach to multi-objective optimisation because it enables rapid policy adaptation across changing environments and preference settings. However, conventional few-shot methods usually fine-tune from a single shared meta-policy, which can reduce solution diversity and limit exploration of the Pareto front, especially in high-dimensional combinatorial problems such as supply chain optimisation. We propose a population-based Meta-reinforcement learning framework that combines decomposition with evolutionary search in scalarisation weight space. The framework maintains a population of weight vectors, each associated with a distinct meta-policy trained through gradient-based meta-learning, and iteratively refines this population through elitist selection, crossover, and mutation guided by hypervolume and entropy contributions. We evaluate the method in a multi-objective supply chain setting with conflicting economic, environmental, and social goals, and further test its generality on standard reinforcement learning problems. The results show that the proposed approach yields more diverse, better distributed Pareto front approximations, improves cross-task adaptation, increases hypervolume by up to 32% over Meta-multi-objective reinforcement learning in the complex case, and attains the lowest average Hausdorff distance among all compared methods.

Rifny Rachman, Bahrul Ilmi Nasution, Josh Tingey +3

The University of Manchester, United Kingdom · Peak AI, Ltd, United Kingdom

Multi-Objective Reinforcement Learning Multi-Objective Evolutionary Optimization Combinatorial Optimization Meta-Reinforcement Learning RL for Combinatorial Optimization Multi-Objective Optimization

Jun 19, 2026cs.LG

Fusing Backdoors, Machine Learning, and Optimization for Large-Scale Parametric Mixed-Integer Programs

Large-scale optimization problems are often solved repeatedly under similar structural conditions, leading to substantial computational overhead. This occurs in applications such as power systems, transportation, and supply chain networks, where the underlying structure is fixed while parameters frequently vary under perturbations. This paper proposes a Learning to Optimize (LTO) framework that accelerates the solution of large-scale general mixed-integer problems by leveraging the concept of a backdoor, i.e., a subset of variables that drive most of the computational complexity. The proposed BIPC framework consists of three phases. Phase I is an identification procedure that discovers a backdoor for a set of instances in the distribution. Phase II uses supervised learning to develop machine learning models that, given an instance, predict values for bounded-domain backdoor variables and intervals for wide-domain backdoor variables. These predictions define a reduced optimization problem where the predictions constrain the backdoor variables, while the other variables remain free. Phase III optimizes this reduced problem and, if necessary, applies a correction step to restore feasibility or the optimality guarantees. Experiments on real-world, large-scale problems show substantial reductions in solution time with only a limited loss in solution quality. The framework enables organizations to solve large-scale optimization problems efficiently in the presence of frequent perturbations, such as unexpected events, demand fluctuations, or operational changes. Because these changes affect parameters rather than the problem structure, BIPC can quickly provide high-quality, feasible solutions, offering a practical approach to integrating machine learning into existing optimization pipelines.

El Mehdi Er Raqabi, Pascal Van Hentenryck

Department of Operations and Decision Systems, Université Laval, Québec, Canada · H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, USA

Learning to Optimize Combinatorial Optimization Constrained Optimization Mixed-Integer QP

Jun 19, 2026cs.GT

Simultaneously Efficient Allocation of Indivisible Items Across Multiple Dimensions

Many allocation problems are intrinsically multidimensional, since an item may contribute differently to several criteria, and optimizing a single aggregate objective can hide severe losses in other dimensions. We study how much efficiency can be guaranteed simultaneously when indivisible items have multiple attributes. To this end, we introduce the \emph{multidimensional efficient allocation} (MDEA) model, where each agent has an additive valuation in each dimension, and investigate simultaneous efficiency under utilitarian social welfare (USW) and egalitarian social welfare (ESW). Our results reveal a sharp worst-case frontier. For exact efficiency, maximizing the number of dimensions attaining the USW optimum admits a

c/\ell

-approximation for every fixed constant

c

, and this dependence on the number

\ell

of dimensions is essentially unavoidable; for ESW, even deciding whether two dimensions can be optimized simultaneously is NP-hard with binary valuations. For approximate simultaneous efficiency in every dimension, we identify a tight threshold of order

1/\ell

, showing that such guarantees always exist for both USW and ESW, while any asymptotically better dependence on

\ell

is impossible, even for binary valuations. Finally, we introduce three natural multidimensional Pareto notions and characterize both their relationships and their computational complexity.

Yasushi Kawase, Bodhayan Roy, Mohammad Azharuddin Sanpui

Chuo University, Tokyo, Japan · Indian Institute of Technology Kharagpur, Kharagpur, India

Combinatorial Optimization Approximation Algorithms Multi-Objective Optimization Pareto Optimization

Jun 17, 2026cs.AR

A Tool for the Synthesis of Adaptive Probabilistic Processors Based on the Ising Model

This work presents a tool for the synthesis and simulation of probabilistic architectures for solving combinatorial optimization problems by mapping them to the Ising model. The proposed approach automatically constructs the Ising Hamiltonian and determines the number of probabilistic elements (p-bits) based on problem characteristics such as size and topology. Furthermore, the tool introduces an adaptive strategy for selecting the most suitable update algorithm among Gibbs Sampling, Simulated Annealing (SA), Simulated Quantum Annealing (SQA), and cluster-based methods. Experimental results using benchmark problems demonstrate improved convergence behavior and flexibility compared to fixed approaches. The proposed framework enables systematic evaluation of probabilistic computing strategies and supports the development of future hardware implementations based on MTJs and p-bits.

Jonathan Juracy Carneiro da Silva, Leonardo R. Gobatto, Jose Rodrigo Azambuja

Federal University of Rio Grande do Sul (UFRGS) – Institute of Informatics – PGMicro, Porto Alegre, Brazil · Center for Embedded Devices and Research in Digital Agriculture (CEDRA), S˜ao Leopoldo, Brazil

Algorithm Selection Metaheuristic Optimization Combinatorial Optimization

Jun 17, 2026cs.LG

AGDN: Learning to Solve Traveling Salesman Problem with Anisotropic Graph Diffusion Network

The Traveling Salesman Problem (TSP) is a cornerstone of combinatorial optimization and arises in many practical scenarios. Although graph-based learning approaches have been explored for TSP, the question of how to exploit graph structure more effectively remains open. We present the Anisotropic Graph Diffusion Network (AGDN), a new Graph Neural Network framework designed to solve TSP. Our method tackles two central difficulties: (1) the lack of informative topological prior in fully connected TSP graphs, and (2) losing connected nodes in the optimal solution after the commonly used graph sparsification techniques. To overcome these issues, we construct a MixScore transition matrix that merges node similarity with pairwise distance, and we develop an anisotropic graph diffusion strategy that supports efficient information exchange across multiple hops. Comprehensive experiments spanning diverse instance sizes and node distributions show that AGDN consistently outperforms existing methods while keeping computation time competitive. Furthermore, AGDN generalizes well to problem sizes and distributions beyond those seen during training. The implementation is publicly available at: https://github.com/LabRAI/AGDN.

Bolin Shen, Ziwei Huang, Zhiguang Cao +1

Florida State University · Tallahassee, United States · Singapore Management University +1

Traveling Salesperson Problem Graph Neural Networks Combinatorial Optimization Neural Combinatorial Optimization Graph Diffusion

Jun 17, 2026cs.LG

Prioritizing Search Space Regions in the Low Autocorrelation Binary Sequences Problem

Low autocorrelation binary sequences problem (LABS) is a hard combinatorial optimization challenge with important applications in communications, signal processing, and satellite navigation. This paper proposes a hybrid search framework that combines Thompson sampling with parallel self-avoiding walks to adaptively allocate computational effort across restriction classes of the LABS search space. By modeling partitions as arms in a multi-armed bandit setting, the proposed method dynamically shifts search resources toward partitions that empirically produce higher merit factors while maintaining exploration of less-sampled regions. The approach is further accelerated through GPU-parallel execution, shared posterior updates, efficient neighborhood evaluation, and a Bloom filter for cycle prevention. In addition, we use a two-stage optimization strategy that first searches constrained partitioned skew-symmetric spaces and then refines the best candidates in the unrestricted space. Experiments on long binary sequences show that the proposed method improves the previously best-known results for 35 sequence lengths in the range

450 \le L \le 527

and for

L=573

. In particular, we report a new longest sequence with merit factor exceeding

8.0

, obtained for

L=451

. The results also show that Thompson sampling effectively prioritizes partitions with better observed performance, confirming the value of online, data-driven resource allocation in LABS optimization. Overall, the proposed framework provides a scalable and effective strategy for high-performance merit factor maximization.

Blaž Pšeničnik, Borko Bošković, Jan Popić +1

Computer Architecture and Languages Laboratory Faculty of Electrical Engineering and Computer Science University of Maribor · Computer Architecture and Languages LaboratoryJun Faculty of Electrical Engineering and Computer Science University of Maribor · Computer Architecture and Languages Laboratory Faculty of Electrical Engineering and Computer Science University of Maribor[cs.LG]

Combinatorial Optimization

Jun 17, 2026cs.RO

Two-Phase Bilevel Search for the Moving-Target Traveling Salesman Problem with Moving Obstacles

The Moving-Target Traveling Salesman Problem (MT-TSP) seeks a minimum cost trajectory for an agent that departs from a static depot, visits a set of moving targets, each within one of their assigned time windows, and returns to the depot. In this article, we study the Moving-Target Traveling Salesman Problem with Moving Obstacles (MT-TSP-MO), a generalization of the MT-TSP where the agent trajectory must avoid moving obstacles. We present a Mixed-Integer Conic Programming (MICP) formulation that can be solved using off-the-shelf solvers, as well as a fast and scalable Two-Phase Bilevel Search (TPBS) algorithm that computes high-quality feasible solutions for the problem. We evaluate our approaches against an existing baseline algorithm on a broad range of problem instances with up to 40 targets and 40 obstacles. The results demonstrate that both the proposed methods significantly outperform the baseline with respect to success rates, solution costs, and computation time.

Allen George Philip, Anoop Bhat, Sivakumar Rathinam +1

Mechanical Engineering, Texas A&M University, College Station, TX 77843-3123 · Robotics Institute, Carnegie Mellon University, 5000 Forbes Ave., Pittsburgh, PA 15213, USA · Mechanical Engineering, and Computer Science and Engineering, Texas A&M University, College Station, TX 77843-3123

Traveling Salesperson Problem Combinatorial Optimization Constrained Optimization Dynamic Obstacle Avoidance Robot Motion Planning

Jun 17, 2026quant-ph

Dimensionality Reduction of QAOA Parameter Space with Kernel PCA for Max-Cut

The Quantum Approximate Optimization Algorithm (QAOA) is a leading variational algorithm for combinatorial optimization on near term quantum devices. As circuit depth increases, the number of optimization parameters grows, making the search landscape increasingly nonlinear and difficult to optimize. Previous studies have shown that optimal QAOA parameters often lie on a low dimensional manifold that can be approximated using Principal Component Analysis (PCA) at shallow circuit depths. However, the effectiveness of PCA decreases at higher depths because the underlying parameter manifold becomes increasingly nonlinear. In this work, we investigate Kernel Principal Component Analysis (KPCA) with a radial basis function kernel as a nonlinear dimensionality reduction technique for QAOA parameter optimization. The model is trained using 200 graphs from each of 3 graph families, namely Erdos-Renyi, Barabasi-Albert, and Watts-Strogatz, with graph sizes ranging from 7 to 10 nodes. Performance is evaluated on 30 test graphs containing 12 nodes at circuit depths 1, 2, 4, and 8. Experimental results demonstrate that KPCA consistently outperforms PCA at deeper circuit depths across all graph families. At depth 8, KPCA achieves approximation ratios above 0.86, while PCA declines to approximately 0.81 to 0.83. Both methods reduce the number of quantum circuit evaluations by more than 93 percent relative to unrestricted QAOA optimization. These findings suggest that nonlinear kernel methods more effectively capture the structure of the QAOA parameter manifold and provide a practical approach for scaling variational quantum optimization to deeper circuits.

Sidharth Brahmandam, Vayd Ramkumar

Naperville North High School · Independent Researcher

Principal Component Analysis Combinatorial Optimization Dimensionality Reduction Quantum Approximate Optimization Algorithm

Jun 16, 2026cs.RO

N(CO) $^2$ : Neural Combinatorial Optimization with Chance Constraints to Solve Stochastic Orienteering

Neural combinatorial optimization (NCO) offers a promising alternative to traditional heuristic-based methods for solving complex graph optimization problems by proposing to learn heuristics through data. This class of problems frequently arises in automation, as it can be used to model a variety of applications. While NCO has been extensively studied for deterministic combinatorial optimization problems, there are only a few works that aim to solve stochastic combinatorial optimization problems. In this work, we present N(CO)

^2

: Neural Combinatorial Optimization with Chance cOnstraints to solve the Stochastic Orienteering Problem (SOP) without the use of hand-crafted heuristics. By integrating a reinforcement learning (RL) framework, the model optimizes path selection under uncertainty, effectively balancing exploration and exploitation. Empirical results demonstrate that our method generalizes well across diverse SOP instances, achieving competitive performance compared to the state-of-the-art mixed-integer linear program (MILP) for the task. The proposed approach reduces human effort in heuristic design while enabling adaptive and efficient decision-making in uncertain environments.

Anas Saeed, Marcos Abel Zuzuárregui, Stefano Carpin

Department of Computer Science and Engineering, University of California, Merced, CA, USA

Stochastic Optimization Chance-Constrained Optimization Combinatorial Optimization RL for Combinatorial Optimization Neural Combinatorial Optimization

Jun 16, 2026cs.LG

Deep Reinforcement Learning for Minimum Zero-Forcing Sets

This paper explores the problem of finding the minimum zero-forcing set on undirected graphs and proposes an adapted machine-learning framework to solve the problem. The minimum zero-forcing set problem is a graph coloring problem where the color of an initial set of nodes propagates throughout a network. The set of nodes is zero-forcing if it forces all uncolored nodes to change color under the constraint of the color-change rule. There are several applications to this problem across different domains such as network science, network control, and designing logical circuits. Finding the minimum zero-forcing set is shown to be NP-hard. We propose a reinforcement learning framework, SD-ZFS, that adapts the S2V-DQN architecture to the ZFS problem. We train several models on this adapted framework and analyze the performance across graph datasets that have varying structures. We evaluate how the models trained on the framework generalize, scale, and transfer to different network types. The results demonstrate the effectiveness of the framework when compared against the optimal solution and greedy heuristic. We provide further insight into how the ZFS problem can be solved through machine-learning and the influence of network structure on the problem.

Steve Halley, Maurício Gruppi

Department of Computing Sciences, Villanova University Villanova, Pennsylvania, USA

Reinforcement Learning Combinatorial Optimization RL for Combinatorial Optimization Neural Combinatorial Optimization

Jun 16, 2026cs.NI

OmniPlan: An Adaptive Framework for Timely and Near-Optimal Network Planning Optimization

Network planning optimization is a fundamental problem across diverse domains, including transportation systems, communication networks, and power grids. It requires simultaneous optimization of multiple competing objectives under complex constraints. Existing network planning optimization frameworks rely on mixed integer programming (MIP) solvers, heuristics, and deep reinforcement learning (DRL) models to compute planning decisions. However, they lack effective adaptability to diverse and dynamic user intents, thus leading to the trade-off between execution time and optimality. In this paper, we propose OmniPlan, an adaptive framework that achieves both timeliness and near-optimality in network planning optimization. To achieve the adaptability lacking in existing solutions, OmniPlan employs a large language model (LLM)-based interpreter to convert heterogeneous natural-language intents into a unified and quantifiable user-preference vector. Then it employs a mixture-of-experts architecture that integrates MIP solvers, heuristics, and DRL models as specialized experts, where OmniPlan adapts to diverse intents by dynamically selecting timely and near-optimal experts. Finally, it incorporates a DRL-based expert configuration module that fine-tunes optimization objective weights to align planning decisions with user-specific preferences. We evaluate OmniPlan with a representative real-world workload, i.e., distributed machine learning (ML), where we leverage OmniPlan to offload a wide spectrum of ML inference tasks, e.g., decision trees, SVM, naive Bayes, XGBoost, and random forests, onto a network of hardware devices. Our experiments on a real-world testbed indicate that OmniPlan achieves near-optimal and low-execution-time offloading for real-world ML inference tasks, reducing latency by up to 97.8% and network device resource consumption by up to 11.5%.

Longlong Zhu, Jiashuo Yu, Zedi Chen +12

Zhejiang University Hangzhou, Zhejiang, China · College of Computer and Data Science Fuzhou University Fuzhou, Fujian, China · Yangzhou University Yangzhou, Jiangsu, China +1

Algorithm Selection Large Language Model-Guided Optimization Combinatorial Optimization

Jun 15, 2026cs.AI

Phase-Aware Guidance Injection for Recurrent MAPPO in Assembly-Line Disruption Recovery

Disruption recovery in industrial assembly lines requires timely decisions under machine faults, worker absence, and emergency orders. Existing methods either rely on rigid handcrafted recovery logic or learn adaptive policies that do not readily exploit heterogeneous external recovery knowledge at decision time to reduce abnormal recovery time (ART) and preserve on-time delivery (OTD). To address this gap, we propose a phase-aware guidance injection framework that augments a trained recurrent MAPPO (RMAPPO) scheduling policy through logit-level action bias during evaluation. The framework provides a unified decision-time interface for rule-based, replay-based, and online LLM-based guidance, while activating intervention only during abnormal and recovery phases. Experiments on a custom AssemblyLineEnv show that high-quality rule guidance yields the strongest gains, replay-based guidance degrades smoothly under imperfect availability, and online LLM guidance still provides useful intermediate improvements. These results show that decision-time guidance injection can exploit heterogeneous recovery hints without redesigning the actor.

Xin Huang, Yongcai Wang, Fengyi Zhang +3

School of Information, Renmin University of China, Beijing 100872, China · State Key Laboratory of Multimodal Artificial Intelligence Systems, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China · The Information Science Academy, China Electronics Technology Group Corporation, Beijing 100043, China +2

Combinatorial Optimization LLM-Guided RL Decision-Making under Uncertainty Inference-Time Guidance Multi-Agent Reinforcement Learning

Jun 13, 2026cs.NE

Large Language Model-Driven Cooperative Operator Ensemble Evolution for Permutation Flow Shop Scheduling

The permutation flow shop scheduling problem (PFSP) is a classical NP-hard combinatorial optimization problem in intelligent manufacturing. In practice, PFSP is commonly addressed using metaheuristic algorithms, among which the iterated greedy (IG) algorithm is widely adopted due to its simplicity and strong empirical performance. However, classical IG relies on a single fixed destruction operator, which often limits exploration and leads to search stagnation on large and complex problem instances. To address this issue, this work proposes a multi-operator IG algorithm, termed IG-DOE, which enhances exploration by switching among heterogeneous destruction operators along a single search trajectory. The core mechanism, called stagnation-triggered sequential switching, activates the next destruction operator in an ordered destruction operator ensemble (DOE) when stagnation is detected, thereby enriching the perturbation behavior of classical IG. Moreover, to reduce reliance on expert-crafted operators, a large language model (LLM)-assisted framework, termed SCOE, is introduced to automatically construct a high-quality DOE through stagewise evolution, state-awareness, and cooperative evaluation. Experiments on the challenging VRF-hard-large benchmark show that the DOE evolved from smaller problem instances generalizes well to larger unseen instances. Under the same CPU-time limit, IG-DOE obtained much better average performance than QIG, a state-of-the-art IG algorithm. Additional experiments on real-world industrial-data-derived instances further show that the evolved DOE can generalize effectively to different data distributions without additional adaptation.

Rui Xu, Yufan Liao, Haoze Lv +3

School of Business, Hohai University, Nanjing 211100, China · Guangdong Provincial Key Laboratory of Brain-inspired Intelligent Computation, Department of Computer Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China · School of Engineering and Computer Science, Victoria University of Wellington, Wellington 6140, New Zealand

Evolutionary Optimization Metaheuristic Optimization Large Language Model-Guided Optimization Combinatorial Optimization

Jun 11, 2026cs.DS

Learning-Augmented Approximation for Unrelated-Machines Makespan Scheduling

Recently, Antoniadis et al. (ICLR 2025) proposed a framework for incorporating predictions to approximate NP-hard selection problems. Despite its simplicity, this approach tightly matches theoretical lower bounds, making its generalization highly compelling. We address an open question raised in the work of Antoniadis et al., concerning the extension of this approach to other important problems outside the class of selection problems, such as scheduling. We develop a learning-augmented algorithm for the makespan minimization problem on unrelated machines, denoted by

R\|C_{\max}

. By using predictions of heavy job assignments, we achieve a polynomial-time

(1+\varepsilon)

-approximation for accurate predictions that smoothly degrades to a worst-case 2-approximation as the error increases. We conclude our work with an empirical analysis of our method.

Kaito Baba, Evripidis Bampis, Giorgos Mitropoulos

The University of Tokyo, Tokyo, Japan · Sorbonne Université, CNRS, LIP6, F-75005 Paris, France

Combinatorial Optimization Learning-Augmented Algorithms Approximation Algorithms

Jun 10, 2026cs.NI

Free-Placement Optimization of Ground Station Locations for Low-Earth Orbit Satellites

Rapidly expanding low Earth orbit satellite constellations are placing increasing demands on terrestrial ground networks, motivating the development of more efficient ground station network designs. Current approaches select sites from predefined locations, limiting optimization to existing infrastructure and constraining performance. In contrast, free-placement optimization operates over a continuous spatial domain on Earth, broadening the search space and allowing higher-throughput configurations at the cost of potentially requiring new infrastructure deployment. In this work, we introduce SCORE (Sequential Cyclic Optimization via Refinement & Evaluation), a two-stage free-placement method for ground station design. SCORE combines sequential coordinate selection with cyclic refinement to manage high-dimensionality, non-convexity, and local minima that challenge global optimizers. We benchmark SCORE against one-shot methods such as differential evolution (DE) and integer programming approaches using locations from Kongsberg Satellite Services and the World Teleport Association. Tests across two commercial Earth observation constellations (Capella Space and ICEYE) and one synthetic Walker-Star constellation show that SCORE requires up to 5x fewer function evaluations to converge relative to DE while improving downlink throughput by up to 13%. Compared to fixed-site methods, unconstrained SCORE achieves up to 15% greater total downlink, establishing a strong empirical performance benchmark for flexible placement; infrastructure-constrained SCORE retains over 92% of this gain while restricting placement to within proximity of existing fiber and power infrastructure. We also explore trade-offs between expanding existing stations and deploying new sites, informing future ground network design for operational constellations.

Grace Ra Kim, Duncan Eddy, Vedant Srinivas +1

Stanford University, Stanford, CA, 94305 · Stanford, CA · Stanford University, Stanford, CA

Combinatorial Optimization Wireless Communications LEO Satellite Networks

Jun 9, 2026cs.LG

Baseline-Free Policy Optimization for Neural Combinatorial Optimization

Neural combinatorial optimization (NCO) trains autoregressive policies to solve routing problems. The standard training algorithm, REINFORCE with a rollout baseline, requires maintaining and periodically updating a frozen copy of the policy for variance reduction. This baseline introduces a structural vulnerability: on harder instances, a poor baseline produces noisy gradient estimates that can destabilize training. We evaluate Group Relative Policy Optimization (GRPO), an algorithm from large language model alignment that eliminates the baseline entirely by normalizing advantages within groups of sampled trajectories. In a controlled comparison of five RL algorithms on TSP and CVRP benchmarks within the RL4CO framework, we find that: (i) GRPO avoids the training collapse observed with REINFORCE on TSP-100, where performance degrades from cost 9.8 to 52.1 immediately after the warmup phase and does not recover under extended training; (ii) at matched gradient updates, GRPO achieves solution quality within 2% of POMO, a strong AM-based multi-start baseline, while requiring no external baseline; and (iii) P3O, a pairwise preference algorithm also from the alignment literature, is competitive on TSP but shows higher variability on CVRP. These results identify GRPO as a promising baseline-free alternative for NCO, particularly in settings where baseline-dependent training becomes fragile.

Carlos S. Sepúlveda, Gonzalo A. Ruz

Traveling Salesperson Problem Group Relative Policy Optimization Combinatorial Optimization Vehicle Routing RL for Combinatorial Optimization Neural Combinatorial Optimization

Jun 8, 2026cs.NE

Hybrid Metaheuristic Combining the Dragonfly Algorithm and Tabu Search for the Traveling Salesman Problem

The Traveling Salesman Problem (TSP) is a classical NP-hard combinatorial optimization problem that aims to find the shortest Hamiltonian cycle visiting each city exactly once and returning to the starting point. This paper proposes a hybrid metaheuristic for the TSP by combining the Dragonfly Algorithm (DA), a swarm-intelligence-based global search method, with Tabu Search (TS), a memory-based local search technique. The proposed method follows a High-Level Relay Hybridization (HRH) scheme, in which DA is first used to explore the solution space and generate a promising initial tour, while TS subsequently refines this solution through neighbourhood-based improvement and tabu memory. The hybrid approach is evaluated on standard TSPLIB benchmark instances, including burma14, att48, and ch150, and compared with standalone DA, standalone TS, and several classical metaheuristics such as Genetic Algorithm, Ant Colony Optimization, Particle Swarm Optimization, and Random Search. A systematic grid-search procedure is also conducted to study the influence of the main hyperparameters on solution quality and execution time. The experimental results indicate that the proposed hybrid can improve tour quality compared with the standalone DA and TS on the tested instances, highlighting the benefit of combining global exploration with local exploitation. However, the results also suggest that performance remains sensitive to parameter settings and problem size, motivating further validation on larger benchmarks and stronger TSP-specific baselines.

Ammar Bouketta

Ecole Nationale Superieure d’Informatique (ESI), Algiers, Algeria

Traveling Salesperson Problem Metaheuristic Optimization Combinatorial Optimization