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This paper surveys the trend of leveraging machine learning to solve mixed integer programming (MIP) problems. Theoretically, MIP is an NP-hard problem, and most of the combinatorial optimization (CO) problems can be formulated as the MIP.…

Artificial Intelligence · Computer Science 2022-03-08 Jiayi Zhang , Chang Liu , Junchi Yan , Xijun Li , Hui-Ling Zhen , Mingxuan Yuan

The Traveling Salesman Problem (TSP) is a classic NP-hard combinatorial optimization task with numerous practical applications. Classic heuristic solvers can attain near-optimal performance for small problem instances, but become…

Machine Learning · Computer Science 2025-08-13 Michael Li , Eric Bae , Christopher Haberland , Natasha Jaques

Many problems in real life can be converted to combinatorial optimization problems (COPs) on graphs, that is to find a best node state configuration or a network structure such that the designed objective function is optimized under some…

Machine Learning · Computer Science 2019-09-17 Jing Liu , Fei Gao , Jiang Zhang

The design of good heuristics or approximation algorithms for NP-hard combinatorial optimization problems often requires significant specialized knowledge and trial-and-error. Can we automate this challenging, tedious process, and learn the…

Machine Learning · Computer Science 2018-02-23 Hanjun Dai , Elias B. Khalil , Yuyu Zhang , Bistra Dilkina , Le Song

Recent neural combinatorial optimization (NCO) methods have shown promising problem-solving ability without requiring domain-specific expertise. Most existing NCO methods use training and testing data with a fixed constraint value and lack…

Machine Learning · Computer Science 2025-10-31 Fu Luo , Yaoxin Wu , Zhi Zheng , Zhenkun Wang

Engineers learn from every design they create, building intuition that helps them quickly identify promising solutions for new problems. Topology optimization (TO) - a well-established computational method for designing structures with…

Computational Engineering, Finance, and Science · Computer Science 2025-02-05 Igor Kuszczak , Gawel Kus , Federico Bosi , Miguel A. Bessa

The Traveling Salesman Problem (TSP) is a well-known NP-hard combinatorial optimization problem with wide-ranging applications in logistics, routing, and intelligent systems. Due to its factorial complexity, solving large-scale instances…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-05-27 Rabab Alkhalifa , Fatima Alkhomayes , Boushra Almazroua , Dana Alhaidan , Maryam Alothman , Jumana Almuhaidib

In the last years, there has been a great interest in machine-learning-based heuristics for solving NP-hard combinatorial optimization problems. The developed methods have shown potential on many optimization problems. In this paper, we…

Optimization and Control · Mathematics 2022-12-19 Mouad Morabit , Guy Desaulniers , Andrea Lodi

Combinatorial optimization is the field devoted to the study and practice of algorithms that solve NP-hard problems. As Machine Learning (ML) and deep learning have popularized, several research groups have started to use ML to solve…

Artificial Intelligence · Computer Science 2019-10-01 Antoine François , Quentin Cappart , Louis-Martin Rousseau

In real-world recommendation scenarios, users engage with items through various types of behaviors. Leveraging diversified user behavior information for learning can enhance the recommendation of target behaviors (e.g., buy), as…

Information Retrieval · Computer Science 2025-02-05 Chenhao Zhai , Chang Meng , Yu Yang , Kexin Zhang , Xuhao Zhao , Xiu Li

Finding a feasible and prompt solution to the Vehicle Routing Problem (VRP) is a prerequisite for efficient freight transportation, seamless logistics, and sustainable mobility. Traditional optimization methods reach their limits when…

Machine Learning · Computer Science 2024-11-08 Elija Deineko , Carina Kehrt

This paper presents a framework to tackle combinatorial optimization problems using neural networks and reinforcement learning. We focus on the traveling salesman problem (TSP) and train a recurrent network that, given a set of city…

Artificial Intelligence · Computer Science 2017-01-16 Irwan Bello , Hieu Pham , Quoc V. Le , Mohammad Norouzi , Samy Bengio

In the last decade, a plethora of algorithms for single-objective Boolean optimization has been proposed that rely on the iterative usage of a highly effective Propositional Satisfiability (SAT) solver. But the use of SAT solvers in…

Artificial Intelligence · Computer Science 2022-04-26 João Cortes , Inês Lynce , Vasco Manquinho

This paper introduces the Random-Key Optimizer (RKO), a versatile and efficient stochastic local search method tailored for combinatorial optimization problems. Using the random-key concept, RKO encodes solutions as vectors of random keys…

Although several surveys on Neural Combinatorial Optimization (NCO) solvers specifically designed to solve Vehicle Routing Problems (VRPs) have been conducted, they did not cover the state-of-the-art (SOTA) NCO solvers emerged recently.…

Artificial Intelligence · Computer Science 2025-04-28 Xuan Wu , Di Wang , Lijie Wen , Yubin Xiao , Chunguo Wu , Yuesong Wu , Chaoyu Yu , Douglas L. Maskell , You Zhou

Neural Combinatorial Optimization attempts to learn good heuristics for solving a set of problems using Neural Network models and Reinforcement Learning. Recently, its good performance has encouraged many practitioners to develop neural…

Artificial Intelligence · Computer Science 2022-05-04 Andoni I. Garmendia , Josu Ceberio , Alexander Mendiburu

Combinatorial optimization problems (COPs) on the graph with real-life applications are canonical challenges in Computer Science. The difficulty of finding quality labels for problem instances holds back leveraging supervised learning…

Machine Learning · Computer Science 2021-08-10 Mostafa Pashazadeh , Kui Wu

Multi-objective combinatorial optimization (MOCO) problems are prevalent in various real-world applications. Most existing neural MOCO methods rely on problem decomposition to transform an MOCO problem into a series of singe-objective…

Machine Learning · Computer Science 2025-01-28 Yongfan Lu , Zixiang Di , Bingdong Li , Shengcai Liu , Hong Qian , Peng Yang , Ke Tang , Aimin Zhou

This article explores the integration of deep learning models into combinatorial optimization pipelines, specifically targeting NP-hard problems. Traditional exact algorithms for such problems often rely on heuristic criteria to guide the…

Machine Learning · Computer Science 2026-04-28 Lorenzo Sciandra , Roberto Esposito , Andrea Cesare Grosso , Laura Sacerdote , Cristina Zucca

The constructive approach within Neural Combinatorial Optimization (NCO) treats a combinatorial optimization problem as a finite Markov decision process, where solutions are built incrementally through a sequence of decisions guided by a…

Machine Learning · Computer Science 2024-11-05 Jonathan Pirnay , Dominik G. Grimm