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Recent work on neural scaling laws demonstrates that model performance scales predictably with compute budget, model size, and dataset size. In this work, we develop scaling laws based on problem complexity. We analyze two fundamental…

Machine Learning · Computer Science 2025-10-28 Lowell Weissman , Michael Krumdick , A. Lynn Abbott

Neural implicit mapping has emerged as a powerful paradigm for robotic navigation and scene understanding. However, real-world robotic deployment requires continual adaptation to changing environments under strict memory and computation…

Robotics · Computer Science 2026-05-29 Xunlan Zhou , Hongrui Zhao , Negar Mehr

This paper reviews the current progress in applying machine learning (ML) tools to solve NP-hard combinatorial optimization problems, with a focus on routing problems such as the traveling salesman problem (TSP) and the vehicle routing…

Artificial Intelligence · Computer Science 2025-10-09 Fangting Zhou , Attila Lischka , Balazs Kulcsar , Jiaming Wu , Morteza Haghir Chehreghani , Gilbert Laporte

Numerous Neural Combinatorial Optimization (NCO) solvers have been proposed to address Vehicle Routing Problems (VRPs). However, most of these solvers focus exclusively on single-vehicle VRP variants, overlooking the more realistic min-max…

Machine Learning · Computer Science 2026-03-17 Xuan Wu , Di Wang , Chunguo Wu , Kaifang Qi , Chunyan Miao , Yubin Xiao , Jian Zhang , You Zhou

The performance of Conflict-Driven Clause Learning solvers hinges on internal heuristics, yet the heterogeneity of SAT problems makes a single, universally optimal configuration unattainable. While prior automated methods can find…

Artificial Intelligence · Computer Science 2025-09-17 Minyu Chen , Guoqiang Li

Multi-objective unconstrained combinatorial optimization problems (MUCO) are in general hard to solve, i.e., the corresponding decision problem is NP-hard and the outcome set is intractable. In this paper we explore special cases of MUCO…

Discrete Mathematics · Computer Science 2024-12-03 José Rui Figueira , Kathrin Klamroth , Michael Stiglmayr , Julia Sudhoff Santos

The surge of explainable artificial intelligence methods seeks to enhance transparency and explainability in machine learning models. At the same time, there is a growing demand for explaining decisions taken through complex algorithms used…

Optimization and Control · Mathematics 2025-06-19 Daan Otto , Jannis Kurtz , S. Ilker Birbil

We introduce a framework for applying metaheuristic algorithms, such as ant colony optimization (ACO), to combinatorial optimization problems (COPs) like the traveling salesman problem (TSP). The framework consists of three sequential…

Neural and Evolutionary Computing · Computer Science 2025-10-07 Ethan Davis

Routing Problems are central to many real-world applications, yet remain challenging due to their (NP-)hard nature. Amongst existing approaches, heuristics often offer the best trade-off between quality and scalability, making them suitable…

Artificial Intelligence · Computer Science 2025-11-04 Felix Chalumeau , Refiloe Shabe , Noah De Nicola , Arnu Pretorius , Thomas D. Barrett , Nathan Grinsztajn

Automated machine learning aims to automate the whole process of machine learning, including model configuration. In this paper, we focus on automated hyperparameter optimization (HPO) based on sequential model-based optimization (SMBO).…

Machine Learning · Computer Science 2019-09-11 Ying Wei , Peilin Zhao , Huaxiu Yao , Junzhou Huang

Many real-world problems can be formulated as a constrained Traveling Salesman Problem (TSP). However, the constraints are always complex and numerous, making the TSPs challenging to solve. When the number of complicated constraints grows,…

Artificial Intelligence · Computer Science 2024-03-11 Jingxiao Chen , Ziqin Gong , Minghuan Liu , Jun Wang , Yong Yu , Weinan Zhang

Heuristic algorithms such as simulated annealing, Concorde, and METIS are effective and widely used approaches to find solutions to combinatorial optimization problems. However, they are limited by the high sample complexity required to…

Machine Learning · Computer Science 2019-06-18 Qingpeng Cai , Will Hang , Azalia Mirhoseini , George Tucker , Jingtao Wang , Wei Wei

This paper proposes a problem-independent GRASP metaheuristic using the random-key optimizer (RKO) paradigm. GRASP (greedy randomized adaptive search procedure) is a metaheuristic for combinatorial optimization that repeatedly applies a…

Neural and Evolutionary Computing · Computer Science 2024-11-08 Antonio A. Chaves , Mauricio G. C. Resende , Ricardo M. A. Silva

Model-free deep-reinforcement-based learning algorithms have been applied to a range of COPs~\cite{bello2016neural}~\cite{kool2018attention}~\cite{nazari2018reinforcement}. However, these approaches suffer from two key challenges when…

Machine Learning · Computer Science 2022-06-01 Nasrin Sultana , Jeffrey Chan , Tabinda Sarwar , A. K. Qin

Over the recent years, reinforcement learning (RL) starts to show promising results in tackling combinatorial optimization (CO) problems, in particular when coupled with curriculum learning to facilitate training. Despite emerging empirical…

Machine Learning · Computer Science 2023-11-07 Runlong Zhou , Zelin He , Yuandong Tian , Yi Wu , Simon S. Du

An increasingly popular method for solving a constrained combinatorial optimisation problem is to first convert it into a quadratic unconstrained binary optimisation (QUBO) problem, and solve it using a standard QUBO solver. However, this…

Machine Learning · Computer Science 2021-03-22 Tian Huang , Siong Thye Goh , Sabrish Gopalakrishnan , Tao Luo , Qianxiao Li , Hoong Chuin Lau

Recent studies in using deep learning to solve routing problems focus on construction heuristics, the solutions of which are still far from optimality. Improvement heuristics have great potential to narrow this gap by iteratively refining a…

Artificial Intelligence · Computer Science 2020-05-12 Yaoxin Wu , Wen Song , Zhiguang Cao , Jie Zhang , Andrew Lim

Many complex problems encountered in both production and daily life can be conceptualized as combinatorial optimization problems (COPs) over graphs. Recent years, reinforcement learning (RL) based models have emerged as a promising…

Machine Learning · Computer Science 2024-04-09 Tianle Pu , Changjun Fan , Mutian Shen , Yizhou Lu , Li Zeng , Zohar Nussinov , Chao Chen , Zhong Liu

Combinatorial optimization problems play crucial roles in real-world applications, and many studies from a physics perspective have contributed to specialized hardware for high-speed computation. However, some combinatorial optimization…

Applied Physics · Physics 2025-01-07 Tatsuya Naoi , Tatsuya Kishimoto , Jun Ohkubo

The hardness of combinatorial optimization (CO) problems hinders collecting solutions for supervised learning. However, learning neural networks for CO problems is notoriously difficult in lack of the labeled data as the training is easily…

Machine Learning · Computer Science 2022-07-26 Haoran Sun , Etash K. Guha , Hanjun Dai