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Using machine learning to solve combinatorial optimization (CO) problems is challenging, especially when the data is unlabeled. This work proposes an unsupervised learning framework for CO problems. Our framework follows a standard…
We reduce a broad class of machine learning problems, usually addressed by EM or sampling, to the problem of finding the $k$ extremal rays spanning the conical hull of a data point set. These $k$ "anchors" lead to a global solution and a…
Graph-structured data is ubiquitous throughout natural and social sciences, and Graph Neural Networks (GNNs) have recently been shown to be effective at solving prediction and inference problems on graph data. In this paper, we propose and…
As a well-known optimization framework, the Alternating Direction Method of Multipliers (ADMM) has achieved tremendous success in many classification and regression applications. Recently, it has attracted the attention of deep learning…
This paper presents a framework to tackle constrained combinatorial optimization problems using deep Reinforcement Learning (RL). To this end, we extend the Neural Combinatorial Optimization (NCO) theory in order to deal with constraints in…
Despite the success of neural-based combinatorial optimization methods for end-to-end heuristic learning, out-of-distribution generalization remains a challenge. In this paper, we present a novel formulation of Combinatorial Optimization…
Unsupervised learning (UL)-based solvers for combinatorial optimization (CO) train a neural network that generates a soft solution by directly optimizing the CO objective using a continuous relaxation strategy. These solvers offer several…
Distributed optimization is an essential paradigm to solve large-scale optimization problems in modern applications where big-data and high-dimensionality creates a computational bottleneck. Distributed optimization algorithms that exhibit…
Divide and Conquer (D&C) is a widely used algorithmic strategy for symmetric eigenvalue decomposition. Its natural parallelism makes D&C attractive on modern multicore CPUs and GPUs, but existing eigenvalue-only routines often default to…
Deep unfolding networks (DUN) have emerged as a popular iterative framework for accelerated magnetic resonance imaging (MRI) reconstruction. However, conventional DUN aims to reconstruct all the missing information within the entire null…
We propose a novel decomposition framework for the distributed optimization of Difference Convex (DC)-type nonseparable sum-utility functions subject to coupling convex constraints. A major contribution of the paper is to develop for the…
Chain-of-Thought (CoT) reasoning has been widely adopted to enhance Large Language Models (LLMs) by decomposing complex tasks into simpler, sequential subtasks. However, extending CoT to vision-language reasoning tasks remains challenging,…
Deep convolutional neural networks (CNNs) have been intensively used for multi-class segmentation of data from different modalities and achieved state-of-the-art performances. However, a common problem when dealing with large, high…
Traditional solvers for tackling combinatorial optimization (CO) problems are usually designed by human experts. Recently, there has been a surge of interest in utilizing deep learning, especially deep reinforcement learning, to…
Unit Commitment (UC) is a fundamental problem in power system operations. When coupled with generation maintenance, the joint optimization problem poses significant computational challenges due to coupling constraints linking maintenance…
Neural Combinatorial Optimization (NCO) has emerged as a promising learning-based paradigm for addressing Vehicle Routing Problems (VRPs) by minimizing the need for extensive manual engineering. While existing NCO methods, trained on…
In recent years, graph neural networks (GNNs) have become increasingly popular for solving NP-hard combinatorial optimization (CO) problems, such as maximum cut and maximum independent set. The core idea behind these methods is to represent…
Neural network-based Combinatorial Optimization (CO) methods have shown promising results in solving various NP-complete (NPC) problems without relying on hand-crafted domain knowledge. This paper broadens the current scope of neural…
Collecting the large datasets needed to train deep neural networks can be very difficult, particularly for the many applications for which sharing and pooling data is complicated by practical, ethical, or legal concerns. However, it may be…
Quadratic Unconstrained Binary Optimization (QUBO) is a broad class of optimization problems with many practical applications. To solve its hard instances in an exact way, known classical algorithms require exponential time and several…