Advancements in Combinatorial Optimization

The field of combinatorial optimization is experiencing significant innovations, particularly in the integration of machine learning and reinforcement learning techniques. Researchers are exploring novel approaches to solve complex optimization problems, such as multicommodity flows and normalized cut problems, by leveraging constrained action spaces and graph neural networks. These advancements have the potential to improve the efficiency and effectiveness of optimization algorithms, leading to breakthroughs in various domains. Notably, the use of reinforcement learning from algorithm feedback is showing promise in guiding solver branching heuristics, resulting in significant speedups. Furthermore, graph-supported dynamic algorithm configuration is emerging as a powerful tool for multi-objective combinatorial optimization. Some noteworthy papers include: Learning from Algorithm Feedback: One-Shot SAT Solver Guidance with GNNs, which introduces a novel paradigm for learning to guide SAT solver branching heuristics, and Solving Normalized Cut Problem with Constrained Action Space, which proposes a first RL solution using constrained action spaces to guide the normalized cut problem. Graph-Supported Dynamic Algorithm Configuration for Multi-Objective Combinatorial Optimization is also a notable work, presenting a novel graph neural network based DRL to configure multi-objective evolutionary algorithms.

Sources

Unsplittable Multicommodity Flows in Outerplanar Graphs

Solving Normalized Cut Problem with Constrained Action Space

Learning from Algorithm Feedback: One-Shot SAT Solver Guidance with GNNs

Graph-Supported Dynamic Algorithm Configuration for Multi-Objective Combinatorial Optimization

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