Title: Balancing Objective Function and Search Nodes in MCTS  for Constraint Optimization Problems
Primary area: optimization
Keywords: Constraint Optimization problems, Monte Carlo Tree Search, Graph neural network

Abstract: Constraint Optimization Problems (COPs) present significant challenges in combinatorial problem solving, traditionally tackled using Branch and Bound (B\&B) methods that rely on priority queues and iterative branch selection. While recent methods have employed machine learning to enhance branch selection, they often require extensive raw features and large training datasets, which can be a limitation. In this paper, we address this issue by modeling COPs with a minimal set of raw features, and we concentrate on identifying a satisfactory near-optimal or optimal solution within the top $n$ solutions.
  We propose a novel heuristic neural network algorithm grounded in Monte Carlo Tree Search (MCTS), designed for simultaneous search and training, empowering the neural network to act as an effective heuristic during Backtracking. Furthermore, our approach incorporates encoding COP problems and utilizing graph neural networks to aggregate information about variables and constraints, offering more appropriate variables for assignments. 
  The experiments demonstrate that BalMCTS significantly improves search efficiency, consistently achieving fewer search nodes. For Constraint Satisfaction Problem (CSP) instances, our method reduces the number of search nodes by more than 9.25\% compared to state-of-the-art approaches.