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Constraint Optimization Problems (COP) pose intricate challenges incombinatorial problems usually addressed through Branch and Bound (B\&B)methods, which involve maintaining priority queues and iteratively selectingbranches to search for solutions. However, conventional approaches take aconsiderable amount of time to find optimal solutions, and it is also crucialto quickly identify a near-optimal feasible solution in a shorter time. In thispaper, we aim to investigate the effectiveness of employing a depth-firstsearch algorithm for solving COP, specifically focusing on identifying optimalor near-optimal solutions within top $n$ solutions. Hence, we propose a novelheuristic neural network algorithm based on MCTS, which, by simultaneouslyconducting search and training, enables the neural network to effectively serveas a heuristic during Backtracking. Furthermore, our approach incorporatesencoding COP problems and utilizing graph neural networks to aggregateinformation about variables and constraints, offering more appropriatevariables for assignments. Experimental results on stochastic COP instancesdemonstrate that our method identifies feasible solutions with a gap of lessthan 17.63% within the initial 5 feasible solutions. Moreover, when applied toattendant Constraint Satisfaction Problem (CSP) instances, our method exhibitsa remarkable reduction of less than 5% in searching nodes compared tostate-of-the-art approaches.

BalMCTS: Balancing Objective Function and Search Nodes in MCTS for Constraint Optimization Problems