Local search has been demonstrated as an efficient approach for two practical generalizations of the MaxSAT problem, namely Partial MaxSAT (PMS) and Weighted PMS (WPMS). In this work, we observe that most local search (W)PMS solvers usually flip a single variable per iteration. Such a mechanism may lead to relatively low-quality local optimal solutions, and may limit the diversity of search directions to escape from local optima. To address this issue, we propose a general strategy, called farsighted probabilistic sampling (FPS), to replace the single flipping mechanism so as to boost the local search (W)PMS algorithms. FPS considers the benefit of continuously flipping a pair of variables in order to find higher-quality local optimal solutions. Moreover, FPS proposes an effective approach to escape from local optima by preferring the best to flip among the best sampled single variable and the best sampled variable pair. Extensive experiments demonstrate that our proposed FPS strategy significantly improves the state-of-the-art (W)PMS solvers, and FPS has an excellent generalization capability to various local search MaxSAT solvers.

We address Partial MaxSAT (PMS) and Weighted PMS (WPMS), two practical generalizations of the MaxSAT problem, and propose a local search algorithm called BandMaxSAT, that applies a multi-armed bandit to guide the search direction, for these problems. The bandit in our method is associated with all the soft clauses in the input (W)PMS instance. Each arm corresponds to a soft clause. The bandit model can help BandMaxSAT to select a good direction to escape from local optima by selecting a soft clause to be satisfied in the current step, that is, selecting an arm to be pulled. We further propose an initialization method for (W)PMS that prioritizes both unit and binary clauses when producing the initial solutions. Extensive experiments demonstrate that BandMaxSAT significantly outperforms the state-of-the-art (W)PMS local search algorithm SATLike3.0. Specifically, the number of instances in which BandMaxSAT obtains better results is about twice that obtained by SATLike3.0. We further combine BandMaxSAT with the complete solver TT-Open-WBO-Inc. The resulting solver BandMaxSAT-c also outperforms some of the best state-of-the-art complete (W)PMS solvers, including SATLike-c, Loandra and TT-Open-WBO-Inc.

We propose a new and strengthened Branch-and-Bound (BnB) algorithm for the maximum common (connected) induced subgraph problem based on two new operators, Long-Short Memory (LSM) and Leaf vertex Union Match (LUM). Given two graphs for which we search for the maximum common (connected) induced subgraph, the first operator of LSM maintains a score for the branching node using the short-term reward of each vertex of the first graph and the long-term reward of each vertex pair of the two graphs. In this way, the BnB process learns to reduce the search tree size significantly and boost the algorithm performance. The second operator of LUM further improves the performance by simultaneously matching the leaf vertices connected to the current matched vertices, and allows the algorithm to match multiple vertex pairs without affecting the optimality of solution. We incorporate the two operators into the state-of-the-art BnB algorithm McSplit, and denote the resulting algorithm as McSplit+LL. Experiments show that McSplit+LL outperforms McSplit+RL, a more recent variant of McSplit using reinforcement learning that is superior than McSplit.

We address the Traveling Salesman Problem (TSP), a famous NP-hard combinatorial optimization problem. And we propose a variable strategy reinforced approach, denoted as VSR-LKH, which combines three reinforcement learning methods (Q-learning, Sarsa and Monte Carlo) with the well-known TSP algorithm, called Lin-Kernighan-Helsgaun (LKH). VSR-LKH replaces the inflexible traversal operation in LKH, and lets the program learn to make choice at each search step by reinforcement learning. Experimental results on 111 TSP benchmarks from the TSPLIB with up to 85,900 cities demonstrate the excellent performance of the proposed method.