The maximum satisfiability problem (MaxSAT) is a crucial combinatorial optimization problem with widespread applications across various critical domains. This paper presents CASHWMaxSAT, an efficient core-guided MaxSAT solver based on two novel ideas. The first and most important idea is the introduction of an extended stratification technique that progressively focuses on solving high-weight soft clauses. Second, we integrate disjoint unsatisfiable cores with the goal of minimizing the unsatisfiable core, allowing the solver to learn multiple high-quality clauses in a single conflict analysis step. These innovations enable our MaxSAT solver to efficiently identify key constraints and reduce redundant reasoning, significantly enhancing solving efficiency. Experimental results on benchmarks from the complete weighted track of the MaxSAT Evaluations 2022-2024 demonstrate that the proposed methods lead to substantial improvements, with CASHWMaxSAT outperforming state-of-the-art MaxSAT solvers across all benchmarks. Additionally, it enabled us to achieve the top two positions in the exact weighted category of the MaxSAT Evaluation 2024.

The Latin square completion (LSC) problem is an important NP-complete problem with numerous applications. Given its theoretical and practical importance, several algorithms are designed for solving the LSC problem. In this work, to further improve the performance, a fast local search algorithm is developed based on three main ideas. Firstly, a reduction reasoning technique is used to reduce the scale of search space. Secondly, we propose a novel conflict value selection heuristic, which considers the history conflicting information of vertices as a selection criterion when more than one vertex have equal values on the primary scoring function. Thirdly, during the search phase, we record previous history search information and then make use of these information to restart the candidate solution. Experimental results show that our proposed algorithm significantly outperforms the state-of-the-art heuristic algorithms on almost all instances in terms of success rate and run time.

The maximum quasi-clique problem (MQCP) is an important extension of maximum clique problem with wide applications. Recent heuristic MQCP algorithms can hardly solve large and hard graphs effectively. This paper develops an efficient local search algorithm named NuQClq for the MQCP, which has two main ideas. First, we propose a novel vertex selection strategy, which utilizes cumulative saturation information to be a selection criterion when the candidate vertices have equal values on the primary scoring function. Second, a variant of configuration checking named BoundedCC is designed by setting an upper bound for the threshold of forbidding strength. When the threshold value of vertex exceeds the upper bound, we reset its threshold value to increase the diversity of search process. Experiments on a broad range of classic benchmarks and sparse instances show that NuQClq significantly outperforms the state-of-the-art MQCP algorithms for most instances.

The weighted graph coloring problem (WGCP) is an important extension of the graph coloring problem (GCP) with wide applications. Compared to GCP, where numerous methods have been developed and even massive graphs with millions of vertices can be solved well, fewer works have been done for WGCP, and no solution is available for solving WGCP for massive graphs. This paper explores techniques for solving WGCP, including a lower bound and a reduction rule based on clique sampling, and a local search algorithm based on two selection rules and a new variant of configuration checking. This results in our algorithm RedLS (Reduction plus Local Search). Experiments are conducted to compare RedLS with the state-of-the-art algorithms on massive graphs as well as conventional benchmarks studied in previous works. RedLS exhibits very good performance and robustness. It significantly outperforms previous algorithms on all benchmarks.