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Shaowei Cai

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58 papers

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FM Conference 2026 Conference Paper

FastLEC: Parallel Datapath Equivalence Checking with Hybrid Engines

Xindi Zhang
Furong Ye
Zhihan Chen
Shaowei Cai

Abstract Combinational equivalence checking (CEC) remains a challenge EDA task in the formal verification of datapath circuits due to their complex arithmetic structures and the limited capability or scalability of SAT, BDD, and exact-simulation (ES) based techniques when used independently. This work presents FastLEC, a hybrid prover that unifies these three formal reasoning engines and introduces three strategies that substantially enhance verification efficiency. First, a regression-based engine-scheduling heuristic predicts solver effectiveness, enabling more accurate and balanced allocation of computational resources. Second, datapath-structure-aware partitioning strategies, along with a dynamic divide-and-conquer SAT prover, exploit the regularity of arithmetic designs while preserving completeness. Third, the memory overhead of ES is significantly reduced through address-reference-count tracking, and simulation is further accelerated through a GPU-enabled backend. FastLEC is evaluated across 368 datapath circuits. Using 32 CPU cores, it proves 5. 07 $$\times $$ × more circuits than the widely used ABC &cec tool. Compared with the latest best datapath-oriented serial and parallel CEC provers, FastLEC outperforms them by 3. 33 $$\times $$ × and 2. 67 $$\times $$ × in PAR-2 time, demonstrating an improvement of 74 newly solved circuits. With the addition of a single GPU, it achieves a further 4. 07 $$\times $$ × improvement. The prover also demonstrates excellent scalability.

DOI

IJCAI Conference 2025 Conference Paper

An Efficient Core-Guided Solver for Weighted Partial MaxSAT

Shiwei Pan
Yiyuan Wang
Shaowei Cai

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.

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AAAI Conference 2025 Conference Paper

Better Understandings and Configurations in MaxSAT Stochastic Local Search Solvers via Anytime Performance Analysis

Furong Ye
Chuan Luo
Shaowei Cai

Though numerous solvers have been proposed for the MaxSAT problem, and the benchmark environment such as MaxSAT Evaluations provides a platform for the comparison of the state-of-the-art solvers, existing assessments were usually evaluated based on the quality, e.g., fitness, of the best-found solutions obtained within a given running time budget. However, concerning solely the final obtained solutions regarding specific time budgets may restrict us from comprehending the behavior of the solvers along the convergence process. This paper demonstrates that Empirical Cumulative Distribution Functions can be used to compare MaxSAT stochastic local search solvers' anytime performance across multiple problem instances and various time budgets. The assessment reveals distinctions in solvers' performance and displays that the (dis)advantages of solvers adjust along different running times. This work also exhibits that the quantitative and high variance assessment of anytime performance can guide machines, i.e., automatic configurators, to search for better parameter settings. Our experimental results show that the hyperparameter optimization tool, i.e., SMAC, can achieve better parameter settings of solvers when using the anytime performance as the cost function, compared to using the metrics based on the fitness of the best-found solutions.

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JAIR Journal 2025 Journal Article

Improving Local Search Algorithm for Pseudo Boolean Optimization

Yujiao Zhao
Yiyuan Wang
Yi Chu
Wenbo Zhou
Shaowei Cai
Minghao Yin

Pseudo-Boolean optimization (PBO) is usually used to model combinatorial optimization problems, especially for some real-world applications. Despite its significant importance in both theory and applications, the performance of current PBO solvers is still limited. This paper develops a novel local search algorithm for PBO, which has four main ideas. First, we design a new primary scoring function and a two-level selection strategy to evaluate all candidate variables. Second, we introduce a new weighting scheme to accurately guide the search process toward more promising directions. Third, we propose a novel deep optimization strategy to disturb some search processes. Fourth, an efficient solution space exploration mechanism is applied to help the algorithm jump out of local optimum. We conduct experiments on a broad range of public benchmarks, including three large-scale practical application benchmarks, two benchmarks from PB competitions, an integer linear programming optimization benchmark, a crafted combinatorial benchmark, and a combinatorial optimization knapsack benchmark to compare our proposed algorithm against twelve state-of-the-art competitors, including seven recently-proposed pure stochastic local search PBO solvers, a non-traditional stochastic local search combined with complete oracle, two complete PB solvers, and two mixed integer programming (MIP) solvers. Our proposed algorithm has been shown to perform best on these three real-world benchmarks. On the other five benchmarks, our algorithm shows competitive performance compared to state-of-the-art competitors, and it significantly outperforms all other local search algorithms, indicating that our algorithm greatly advances the state of the art in local search for solving PBO.

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AIJ Journal 2025 Journal Article

Local-MIP: Efficient local search for mixed integer programming

Peng Lin
Shaowei Cai
Mengchuan Zou
Jinkun Lin

Mixed Integer Programming (MIP) is a fundamental model in operations research with broad industrial applications. Local search is a powerful methodology for solving complex optimization problems; however, the development of local search algorithms for MIP still needs exploration. In this work, we propose Local-MIP, an efficient local search algorithm tailored for MIP that integrates novel operators and employs a two-mode architecture to adaptively apply operators based on the current solution's feasibility. For the feasible mode, we propose the lift move operator and a corresponding lift process to improve the objective value while maintaining feasibility. For the infeasible mode, we propose the breakthrough move and mixed tight move operators to respectively optimize the objective function and satisfy constraints. To apply operators intelligently, we develop a dynamic weighting scheme that balances the priorities of the objective function and constraints. Furthermore, we propose a two-level scoring function structure that hierarchically selects operations, guiding the search toward high-quality feasible solutions. Experiments are conducted on public benchmarks to compare Local-MIP with state-of-the-art MIP solvers in finding high-quality solutions. The results show that Local-MIP significantly outperforms CPLEX, HiGHS, SCIP, and Feasibility Jump while remaining competitive with the commercial solver Gurobi on challenging problems within short time limits. Moreover, Local-MIP establishes 10 new records on MIPLIB open instances.

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TCS Journal 2024 Journal Article

A local search approach to protocol verification

Kun Ma
Yongjian Li
Shaowei Cai
Yongxin Zhao

Verification of parameterized protocols is of great interest in the area of formal verification, mainly due to the practical importance of such systems. Explicit-state model checking is an essential approach in which states for a system are maintained in explicit form, as are all state transitions. In order to reduce the search space to a minimum, we propose a local search strategy. In detail, first, heuristic functions are designed to guide the searching of bugs more effectively, which exploits information extracted from invariants and rulesets, to improve the calculation of a distance between two states. Second, candidate solutions with poor scores are dropped for further compression of the state space explored. Especially, we apply successfully our local search algorithm to the reachable analysis of a real-world implementation of TileLink protocol.

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IJCAI Conference 2024 Conference Paper

ParaILP: A Parallel Local Search Framework for Integer Linear Programming with Cooperative Evolution Mechanism

Peng Lin
Mengchuan Zou
Zhihan Chen
Shaowei Cai

The integer linear programming (ILP) problem is a fundamental research topic in operations research, and the local search method is an important class of algorithms for quickly solving many combinatorial optimization problems. With rapidly increasing computing power, parallelism turns out to be a promising approach to enhancing the efficiency of problem-solving. However, rare studies investigate parallel local search algorithms for solving the general ILP problem. We propose the first parallel local search framework (ParaILP) for solving the general ILP problem, based on two novel ideas: a new initialization method named polarity initialization to construct different initial solutions for local search threads and a cooperative evolution mechanism for managing and generating high-quality solutions using information shared by different threads. Extensive experiments demonstrate that ParaILP is significantly better than the state-of-the-art academic parallel solvers FiberSCIP and HiGHS, and is competitive with the state-of-the-art commercial parallel solver Gurobi. Experiments are also conducted to analyze the parallelization scalability and the effectiveness of our techniques.

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AIJ Journal 2024 Journal Article

PathLAD+: Towards effective exact methods for subgraph isomorphism problem

Yiyuan Wang
Chenghou Jin
Shaowei Cai

The subgraph isomorphism problem (SIP) is a challenging problem with wide practical applications. In the last decade, despite being a theoretical hard problem, researchers designed various algorithms for solving SIP. In this work, we propose five main strategies and develop an improved exact algorithm for SIP. First, we design a probing search procedure to try whether the search procedure can successfully obtain a solution at first sight. Second, we design a novel matching ordering strategy as a value-ordering heuristic, which uses some useful information obtained from the probing search procedure to preferentially select some promising target vertices. Third, we discuss the characteristics of different propagation methods in the context of SIP and present an adaptive propagation method to make a good balance between these methods. Moreover, to further improve the performance of solving large graphs, we propose an enhanced implementation of the edge constraint method and a domain limitation strategy, which aims to accelerate the search process. Experimental results on a broad range of classic and graph-database benchmarks show that our proposed algorithm performs better than several state-of-the-art algorithms for the SIP.

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AAAI Conference 2023 Short Paper

Can Graph Neural Networks Learn to Solve the MaxSAT Problem? (Student Abstract)

Minghao Liu
Pei Huang
Fuqi Jia
Fan Zhang
Yuchen Sun
Shaowei Cai
Feifei Ma
Jian Zhang

The paper presents an attempt to bridge the gap between machine learning and symbolic reasoning. We build graph neural networks (GNNs) to predict the solution of the Maximum Satisfiability (MaxSAT) problem, an optimization variant of SAT. Two closely related graph representations are adopted, and we prove their theoretical equivalence. We also show that GNNs can achieve attractive performance to solve hard MaxSAT problems in certain distributions even compared with state-of-the-art solvers through experimental evaluation.

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AIJ Journal 2023 Journal Article

Improved local search for the minimum weight dominating set problem in massive graphs by using a deep optimization mechanism

Jiejiang Chen
Shaowei Cai
Yiyuan Wang
Wenhao Xu
Jia Ji
Minghao Yin

The minimum weight dominating set (MWDS) problem is an important generalization of the minimum dominating set problem with various applications. In this work, we develop an efficient local search scheme that can dynamically adjust the number of added and removed vertices according to the information of the candidate solution. Based on this scheme, we further develop three novel ideas to improve performance, resulting in our so-called DeepOpt-MWDS algorithm. First, we use a new construction method with five reduction rules to significantly reduce massive graphs and construct an initial solution efficiently. Second, an improved configuration checking strategy called CC2V3+ is designed to reduce the cycling phenomenon in local search. Third, a general perturbation framework called deep optimization mechanism (DeepOpt) is proposed to help the algorithm avoid local optima and to converge to a new solution quickly. Extensive experiments based on eight popular benchmarks of different scales are carried out to evaluate the proposed algorithm. Compared to seven state-of-the-art heuristic algorithms, DeepOpt-MWDS performs better on random and classic benchmarks and obtains the best solutions on almost all massive graphs. We investigate three main algorithmic ingredients to understand their impacts on the performance of the proposed algorithm. Moreover, we adapt the proposed general framework DeepOpt to another NP-hard problem to verify its generality and achieve good performance.

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AAAI Conference 2023 Conference Paper

NuWLS: Improving Local Search for (Weighted) Partial MaxSAT by New Weighting Techniques

Yi Chu
Shaowei Cai
Chuan Luo

Maximum Satisfiability (MaxSAT) is a prototypical constraint optimization problem, and its generalized version is the (Weighted) Partial MaxSAT problem, denoted as (W)PMS, which deals with hard and soft clauses. Considerable progress has been made on stochastic local search (SLS) algorithms for solving (W)PMS, which mainly focus on clause weighting techniques. In this work, we identify two issues of existing clause weighting techniques for (W)PMS, and propose two ideas correspondingly. First, we observe that the initial values of soft clause weights have a big effect on the performance of the SLS solver for solving (W)PMS, and propose a weight initialization method. Second, we propose a new clause weighting scheme that for the first time employs different conditions for updating hard and soft clause weights. Based on these two ideas, we develop a new SLS solver for (W)PMS named NuWLS. Through extensive experiments, NuWLS performs much better than existing SLS solvers on all 6 benchmarks from the incomplete tracks of MaxSAT Evaluations (MSEs) 2019, 2020, and 2021. In terms of the number of winning instances, NuWLS outperforms state-of-the-art SAT-based incomplete solvers on all the 6 benchmarks. More encouragingly, a hybrid solver that combines NuWLS and an SAT-based solver won all four categories in the incomplete track of the MaxSAT Evaluation 2022.

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IJCAI Conference 2023 Conference Paper

PathLAD+: An Improved Exact Algorithm for Subgraph Isomorphism Problem

Yiyuan Wang
Chenghou Jin
Shaowei Cai
Qingwei Lin

The subgraph isomorphism problem (SIP) is a challenging problem with wide practical applications. In the last decade, despite being a theoretical hard problem, researchers design various algorithms for solving SIP. In this work, we propose three main heuristics and develop an improved exact algorithm for SIP. First, we design a probing search procedure to try whether the search procedure can successfully obtain a solution at first sight. Second, we design a novel matching ordering as a value-ordering heuristic, which uses some useful information obtained from the probing search procedure to preferentially select some promising target vertices. Third, we discuss the characteristics of different propagation methods in the context of SIP and present an adaptive propagation method to make a good balance between these methods. Experimental results on a broad range of real-world benchmarks show that our proposed algorithm performs better than state-of-the-art algorithms for the SIP.

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JAIR Journal 2022 Journal Article

Better Decision Heuristics in CDCL through Local Search and Target Phases

Shaowei Cai
Xindi Zhang
Mathias Fleury
Armin Biere

On practical applications, state-of-the-art SAT solvers dominantly use the conflict-driven clause learning (CDCL) paradigm. An alternative for satisfiable instances is local search solvers, which is more successful on random and hard combinatorial instances. Although there have been attempts to combine these methods in one framework, a tight integration which improves the state of the art on a broad set of application instances has been missing. We present a combination of techniques that achieves such an improvement. Our first contribution is to maximize in a local search fashion the assignment trail in CDCL, by sticking to and extending promising assignments via a technique called target phases. Second, we relax the CDCL framework by again extending promising branches to complete assignments while ignoring conflicts. These assignments are then used as starting point of local search which tries to find improved assignments with fewer unsatisfied clauses. Third, these improved assignments are imported back to the CDCL loop where they are used to determine the value assigned to decision variables. Finally, the conflict frequency of variables in local search can be exploited during variable selection in branching heuristics of CDCL. We implemented these techniques to improve three representative CDCL solvers (Glucose, MapleLcm DistChronoBT, and Kissat). Experiments on benchmarks from the main tracks of the last three SAT Competitions from 2019 to 2021 and an additional benchmark set from spectrum allocation show that the techniques bring significant improvements, particularly and not surprisingly, on satisfiable real-world application instances. We claim that these techniques were essential to the large increase in performance witnessed in the SAT Competition 2020 where Kissat and Relaxed LcmdCbDl NewTech were leading the field followed by CryptoMiniSAT-Ccnr, which also incorporated similar ideas.

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IJCAI Conference 2022 Conference Paper

Deep Cooperation of CDCL and Local Search for SAT (Extended Abstract)

Shaowei Cai
Xindi Zhang

Modern SAT solvers are based on a paradigm named conflict driven clause learning (CDCL), while local search is an important alternative. Although there have been attempts combining these two methods, this work proposes deeper cooperation techniques. First, we relax the CDCL framework by extending promising branches to complete assignments and calling a local search solver to search for a model nearby. More importantly, the local search assignments and the conflict frequency of variables in local search are exploited in the phase selection and branching heuristics of CDCL. We use our techniques to improve three typical CDCL solvers (glucose, MapleLCMDistChronoBT and Kissat). Experiments on benchmarks from the Main tracks of SAT Competitions 2017-2020 and a real world benchmark of spectrum allocation show that the techniques bring significant improvements, particularly on satisfiable instances. A resulting solver won the Main Track SAT category in SAT Competition 2020 and also performs very well on the spectrum allocation benchmark. As far as we know, this is the first work that meets the standard of the challenge ``Demonstrate the successful combination of stochastic search and systematic search techniques, by the creation of a new algorithm that outperforms the best previous examples of both approaches. '' (AAAI 1997) on standard application benchmarks.

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AAAI Conference 2022 Conference Paper

Improving Local Search Algorithms via Probabilistic Configuration Checking

Weilin Luo
Rongzhen Ye
Hai Wan
Shaowei Cai
Biqing Fang
Delong Zhang

Configuration checking (CC) has been confirmed to alleviate the cycling problem in local search for combinatorial optimization problems (COPs). When using CC heuristics in local search for graph problems, a critical concept is the configuration of the vertices. All existing CC variants employ either 1- or 2-level neighborhoods of a vertex as its configuration. Inspired by the idea that neighborhoods with different levels should have different contributions to solving COPs, we propose the probabilistic configuration (PC), which introduces probabilities for neighborhoods at different levels to consider the impact of neighborhoods of different levels on the CC strategy. Based on the concept of PC, we first propose probabilistic configuration checking (PCC), which can be developed in an automated and lightweight favor. We then apply PCC to two classic COPs which have been shown to achieve good results by using CC, and our preliminary results confirm that PCC improves the existing algorithms because PCC alleviates the cycling problem.