An improved genetic algorithm for solving 3-SAT problems based on effective restart and greedy strategy

Fu, Huimin; Xu, Yang; Wu, Guanfeng; Ning, Xinran

doi:10.1109/iske.2017.8258797

Cited by 5 publications

(4 citation statements)

References 24 publications

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“…1) 7-SAT_huge: The benchmark contains all 40 huge random 7-SAT instances from SAT Competition 2017 1 , n= 250000, two instances each size).…”

Section: Experiments Preliminariesmentioning

confidence: 99%

“…The propositional satisfiability (SAT) problem is one of the most widely studied NP-complete problems and plays an outstanding role in many domains of computer science and artificial intelligence due to its significant importance in both theory and applications [1]. Considering a propositional formula F in the Conjunctive Normal Form (CNF) defined on a set of Boolean variables, the SAT problem asks whether there exists a truth assignment to the variables of F that satisfies all clauses in F. The SAT problem is fundamental in solving many practical problems in combinatorial optimization, statistical physics, circuit verification, mathematical logic, machine learning, constraint satisfaction, real-time scheduling, and computing theory [2].…”

Section: Introductionmentioning

confidence: 99%

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Focused random walk with probability distribution for SAT with long clauses

2020

Appl Intell

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Focused random walk (FRW) is one of the most influential paradigm of stochastic local search (SLS) algorithms for the propositional satisfiability (SAT) problem. Recently, an interesting probability distribution (PD) strategy for variable selection was proposed and has been successfully used to improve SLS algorithms, resulting in state-of-the-art solvers. However, most solvers based on the PD strategy only use polynomial function (PoF) to handle the exponential decay and are still unsatisfactory in dealing with medium and huge k-SAT instances at and near the phase transition. The present paper is focused on handling all k-SAT instances with long clauses. Firstly, an extensive empirical study of one state-of-the-art FRW solver WalkSATlm on a wide range of SAT problems is presented with the focus given on fitting the distribution of the break value of variable selected in each step, which turns out to be a Boltzmann function. Using theses case studies as a basis, we propose a pseudo normal function (PNF) to fit the distribution of the break value of variable selected, which is actually a variation of the Boltzmann function. In addition, a new tie-breaking flipping (TBF) strategy is proposed to prevent the same variable from being flipped in consecutive steps. The PNF based PD strategy combined with the TBF strategy lead to a new variable selection heuristic named PNF-TBF. The PNF-TBF heuristic along with a variable allocation value (Vav) function are used to significantly improve ProbSAT, a state-of-the-art SLS solver, leads to a new FRW algorithm dubbed PNFSat, which achieves the state-of-the-art performance on a broad range of huge random 7-SAT instance near the phase transition as demonstrated via the extensive experimental studies. Some further improved versions on top of PNFSat are presented respectively, including PNFSat_alt, which achieves the state-of-the-art performance on the medium 7-SAT instances at the phase transition; PN&PoFSat, which achieves the state-of-the-art performance on a broad range of random 5-SAT benchmarks; as well as an integrated version of these three algorithms, named PDSat, which achieves the state-of-the-art performances on all huge and medium random k-SAT instances with long clauses as demonstrated via the comparative studies using different benchmarks.

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“…1) 7-SAT_huge: The benchmark contains all 40 huge random 7-SAT instances from SAT Competition 2017 1 , n= 250000, two instances each size).…”

Section: Experiments Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Focused random walk with probability distribution for SAT with long clauses

2020

Appl Intell

Self Cite

View full text Add to dashboard Cite

show abstract

“…The propositional satisfiability (SAT) problem is one of the most widely studied NP‐complete problems and has been extensively studied in many domains of computer science and artificial intelligence due to its significant importance in both theory and applications 1,2 . Considering a propositional formula F in the Conjunctive normal form (CNF) defined on a set of Boolean variables, the SAT problem asks whether there exists a truth assignment to the variables of F that satisfies all clauses in F .…”

Section: Introductionmentioning

confidence: 99%

Improving stochastic local search for uniform k‐SAT by generating appropriate initial assignment

Zhang

et al. 2021

Computational Intelligence

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Stochastic local search (SLS) algorithms are well known for their ability to efficiently find models of random instances of the SAT problem, especially for uniform random k‐SAT instances. Two processes affect most SLS solvers—the initial assignment of the variables and the heuristics that select which variable to flip. In the last few years, the work on generating the appropriate initial assignment has not been paid much attention or seen much progress, while most SLS solvers focused on the heuristic algorithm. The present work aims to improve SLS algorithms on uniform random k‐SAT instances by developing effective methods for generating the initial assignment of variables in a controlled way. First, the allocation strategy introduced recently for 3‐SAT instances is extended to initialize the initial assignment on random k‐SAT instances. Then a concept of an initial probability distribution of the clause‐to‐variable ratio of the instance is introduced to determine the parameters of the allocation strategy. This combined method is added to the beginning of six state‐of‐the‐art SLS algorithms in order to generate initial assignments of variables in a controlled way instead of generating them randomly, resulting in six extended SLS algorithms named WalkSATlm_E, DCCASat_E, Score2SAT_E, CSCCSat_E, Probsat_E, and Sparrow_E, respectively. They are then evaluated in terms of their capabilities and efficiency on uniform random k‐SAT instance from the random track of SAT Competitions in 2016, 2017, and 2018. Experimental results show that these improved SLS solvers outperform their original performance, especially WalkSAT_E, Score2SAT_E, and CSCCSat_E outperform the winner of the random track of SAT competition in 2017. In addition, based on the initial probability distribution method, the present work proposes a parameter tuning and analysis of random 3‐SAT instances and provides an additional comparative analysis with the state‐of‐the‐art random SLS solvers based on large‐scale experiments.

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“…Simulation results suggested that this algorithm has a stronger global search ability, faster convergence speed and greater robustness. In the improved adaptive genetic algorithm described by Fu et al [ 25 ], a restart strategy was used to solve the algorithm’s premature convergence problem, while a greedy strategy was employed to improve optimal solution searching speed. These authors also utilized an adaptive crossover operator and a mutation operator to increase the algorithm’s adaptability.…”

Section: Introductionmentioning

confidence: 99%

Predicting human body composition using a modified adaptive genetic algorithm with a novel selection operator

et al. 2020

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Background Changes to human body composition reflect changes in health status to some extent. It has been recognized that these changes occur earlier than diseases. This means that a reasonable prediction of body composition helps to improve model users’ health. To overcome the low accuracy and poor adaptability of existing human body composition prediction models and obtain higher efficiency, we proposed a novel method for predicting human body composition which uses a modified adaptive genetic algorithm (MAGA). Methods Firstly, since there are many parameters for a human body composition model, and these parameters are associated, we designed a new parameter selection approach by combining the improved RReliefF method with the mRMR method. Following this, selected parameters were used to establish a model that fits body composition. Secondly, in order to accurately calculate the weight of parameters in this model, we proposed a solution which used a modified adaptive genetic algorithm, taking advantage of both roulette and optimum reservation strategies. This solution also has an improved selection operator. Thirdly, taking the percentage of body fat (PBF) as an example of body composition, we conducted experiments to compare performance between our algorithm and other algorithms. Results Through our simulations, we demonstrated that the adaptability of the proposed model is 0.9921, the mean relative error is 0.05%, the mean square error is 1.3 and the correlation coefficient is 0.982. When compared with the indexes of other models, our model has the highest adaptability and the smallest error. Additionally, the suggested model, which has a training time of 28.58s and a running time of 2.84s, is faster than some models. Conclusion The PBF prediction model established by MAGA has high accuracy, stronger generalization ability and higher efficiency, which could provide a new method for human composition prediction.

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An improved genetic algorithm for solving 3-SAT problems based on effective restart and greedy strategy

Cited by 5 publications

References 24 publications

Focused random walk with probability distribution for SAT with long clauses

Focused random walk with probability distribution for SAT with long clauses

Improving stochastic local search for uniform k‐SAT by generating appropriate initial assignment

Predicting human body composition using a modified adaptive genetic algorithm with a novel selection operator

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