Improving configuration checking for satisfiable random k-SAT instances

Abramé, André; Habet, Djamal; Toumi, Donia

doi:10.1007/s10472-016-9515-9

Cited by 17 publications

(8 citation statements)

References 12 publications

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“…The third category of variants of CC is the largest one. Many CC rules are added according to analyzing different problems to obtain a better performance, such as NCCA+ (Abramé, Habet, and Toumi 2017) Algorithm 1: CC 2 FS(G, cutof f ) for SAT, SCC (Wang, Cai, and Yin 2016) for MWCP, HC-SCC (Luo et al 2017) for weighted partial maximum satisfiability problem, and CCA (Cai and Su 2012;Li et al 2018) for minimum weighted vertex cover problem, etc.…”

Section: Related Workmentioning

confidence: 99%

Improving Local Search Algorithms via Probabilistic Configuration Checking

Luo

Wan

et al. 2022

AAAI

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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.

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Section: Related Workmentioning

confidence: 99%

Improving Local Search Algorithms via Probabilistic Configuration Checking

Luo

Wan

et al. 2022

AAAI

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“…Then, it attempts to find a solution by repeatedly iteratively this assignment by flipping the Boolean value of one variable (changing its value from false to true, or true to false) according to several variable selection heuristics at a time until seeking out a solution (a solution is found) or timeout. SLS algorithms for SAT differ by the heuristic used in choosing which variable to flip (for examples, see the literature 34‐36 ). Below we briefly overview some popular SLS algorithms with some justifications why they were selected for further improvements.…”

Section: Preliminariesmentioning

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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“…As the MAX-SAT problem is very closely related to the SAT problem, one could adapt effective local search strategies for SAT, such as random walk [32], promising decreasing variable picking [23] and configuration checking (CC) [2,11,13], to solve the MAX-SAT problem. Unfortunately, making these adaptations effective for MAX-SAT is highly non-trivial because of the difference between SAT and MAX-SAT.…”

Section: Introductionmentioning

confidence: 99%

“…In order to make the Path-Relinking method competitive for the MAX-SAT, we identify two drawbacks in the previous Path-Relinking algorithm proposed in [16]: (1) complete trajectories between the two elite solutions are constructed, no matter how the quality of the solutions is in these trajectories, so that many search steps are made in exploring low-quality solutions; (2) the search is not sufficiently diversified, because Path-Relinking is just used to intensify the search around the solutions that have been produced by a GRASP (Greedy Randomized Adaptive Search Procedure) heuristic. Consequently, we propose an effective local search algorithm for the MAX-SAT called IPBMR (Iterated Path-Breaking with Mutation and Restart ) to remedy the above two drawbacks: (1) We establish a condition to break the construction of a trajectory between two elite solutions, allowing the search to focus only on high quality solutions; (2) We randomize the construction of the trajectories between two elite solutions, and if the search falls in a local optimum solution, we perform weak mutations followed by strong mutations that randomly flip a subset of variables of the local optimum solution in order to further diversify the search; (3) We restart [8] the search to explore new regions of the search space if the mutations do not allow to improve the local mimimum solution.…”

Section: Introductionmentioning

confidence: 99%

An iterative Path-Breaking approach with mutation and restart strategies for the MAX-SAT problem

2019

Computers & Operations Research

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Although Path-Relinking is an effective local search method for many combinatorial optimization problems, its application is not straightforward in solving the MAX-SAT, an optimization variant of the satisfiability problem (SAT) that has many real-world applications and has gained more and more attention in academy and industry. Indeed, it was not used in any recent competitive MAX-SAT algorithms in our knowledge. In this paper, we propose a new local search algorithm called IPBMR for the MAX-SAT, that remedies the drawbacks of the Path-Relinking method by using a careful combination of three components: a new strategy named Path-Breaking to avoid unpromising regions of the search space when generating trajectories between two elite solutions; a weak and a strong mutation strategies, together with restarts, to diversify the search; and stochastic path generating steps to avoid premature local optimum solutions. We then present experimental results to show that IPBMR outperforms two of the best state-of-the-art MAX-SAT solvers, and an empirical investigation to identify and explain the effect of the three components in IPBMR.

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Improving configuration checking for satisfiable random k-SAT instances

Cited by 17 publications

References 12 publications

Improving Local Search Algorithms via Probabilistic Configuration Checking

Improving Local Search Algorithms via Probabilistic Configuration Checking

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

An iterative Path-Breaking approach with mutation and restart strategies for the MAX-SAT problem

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