CCLS: An Efficient Local Search Algorithm for Weighted Maximum Satisfiability

Luo, Chuan; Wu, Wei; Zhong, Jie; Su, Kaile

doi:10.1109/tc.2014.2346196

Cited by 86 publications

(50 citation statements)

References 40 publications

(57 reference statements)

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“…We then compared our memcomputing solver against two of the best solvers of the 2016 Max-SAT competition (CCLS [18] and DeciLS [19]-a new version of CnC-LS-kindly provided by their developers) which are specifically designed to solve these types of problems, but employing very different solution strategies.…”

Section: Resultsmentioning

confidence: 99%

Evidence of Exponential Speed‐Up in the Solution of Hard Optimization Problems

et al. 2018

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Optimization problems pervade essentially every scientific discipline and industry. A common form requires identifying a solution satisfying the maximum number among a set of many conflicting constraints. Often, these problems are particularly difficult to solve, requiring resources that grow exponentially with the size of the problem. Over the past decades, research has focused on developing heuristic approaches that attempt to find an approximation to the solution. However, despite numerous research efforts, in many cases even approximations to the optimal solution are hard to find, as the computational time for further refining a candidate solution also grows exponentially with input size. In this paper, we show a noncombinatorial approach to hard optimization problems that achieves an exponential speed-up and finds better approximations than the current state of the art. First, we map the optimization problem into a Boolean circuit made of specially designed, self-organizing logic gates, which can be built with (nonquantum) electronic elements with memory. The equilibrium points of the circuit represent the approximation to the problem at hand. Then, we solve its associated nonlinear ordinary differential equations numerically, towards the equilibrium points. We demonstrate this exponential gain by comparing a sequential MATLAB implementation of our solver with the winners of the 2016 Max-SAT competition on a variety of hard optimization instances. We show empirical evidence that our solver scales linearly with the size of the problem, both in time and memory, and argue that this property derives from the collective behavior of the simulated physical circuit. Our approach can be applied to other types of optimization problems, and the results presented here have far-reaching consequences in many fields.

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Section: Resultsmentioning

confidence: 99%

Evidence of Exponential Speed‐Up in the Solution of Hard Optimization Problems

et al. 2018

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“…We compare our implementation to the best solvers we could find online, respectively CCLS-to-akmaxsat (Luo, Cai, Wu, Jie, & Su, 2014) which was among the best solvers of the Ninth Max-SAT Evaluation (2014), and the latest version of the #SAT solver called sharpSAT (Thurley, n.d., 2006). These solvers handily beat our implementation on most inputs.…”

Section: Resultsmentioning

confidence: 99%

Solving #SAT and MAXSAT by Dynamic Programming

Sæther

Telle

Vatshelle

2015

jair

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We look at dynamic programming algorithms for propositional model counting, also called #SAT, and MaxSAT. Tools from graph structure theory, in particular treewidth, have been used to successfully identify tractable cases in many subfields of AI, including SAT, Constraint Satisfaction Problems (CSP), Bayesian reasoning, and planning. In this paper we attack #SAT and MaxSAT using similar, but more modern, graph structure tools. The tractable cases will include formulas whose class of incidence graphs have not only unbounded treewidth but also unbounded clique-width. We show that our algorithms extend all previous results for MaxSAT and #SAT achieved by dynamic programming along structural decompositions of the incidence graph of the input formula. We present some limited experimental results, comparing implementations of our algorithms to state-of-the-art #SAT and MaxSAT solvers, as a proof of concept that warrants further research.

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“…Classic examples of mathematical programming algorithms are the simplex method in LP [43] and the branch and bound method for integer programming [44], where the algorithm itself is also a schematic of the proof of optimality. As we will show in the following, the ground state problem for a fixed periodicity can be transformed into a maximum satisfiability problem [45], a well-researched class of optimization problems for which highly efficient solvers exist [46,47].…”

Section: B Obtaining the Ground State At A Fixed Periodicitymentioning

confidence: 99%

“…Such an optimization over discrete {0,1} variables can be equivalently posed as a logic problem by converting the minimization problem into the negative of a maximization problem and replacing the discrete variables by Boolean equivalents. Following this insight, the minimization of the finite Hamiltonian can be expressed in the form of a PBO problem, allowing us to solve this optimization as a weighted partial maximum satisfiability (MAX-SAT) [46,47] problem. The essence of MAX-SAT is to model the discrete optimization problem by maximizing the number of logical clauses that can be satisfied in a Boolean formula of conjunctive normal form, weighted by a set of arbitrary coefficients.…”

Section: B Obtaining the Ground State At A Fixed Periodicitymentioning

confidence: 99%

“…Furthermore, the algorithms are run through an annual MAX-SAT competition [49], which tests their correctness, robustness, and efficiency. Under such stringent criteria, by converting our problem into MAX-SAT, we can safely guarantee provability, as well as further investigate the advanced proof schemes and fast algorithms developed over the last 20 years of MAX-SAT research [46,47,50]. The particular MAX-SAT solver we chose, based on the results of the MAX-SAT 2014 competition benchmarking and our own testing, is CCLS_to_akmaxsat [47,53].…”

Section: B Obtaining the Ground State At A Fixed Periodicitymentioning

confidence: 99%

See 1 more Smart Citation

Finding and proving the exact ground state of a generalized Ising model by convex optimization and MAX-SAT

Huang¹,

Kitchaev²,

Dacek³

et al. 2016

Phys. Rev. B

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Lattice models, also known as generalized Ising models or cluster expansions, are widely used in many areas of science and are routinely applied to the study of alloy thermodynamics, solid-solid phase transitions, magnetic and thermal properties of solids, fluid mechanics, and others. However, the problem of finding and proving the global ground state of a lattice model, which is essential for all of the aforementioned applications, has remained unresolved for relatively complex practical systems, with only a limited number of results for highly simplified systems known. In this paper, we present a practical and general algorithm that provides a provable periodically constrained ground state of a complex lattice model up to a given unit cell size and in many cases is able to prove global optimality over all other choices of unit cell. We transform the infinite-discrete-optimization problem into a pair of combinatorial optimization (MAX-SAT) and nonsmooth convex optimization (MAX-MIN) problems, which provide upper and lower bounds on the ground state energy, respectively. By systematically converging these bounds to each other, we may find and prove the exact ground state of realistic Hamiltonians whose exact solutions are difficult, if not impossible, to obtain via traditional methods. Considering that currently such practical Hamiltonians are solved using simulated annealing and genetic algorithms that are often unable to find the true global energy minimum and inherently cannot prove the optimality of their result, our paper opens the door to resolving longstanding uncertainties in lattice models of physical phenomena. An implementation of the algorithm is available at https://github.com/dkitch/maxsat-ising.

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CCLS: An Efficient Local Search Algorithm for Weighted Maximum Satisfiability

Cited by 86 publications

References 40 publications

Evidence of Exponential Speed‐Up in the Solution of Hard Optimization Problems

Evidence of Exponential Speed‐Up in the Solution of Hard Optimization Problems

Solving #SAT and MAXSAT by Dynamic Programming

Finding and proving the exact ground state of a generalized Ising model by convex optimization and MAX-SAT

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