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A continuous-time MaxSAT solver with high analog performance
Botond Molnár1,2,3, Ferenc Molnár4, Melinda Varga4,5
1Faculty of Physics, Babeş-Bolyai University, Cluj-Napoca, 400084, Romania.
Nature Communications
|November 20, 2018
Summary
A new continuous-time analog solver for the NP-hard Maximum Satisfiability (MaxSAT) problem is introduced. Its escape rate predicts optimal solutions and shows potential for discrete optimization challenges.
Area of Science:
- Computational complexity
- Optimization algorithms
- Dynamical systems
Background:
- Many real-world problems are modeled as Maximum Satisfiability (MaxSAT), which is NP-hard.
- Efficient algorithms for MaxSAT are currently unknown, hindering practical applications.
Purpose of the Study:
- To present a novel continuous-time analog solver for MaxSAT problems.
- To demonstrate the solver's ability to predict optimal solutions using its dynamics.
Main Methods:
- Developed a continuous-time analog dynamical system as a solver for MaxSAT.
- Analyzed the scaling of the solver's escape rate, an invariant of its dynamics.
- Simulated the solver on MaxSAT competition instances and Ramsey number problems.
Main Results:
- The escape rate scaling predicts the maximum number of satisfiable constraints, often before finding the exact solution.
- The solver was tested on MaxSAT competition problems.
- Applied to Ramsey number R(m, m) problems, finding colorings for N≤42 and supporting R(5, 5)=43.
Conclusions:
- Continuous-time analog dynamical systems offer a promising algorithmic approach for discrete optimization problems like MaxSAT.
- The escape rate serves as a predictive measure for solution quality in analog solvers.
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