Applications of MaxSAT in Data Analysis

Peer reviewe

Learning to Generate Genotypes with Neural Networks

Neural networks and evolutionary computation have a rich intertwined history. They most commonly appear together when an evolutionary algorithm optimises the parameters and topology of a neural network for reinforcement learning problems, or when a neural network is applied as a surrogate fitness function to aid the evolutionary optimisation of expensive fitness functions. In this paper we take a different approach, asking the question of whether a neural network can be used to provide a mutation distribution for an evolutionary algorithm, and what advantages this approach may offer? Two modern neural network models are investigated, a Denoising Autoencoder modified to produce stochastic outputs and the Neural Autoregressive Distribution Estimator. Results show that the neural network approach to learning genotypes is able to solve many difficult discrete problems, such as MaxSat and HIFF, and regularly outperforms other evolutionary techniques

MaxSAT Evaluation 2022 : Solver and Benchmark Descriptions

Non peer reviewe

Efficiently Explaining CSPs with Unsatisfiable Subset Optimization (extended algorithms and examples)

We build on a recently proposed method for stepwise explaining solutions of Constraint Satisfaction Problems (CSP) in a human-understandable way. An explanation here is a sequence of simple inference steps where simplicity is quantified using a cost function. The algorithms for explanation generation rely on extracting Minimal Unsatisfiable Subsets (MUS) of a derived unsatisfiable formula, exploiting a one-to-one correspondence between so-called non-redundant explanations and MUSs. However, MUS extraction algorithms do not provide any guarantee of subset minimality or optimality with respect to a given cost function. Therefore, we build on these formal foundations and tackle the main points of improvement, namely how to generate explanations efficiently that are provably optimal (with respect to the given cost metric). For that, we developed (1) a hitting set-based algorithm for finding the optimal constrained unsatisfiable subsets; (2) a method for re-using relevant information over multiple algorithm calls; and (3) methods exploiting domain-specific information to speed up the explanation sequence generation. We experimentally validated our algorithms on a large number of CSP problems. We found that our algorithms outperform the MUS approach in terms of explanation quality and computational time (on average up to 56 % faster than a standard MUS approach).Comment: arXiv admin note: text overlap with arXiv:2105.1176

Quantum Algorithm for Variant Maximum Satisfiability

In this paper, we proposed a novel quantum algorithm for the maximum satisfiability problem. Satisfiability (SAT) is to find the set of assignment values of input variables for the given Boolean function that evaluates this function as TRUE or prove that such satisfying values do not exist. For a POS SAT problem, we proposed a novel quantum algorithm for the maximum satisfiability (MAX-SAT), which returns the maximum number of OR terms that are satisfied for the SAT-unsatisfiable function, providing us with information on how far the given Boolean function is from the SAT satisfaction. We used Grover’s algorithm with a new block called quantum counter in the oracle circuit. The proposed circuit can be adapted for various forms of satisfiability expressions and several satisfiability-like problems. Using the quantum counter and mirrors for SAT terms reduces the need for ancilla qubits and realizes a large Toffoli gate that is then not needed. Our circuit reduces the number of ancilla qubits for the terms T of the Boolean function from T of ancilla qubits to ≈⌈log2⁡T⌉+1. We analyzed and compared the quantum cost of the traditional oracle design with our design which gives a low quantum cost

Momentum-inspired Low-Rank Coordinate Descent for Diagonally Constrained SDPs

We present a novel, practical, and provable approach for solving diagonally constrained semi-definite programming (SDP) problems at scale using accelerated non-convex programming. Our algorithm non-trivially combines acceleration motions from convex optimization with coordinate power iteration and matrix factorization techniques. The algorithm is extremely simple to implement, and adds only a single extra hyperparameter -- momentum. We prove that our method admits local linear convergence in the neighborhood of the optimum and always converges to a first-order critical point. Experimentally, we showcase the merits of our method on three major application domains: MaxCut, MaxSAT, and MIMO signal detection. In all cases, our methodology provides significant speedups over non-convex and convex SDP solvers -- 5X faster than state-of-the-art non-convex solvers, and 9 to 10^3 X faster than convex SDP solvers -- with comparable or improved solution quality.Comment: 10 pages, 8 figures, preprint under revie