Fuzzy Maximum Satisfiability

In this paper, we extend the Maximum Satisfiability (MaxSAT) problem to {\L}ukasiewicz logic. The MaxSAT problem for a set of formulae {\Phi} is the problem of finding an assignment to the variables in {\Phi} that satisfies the maximum number of formulae. Three possible solutions (encodings) are proposed to the new problem: (1) Disjunctive Linear Relations (DLRs), (2) Mixed Integer Linear Programming (MILP) and (3) Weighted Constraint Satisfaction Problem (WCSP). Like its Boolean counterpart, the extended fuzzy MaxSAT will have numerous applications in optimization problems that involve vagueness.Comment: 10 page

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

Special issue on logics and artificial intelligence

There is a significant range of ongoing challenges in artificial intelligence (AI) dealing with reasoning, planning, learning, perception and cognition, among others. In this scenario, many-valued logics emerge as one of the topics in many of the solutions to some of those AI problems. This special issue presents a brief introduction to the relation between logics and AI and collects recent research works on logic-based approaches in AI

IMLI: An Incremental Framework for MaxSAT-Based Learning of Interpretable Classification Rules

The wide adoption of machine learning in the critical domains such as medical diagnosis, law, education had propelled the need for interpretable techniques due to the need for end users to understand the reasoning behind decisions due to learning systems. The computational intractability of interpretable learning led practitioners to design heuristic techniques, which fail to provide sound handles to tradeoff accuracy and interpretability. Motivated by the success of MaxSAT solvers over the past decade, recently MaxSAT-based approach, called MLIC, was proposed that seeks to reduce the problem of learning interpretable rules expressed in Conjunctive Normal Form (CNF) to a MaxSAT query. While MLIC was shown to achieve accuracy similar to that of other state of the art black-box classifiers while generating small interpretable CNF formulas, the runtime performance of MLIC is significantly lagging and renders approach unusable in practice. In this context, authors raised the question: Is it possible to achieve the best of both worlds, i.e., a sound framework for interpretable learning that can take advantage of MaxSAT solvers while scaling to real-world instances? In this paper, we take a step towards answering the above question in affirmation. We propose IMLI: an incremental approach to MaxSAT based framework that achieves scalable runtime performance via partition-based training methodology. Extensive experiments on benchmarks arising from UCI repository demonstrate that IMLI achieves up to three orders of magnitude runtime improvement without loss of accuracy and interpretability.Comment: 10 pages, published in the proceedings of AAAI/ACM Conference on AI, Ethics, and Society (AIES 2019

ASlib: A Benchmark Library for Algorithm Selection

The task of algorithm selection involves choosing an algorithm from a set of algorithms on a per-instance basis in order to exploit the varying performance of algorithms over a set of instances. The algorithm selection problem is attracting increasing attention from researchers and practitioners in AI. Years of fruitful applications in a number of domains have resulted in a large amount of data, but the community lacks a standard format or repository for this data. This situation makes it difficult to share and compare different approaches effectively, as is done in other, more established fields. It also unnecessarily hinders new researchers who want to work in this area. To address this problem, we introduce a standardized format for representing algorithm selection scenarios and a repository that contains a growing number of data sets from the literature. Our format has been designed to be able to express a wide variety of different scenarios. Demonstrating the breadth and power of our platform, we describe a set of example experiments that build and evaluate algorithm selection models through a common interface. The results display the potential of algorithm selection to achieve significant performance improvements across a broad range of problems and algorithms.Comment: Accepted to be published in Artificial Intelligence Journa

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