Backbone Fragility and the Local Search Cost Peak

Uniquely Satisfiable d-Regular (k,s)-SAT Instances

Unique k-SAT is the promised version of k-SAT where the given formula has 0 or 1 solution and is proved to be as difficult as the general k-SAT. For any k≥3, s≥f(k,d) and (s+d)/2>k−1, a parsimonious reduction from k-CNF to d-regular (k,s)-CNF is given. Here regular (k,s)-CNF is a subclass of CNF, where each clause of the formula has exactly k distinct variables, and each variable occurs in exactly s clauses. A d-regular (k,s)-CNF formula is a regular (k,s)-CNF formula, in which the absolute value of the difference between positive and negative occurrences of every variable is at most a nonnegative integer d. We prove that for all k≥3, f(k,d)≤u(k,d)+1 and f(k,d+1)≤u(k,d). The critical function f(k,d) is the maximal value of s, such that every d-regular (k,s)-CNF formula is satisfiable. In this study, u(k,d) denotes the minimal value of s such that there exists a uniquely satisfiable d-regular (k,s)-CNF formula. We further show that for s≥f(k,d)+1 and (s+d)/2>k−1, there exists a uniquely satisfiable d-regular (k,s+1)-CNF formula. Moreover, for k≥7, we have that u(k,d)≤f(k,d)+1.

Artificial Intelligence and Machine Learning Applications in Smart Production: Progress, Trends, and Directions

Adaptation and innovation are extremely important to the manufacturing industry. This development should lead to sustainable manufacturing using new technologies. To promote sustainability, smart production requires global perspectives of smart production application technology. In this regard, thanks to intensive research efforts in the field of artificial intelligence (AI), a number of AI-based techniques, such as machine learning, have already been established in the industry to achieve sustainable manufacturing. Thus, the aim of the present research was to analyze, systematically, the scientific literature relating to the application of artificial intelligence and machine learning (ML) in industry. In fact, with the introduction of the Industry 4.0, artificial intelligence and machine learning are considered the driving force of smart factory revolution. The purpose of this review was to classify the literature, including publication year, authors, scientific sector, country, institution, and keywords. The analysis was done using the Web of Science and SCOPUS database. Furthermore, UCINET and NVivo 12 software were used to complete them. A literature review on ML and AI empirical studies published in the last century was carried out to highlight the evolution of the topic before and after Industry 4.0 introduction, from 1999 to now. Eighty-two articles were reviewed and classified. A first interesting result is the greater number of works published by the USA and the increasing interest after the birth of Industry 4.0.

Evolving combinatorial problem instances that are difficult to solve

This paper demonstrates how evolutionary computation can be used to acquire difficult to solve combinatorial problem instances. As a result of this technique, the corresponding algorithms used to solve these instances are stress-tested. The technique is applied in three important domains of combinatorial optimisation, binary constraint satisfaction, Boolean satisfiability, and the travelling salesman problem. The problem instances acquired through this technique are more difficult than the ones found in popular benchmarks. In this paper, these evolved instances are analysed with the aim to explain their difficulty in terms of structural properties, thereby exposing the weaknesses of corresponding algorithms.

Evolutionary algorithms for the satisfiability problem

Several evolutionary algorithms have been proposed for the satisfiability problem. We review the solution representations suggested in literature and choose the most promising one - the bit string representation - for further evaluation. An empirical comparison on commonly used benchmarks is presented for the most successful evolutionary algorithms and for WSAT, a prominent local search algorithm for the satisfiability problem. The key features of successful evolutionary algorithms are identified, thereby providing useful methodological guidelines for designing new heuristics. Our results indicate that evolutionary algorithms are competitive to WSAT.