A Survey on String Constraint Solving

String constraint solving refers to solving combinatorial problems involving constraints over string variables. String solving approaches have become popular over the past few years given the massive use of strings in different application domains like formal analysis, automated testing, database query processing, and cybersecurity. This article reports a comprehensive survey on string constraint solving by exploring the large number of approaches that have been proposed over the past few decades to solve string constraints.

Algorithms for Weighted Independent Transversals and Strong Colouring

An independent transversal (IT) in a graph with a given vertex partition is an independent set consisting of one vertex in each partition class. Several sufficient conditions are known for the existence of an IT in a given graph and vertex partition, which have been used over the years to solve many combinatorial problems. Some of these IT existence theorems have algorithmic proofs, but there remains a gap between the best existential bounds and the bounds obtainable by efficient algorithms. Recently, Graf and Haxell (2018) described a new (deterministic) algorithm that asymptotically closes this gap, but there are limitations on its applicability. In this article, we develop a randomized algorithm that is much more widely applicable, and demonstrate its use by giving efficient algorithms for two problems concerning the strong chromatic number of graphs.

Probabilistic Combinatorial Model of the Epidemic for a University

The aim of the research was to identify the main causes of infection of teachers and students in a university. Two probabilistic combinatorial problems are considered analytically to determine the probabilities and rates of infection of teachers and students in a university as a result of the appearance of infected persons among the contingent of students. The mathematical apparatus of probability theory and combinatorics is used to solve the problems. For the factorials of combinations arising in the structure, the asymptotic Stirling’s formula is used. Convergent series arise in the final formulas, reflecting the multiplicity of scenarios of the probabilistic approach. Analytical formulas for the sums of series, probabilities and rates of infection of teachers and students are obtained. It is shown that the infection of teachers and students occurs through «dangerous» spatially close contacts, when a teacher and a student talk at a distance of less than 0.5 meter. It is impossible to exclude such contacts in the students’ environment during full-time study. Among teachers, there is also a less probable classroom mechanism of infection through the volume of air infected with viruses.

Emerging Applications of Bio-Inspired Algorithms in Image Segmentation

Image processing is one example of digital media. It consists of a set of operations to handle an image. Image segmentation is among its main important operations. It involves dividing the image into several parts or regions to extract vital information or identify relevant objects. Many techniques of artificial intelligence, including bio-inspired algorithms, have been used in this regard. This article collected the state-of-the-art studies presenting image-segmentation techniques combined with four bio-inspired algorithms including particle swarm optimization (PSO), genetic algorithms (GA), ant colony optimization (ACO), and artificial bee colonies (ABC). This research work aimed at showing the importance of image segmentation and its combination with these algorithms. This article provides insights on how these algorithms are adapted to image-segmentation combinatorial problems, which assist researchers to start the first hands-on application. It also discusses their setting parameters and the highly used algorithms such as PSO, GA, ACO, and ABC. The article presents new research directions in image segmentation based on bio-inspired algorithms.

Dynastic Potential Crossover Operator

An optimal recombination operator for two parent solutions provides the best solution among those that take the value for each variable from one of the parents (gene transmission property). If the solutions are bit strings, the offspring of an optimal recombination operator is optimal in the smallest hyperplane containing the two parent solutions. Exploring this hyperplane is computationally costly, in general, requiring exponential time in the worst case. However, when the variable interaction graph of the objective function is sparse, exploration can be done in polynomial time. In this paper, we present a recombination operator, called Dynastic Potential Crossover (DPX), that runs in polynomial time and behaves like an optimal recombination operator for low-epistasis combinatorial problems. We compare this operator, both theoretically and experimentally, with traditional crossover operators, like uniform crossover and network crossover, and with two recently defined efficient recombination operators: partition crossover and articulation points partition crossover. The empirical comparison uses NKQ Landscapes and MAX-SAT instances. DPX outperforms the other crossover operators in terms of quality of the offspring and provides better results included in a trajectory and a population-based metaheuristic, but it requires more time and memory to compute the offspring.

Real subset sums and posets with an involution

In this paper, we carry out in an abstract order context some real subset combinatorial problems. Specifically, let [Formula: see text] be a finite poset, where [Formula: see text] is an order-reversing and involutive map such that [Formula: see text] for each [Formula: see text]. Let [Formula: see text] be the Boolean lattice with two elements and [Formula: see text] the family of all the order-preserving 2-valued maps [Formula: see text] such that [Formula: see text] if [Formula: see text] for all [Formula: see text]. In this paper, we build a family [Formula: see text] of particular subsets of [Formula: see text], that we call [Formula: see text]-bases on [Formula: see text], and we determine a bijection between the family [Formula: see text] and the family [Formula: see text]. In such a bijection, a [Formula: see text]-basis [Formula: see text] on [Formula: see text] corresponds to a map [Formula: see text] whose restriction of [Formula: see text] to [Formula: see text] is the smallest 2-valued partial map on [Formula: see text] which has [Formula: see text] as its unique extension in [Formula: see text]. Next we show how each [Formula: see text]-basis on [Formula: see text] becomes, in a particular context, a sub-system of a larger system of linear inequalities, whose compatibility implies the compatibility of the whole system.

A Novel Learning-Based Binarization Scheme Selector for Swarm Algorithms Solving Combinatorial Problems

Currently, industry is undergoing an exponential increase in binary-based combinatorial problems. In this regard, metaheuristics have been a common trend in the field in order to design approaches to successfully solve them. Thus, a well-known strategy includes the employment of continuous swarm-based algorithms transformed to perform in binary environments. In this work, we propose a hybrid approach that contains discrete smartly adapted population-based strategies to efficiently tackle binary-based problems. The proposed approach employs a reinforcement learning technique, known as SARSA (State–Action–Reward–State–Action), in order to utilize knowledge based on the run time. In order to test the viability and competitiveness of our proposal, we compare discrete state-of-the-art algorithms smartly assisted by SARSA. Finally, we illustrate interesting results where the proposed hybrid outperforms other approaches, thus, providing a novel option to tackle these types of problems in industry.

Conceptual foundations for the development of developing software systems using multivariate synthesis of design solutions

Considering software systems as developing, changing their structure and characteristics during the entire process of development, implementation and operation is an important task. The difficulties that arise in this case, associated with the large dimension of combinatorial problems that arise in the process of studying software systems, taking into account the dynamics of their development, it is advisable to overcome on the basis of using methods of multivariate synthesis, with the help of which a multi-stage approach to solving emerging problems is formed, including evaluating the effectiveness of the solution at each stage.

A genetic algorithm for optimal assembly of pairwise forced-choice questionnaires

The use of multidimensional forced-choice questionnaires has been proposed as a means of improving validity in the assessment of non-cognitive attributes in high-stakes scenarios. However, the reduced precision of trait estimates in this questionnaire format is an important drawback. Accordingly, this article presents an optimization procedure for assembling pairwise forced-choice questionnaires while maximizing posterior marginal reliabilities. This procedure is performed through the adaptation of a known genetic algorithm (GA) for combinatorial problems. In a simulation study, the efficiency of the proposed procedure was compared with a quasi-brute-force (BF) search. For this purpose, five-dimensional item pools were simulated to emulate the real problem of generating a forced-choice personality questionnaire under the five-factor model. Three factors were manipulated: (1) the length of the questionnaire, (2) the relative item pool size with respect to the questionnaire’s length, and (3) the true correlations between traits. The recovery of the person parameters for each assembled questionnaire was evaluated through the squared correlation between estimated and true parameters, the root mean square error between the estimated and true parameters, the average difference between the estimated and true inter-trait correlations, and the average standard error for each trait level. The proposed GA offered more accurate trait estimates than the BF search within a reasonable computation time in every simulation condition. Such improvements were especially important when measuring correlated traits and when the relative item pool sizes were higher. A user-friendly online implementation of the algorithm was made available to the users.