Boolean Variables Research Articles

Formulation and algorithmization of the interleaved vehicle routing problem

The problem of routing between two types of objects is considered. Two variants of the problem statement are considered: with a single point of collection and without it. An important aspect of the routes is the mandatory alternation of different types of objects. A mathematical model of the problem with boolean variables is proposed for each statement. A meaningful statement can be represented as the task of collecting haystacks in trucks afield. Two algorithms are developed to solve this problem. The first one is based on the “greedy” strategies, and the second one is based on the approach of Ant Colony Optimization (ACO) algorithms. To configure the parameters of the second algorithm it is carried out the computational experiment. The results of the experiment are provided. In conclusion, the main results of the work are presented.

Dynamic optimization model of formation of an optimal portfolio of regional strategic projects for maximal advancement on the development of human capital

This study is conducted within the framework of a relevant scientific research objective consisting in the accumulation and development of regional human capital. In the conditions of uncertainty, risks and resource scarcity, the regional authorities are facing the task of optimal distribution of the budget between strategic projects, which exert direct or indirect influence upon the development of regional human capital. On the example of Primorksy Krai, the goal of this research consists in structuring and approbation of a dynamic optimization model for formation of an optimal portfolio of regional strategic projects form maximally efficient development of human capital in the region. The authors develop a dynamic model in form of a task of a mathematical programming and describing the impact of regional strategic projects upon the human capital indexes in the region. As the target function, the work uses weighted average of the degree of meeting the objective value of regional human capital development indexes on the examined horizon of planning. The functional dependence of human capital indexes upon the volume and structure of investments, forming from the regional budgetary and private spending on the implementation of the projects and ensuring procedural activity on the regional level, serve as lagged econometric models. Variables for conducting optimization are represented by the Boolean variables of inclusion of the project by one or another vector of investing into the project portfolio in a particular moment in time. The optimal portfolio of strategic projects is proposed in annual dynamics, based on the results of the modeling and quantitative calculations made on the example of Primorsky Krai. Such portfolio provides for maximal efficiency in reaching objective values of development of the regional human capital indexes.

Path Planning for Minimizing the Expected Cost Until Success

Consider a general path planning problem of a robot on a graph with edge costs, where each node has a Boolean value of success or failure (with respect to some task) with a given probability. The objective is to plan a path for the robot on the graph that minimizes the expected cost until success. In this paper, it is our goal to bring a foundational understanding to this problem. We start by showing how this problem can be optimally solved by formulating it as an infinite-horizon Markov decision process, but with an exponential space complexity. We then formally prove its NP-hardness. To address the space complexity, we then propose a path planner, using a game-theoretic framework, that asymptotically gets arbitrarily close to the optimal solution. Moreover, we also propose two fast and nonmyopic path planners. To show the performance of our framework, we do extensive simulations for two scenarios: a rover on Mars searching for an object for scientific studies, and a robot looking for a connected spot to a remote station (with real data from downtown San Francisco). Our numerical results show a considerable performance improvement over existing state-of-the-art approaches.

Mass Balance of the Himalayan Glaciers and Their Regional Variations

Aim: Popular methods of glacial mass balance studies are time consuming, laborious and therefore, not repetitive at yearly manner. A compact, user-friendly classification algorithm has been applied to estimate Equilibrium Line Altitude (ELA) and mass balance of mountain or valley glaciers at yearly basis using Synthetic Aperture Radar (SAR) data for a period of 2012 to 2015. Cloud cover over the glacier catchment areas was studied to identify major seasons of precipitation over the study areas. The results were also compared to study the regional characteristics of the glaciers.
 Study Area: The proposed module was used to analyze data over three Himalayan glaciers, namely, Durung Drung, Gangorti and Zemu. Chhota Shigri glacier was also studied with these three glaciers to understand the regional variations of the Himalayan glaciers.
 Methodology: The classification algorithm was fixed for all glaciers and also independent from season, therefore, required least user intervention. The conditional loop based logics, consist of linear equations, classified glaciated region in different physical zones. Purely backscatter based classification result produced error by mixing zones due to overlapped signatures. Altitude thresholds of accumulation zones were employed to segregate the mixing in next level. The method required calibrated ortho-rectified sigma naught dual-pol SAR imagery as primary input. The glaciated area should be provided as Area of Interest (AOI). A Digital Elevation Model (DEM) file is required for altitude threshold. The output classes are saved in separate files with Boolean values. Optical data were used to estimate cloud coverage over the catchments of the glaciers.
 Results: Average mass balance of the selected glaciers is estimated as - 0.44 m w.e.a-1 during the study period. The mass balance of the glaciers are comparatively studied with variation in melting seasons, duration of melting periods, on set and cease of melting for each glacier to understand the regional pattern of mass loss.
 Conclusion: Co and cross polarized SAR data are employed to derived debris size; however, cross polarized SAR backscattering has better correlation with debris size. The accuracy of the result derived from the developed method is ± 50 mm. Collection of field data on the surface topography is difficult for Mountain glaciers, especially over Himalaya. Use of satellite data can generate detailed information of glacier surface which will be further help to understand role of debris in glacier mass balance.

Factoring on a quantum annealing computer

This paper is about quantum factoring all integers in an interval. Our goal is to be able to factor all positive integers N < 1,000. We reached this goal on a D-Wave 2000 qubit processor by minimizing (N - (pxq))^2 by using one routine that calls the interface software dw. We sized p<32 and q<256 as Boolean variables. We factored seven semiprimes that could not be factored by the method in a 2016 D-Wave report. We did not use information about the factors for a specific N. The inputs to our routine are N and values for two parameters.

On the conversion of multivalued to Boolean dynamics

Results and tools on discrete interaction networks are often concerned with Boolean variables, whereas considering more than two levels is sometimes useful. Multivalued networks can be converted to partial Boolean maps, in a way that preserves the asynchronous dynamics. We investigate the problem of extending these maps to non-admissible states, i.e. states that do not have a multivalued counterpart. We observe that attractors are preserved if a stepwise version of the original function is considered for conversion. Different extensions of the Boolean conversion affect the structure of the interaction graphs in different ways. A particular technique for extending the partial Boolean conversion is identified, that ensures that feedback cycles are preserved. This property, combined with the conservation of the asymptotic behaviour, can prove useful for the application of results and analyses defined in the Boolean setting to multivalued networks, and vice versa. As a first application, by considering the conversion of a known example for the discrete multivalued case, we create a Boolean map showing that the existence of a cyclic attractor and the absence of fixed points are compatible with the absence of local negative cycles. We then state a multivalued version of a result connecting mirror states and local feedback cycles.

Regular switching components

We consider a problem of Discrete Tomography which consists of reconstructing a finite lattice set S⊂Z2 from given horizontal and vertical X-rays (i.e. with prescribed numbers of points in each row and column). Without additional requirements, the problem can be solved in polynomial time. Many variants require the solution to be in a chosen class A. For instance, the problem is NP-complete for the class A=H∩V of HV-convex lattice sets and it is polynomial for the class A=H∩V∩P of HV-convex polyominoes. Twenty years after these results, the problem's complexity remains unknown for A=C, the class of C-convex lattice sets (i.e. two-dimensional lattice polytopes).The main difficulty to solve this problem comes from combinatorial structures called switching components. Switching components are closed path with horizontal and vertical edges such that the solutions S are composed of either the elements of even or of odd indices. This binary choice can be encoded by a Boolean variable associated with the switching component and the convexity constraints are simply encoded by SAT clauses (2-clauses for HV-convexity and 3-clauses for C-convexity).The purpose of the paper is to investigate the properties of the switching components and the consequences of the convexity requirements. We divide the switching components in two classes: regular if their turning angle is constant, irregular otherwise. We prove that adjacent regular switching components have the same Boolean values. This property allows us to merge them into extended switching components. We prove that if all switching components are regular, then the extended switching components are all independent (then the number of solutions with the considered feet is 2n, where n is the number of extended switching components). Finally, we prove that they are geometrically ordered.

On the relationships between hybrid generalized Bosbach states and L-filters in non-commutative residuated lattices

States and filters play the essential roles in studying logical algebras. In this paper, we study the relationships between hybrid generalized Bosbach states and L-filters and hybrid L-filters in non-commutative residuated lattices. Particularly, two types of L-filters and hybrid L-filters and their subclasses are defined, and some of their properties are obtained. Then, relationships between special types of (hybrid) L-filters and the hybrid generalized Bosbach states are considered where hybrid generalized Bosbach states are characterized by some type I or type II (hybrid) L-filters with additional conditions. Associated with these relationships, new subclasses of hybrid generalized Bosbach states such as implicative type IV-1, IV-2, V-1, V-2, VI-1, VI-2 states, Involution type IV-1, IV-2 states and Boolean type IV-1, IV-2 states are introduced, and the relationships between various types of hybrid generalized Bosbach states are investigated in detail.

Quantitative separation logic: a logic for reasoning about probabilistic pointer programs

We present quantitative separation logic (QSL). In contrast to classical separation logic, QSL employs quantities which evaluate to real numbers instead of predicates which evaluate to Boolean values. The connectives of classical separation logic, separating conjunction and separating implication, are lifted from predicates to quantities. This extension is conservative: Both connectives are backward compatible to their classical analogs and obey the same laws, e.g. modus ponens, adjointness, etc. Furthermore, we develop a weakest precondition calculus for quantitative reasoning about probabilistic pointer programs in QSL. This calculus is a conservative extension of both Ishtiaq’s, O’Hearn’s and Reynolds’ separation logic for heap-manipulating programs and Kozen’s / McIver and Morgan’s weakest preexpectations for probabilistic programs. Soundness is proven with respect to an operational semantics based on Markov decision processes. Our calculus preserves O’Hearn’s frame rule , which enables local reasoning. We demonstrate that our calculus enables reasoning about quantities such as the probability of terminating with an empty heap, the probability of reaching a certain array permutation, or the expected length of a list.

Machine Learning Based Quantitative Association Rule Mining Method for Evaluating Cellular Network Performance

Cellular network performance is often evaluated by key performance indicator (KPI) and key quality indicator (KQI). The association between KQI and KPI is the most critical step to optimize the performance of cellular network. Traditional association methods between KPI and KQI are based on the end-to-end evaluation. However, these methods require professional engineers to evaluate cellular network performance, and the man-manned evaluation is often inaccurate and labor-consuming, which cannot find out the caused factor of deterioration networks. In order to solve the problem, we propose a machine learning based quantitative association rule mining (QARM) method called SWP-RF, which consists of sliding-window partitioning (SWP) and random forest (RF), to associate KPI with KQI. Specifically, we first use SWP to discretize continuous attributes into boolean values, which is adopted to mine its association rules. The warning intervals and the warning points is obtained by SWP. Next, we use RF feature importance to measure the association between KPI and KQI. The priority of the association strength between all KPIs and each KQI can be obtained by RF. Finally, we select the warning points and the association strength priority as optimal output solution. Experiments are conducted over the actual data from telecom operators and the results confirm the feasibility and accuracy of the proposed method.

An Efficient Algorithm for Decreasing the Granularity Levels of Attributes in Formal Concept Analysis

In the formal concept analysis (FCA), a concept lattice represents the basic structure derived from Boolean data describing the relationships between objects and attributes. One of the basic problems of FCA is to control the structure of concept lattices to extract useful information. To explore a data set, sometimes we need to tune the structure of the corresponding concept lattice by merging a couple of finer attributes to a coarser attribute. The merged attribute can be interpreted as a coarser granularity level. In this paper, we propose an efficient algorithm called fold for decreasing the granularity levels of attributes. We analyzed and explored the relationships between concepts before and after decreasing the granularity level of an attribute. Based on those theoretical proofs, we propose an efficient method of classifying concepts to reduce the comparisons between the concepts compared with the original zoom-out algorithm. Moreover, we provide a preprocessing procedure to search for canonical generators and help restore the covering relation. We describe the algorithm completely, discuss time complexity issues, and present an experimental evaluation of its performance and comparison with the zoom-out algorithm. The theoretical and empirical analyses demonstrate the advantages of our algorithm when applied to various types of formal contexts.

Diagnostics of the pre-fault situation of the bolted current-carrying joint in the conditions of changing regime parameters

The object of research is the methods of non-destructive monitoring of the state of a bolted current-carrying joint under conditions of dynamically changing current load conditions and ambient temperature. One of the most problematic places in the modern conditions of economic development of enterprises is the reduction in the accident rate of production due to the weakening of the bolted current-carrying joint. Studies of the causes of stopping electrical equipment at a number of ferrous metallurgy enterprises, mining and processing complexes, in medical institutions have shown that in 1.5-2 % of cases the cause of an emergency shutdown of electrical equipment is the weakening of the bolted current-carrying joint. The main problem of the bolted current-carrying joint is the mechanical weakening of the contact density. The appearance of a temperature gradient in the place of a bolted joint is influenced by climatic parameters and dynamically changing modes of operating current loads and network voltage.The study of operating parameters of the network and load currents is based on the use of a technique for monitoring the quality of electricity indicators using self-recording spectrum analyzers. In this study, the spectrum analyzer Fluk 435 (Ukraine) is used, the characteristics of which correspond to the ISO 9001 measurement system certificate. Statistical processing methods are used as the basis for processing the experimentally obtained data.In the course of the study, the inequality between the measured temperature of the bolted current-carrying joint and the calculated temperature of the serviceable joint is determined. The inequality is fulfilled in the sections, the stationarity of which is determined for deterministic and random modes of change of the controlled parameters. The functions of Boolean variables are compiled, the disjunctive functions that determine the normal and pre-crash modes of the bolted joint are minimized. The obtained theoretical results allow developing algorithms and devices for diagnosing and protecting equipment.This provides the opportunity to reduce the accident rate of the equipment. Compared with similar well-known protection equipment, taking into account the modes of load currents, mains voltage and ambient temperature provides a high sensitivity and accuracy of detecting the initial moment of loosening of a bolted current-carrying joint.

1 A Novel Minimization Method for Sensor Deployment Via Heuristic 2-Sat Solution

The tasks of guard placement or sensor deployment in an art gallery, a museum or in the corridors of public and security buildings pose the same problem, which requires placing the guards or sensors so as to cover a specified set of nodes with a minimum number of sensors or guards, thereby reducing the overall cost of the system as well assist power consumption. Generally, minimization can be done using optimization techniques such as linear programming, but in case of sensor deployment or guard placement there is a need either to place or not to place the sensor or guard, and hence only Boolean or binary values are used. Therefore, in order to optimize such a problem, we use the special case of linear integer programming known as Boolean integer linear programming (0-1 ILP). Other algorithms like Pseudo-Boolean SAT Solvers can also be used for the minimization purpose. In this paper, we introduce these minimization algorithms for the sensor deployment problem. We also contribute a greed-based heuristic, which utilizes the fact that the pertinent propositional formulas have variables of purely un-complemented literals. This heuristic has much less computational cost compared to those of 0-1 ILP and the Pseudo-Boolean SAT Solvers.

A Novel Minimization Method for Sensor Deployment Via Heuristic 2-Sat Solution

The tasks of guard placement or sensor deployment in an art gallery, a museum or in the corridors of public and security buildings pose the same problem, which requires placing the guards or sensors so as to cover a specified set of nodes with a minimum number of sensors or guards, thereby reducing the overall cost of the system as well assist power consumption. Generally, minimization can be done using optimization techniques such as linear programming, but in case of sensor deployment or guard placement there is a need either to place or not to place the sensor or guard, and hence only Boolean or binary values are used. Therefore, in order to optimize such a problem, we use the special case of linear integer programming known as Boolean integer linear programming (0-1 ILP). Other algorithms like Pseudo-Boolean SAT Solvers can also be used for the minimization purpose. In this paper, we introduce these minimization algorithms for the sensor deployment problem. We also contribute a greed-based heuristic, which utilizes the fact that the pertinent propositional formulas have variables of purely un-complemented literals. This heuristic has much less computational cost compared to those of 0-1 ILP and the Pseudo-Boolean SAT Solvers.

A Novel Minimization Method for Sensor Deployment Via Heuristic 2-Sat Solution

The tasks of guard placement or sensor deployment in an art gallery, a museum or in the corridors of public and security buildings pose the same problem, which requires placing the guards or sensors so as to cover a specified set of nodes with a minimum number of sensors or guards, thereby reducing the overall cost of the system as well assist power consumption. Generally, minimization can be done using optimization techniques such as linear programming, but in case of sensor deployment or guard placement there is a need either to place or not to place the sensor or guard, and hence only Boolean or binary values are used. Therefore, in order to optimize such a problem, we use the special case of linear integer programming known as Boolean integer linear programming (0-1 ILP). Other algorithms like Pseudo-Boolean SAT Solvers can also be used for the minimization purpose. In this paper, we introduce these minimization algorithms for the sensor deployment problem. We also contribute a greed-based heuristic, which utilizes the fact that the pertinent propositional formulas have variables of purely un-complemented literals. This heuristic has much less computational cost compared to those of 0-1 ILP and the Pseudo-Boolean SAT Solvers.

Approximation schemes for r-weighted Minimization Knapsack problems

Stimulated by salient applications arising from power systems, this paper studies a class of non-linear Knapsack problems with non-separable quadratic constrains, formulated in either binary or integer form. These problems resemble the duals of the corresponding variants of 2-weighted Knapsack problem (a.k.a., complex-demand Knapsack problem) which has been studied in the extant literature under the paradigm of smart grids. Nevertheless, the employed techniques resulting in a polynomial-time approximation scheme (PTAS) for the 2-weighted Knapsack problem are not amenable to its minimization version. We instead propose a greedy geometry-based approach that arrives at a quasi PTAS (QPTAS) for the minimization variant with boolean variables. As for the integer formulation, a linear programming-based method is developed that obtains a PTAS. In view of the curse of dimensionality, fast greedy heuristic algorithms are presented, additionally to QPTAS. Their performance is corroborated extensively by empirical simulations under diverse settings and scenarios.

Optimizing the selection of information security remedies in terms of a Markov security model

An information security model expressed in terms of Markov processes is considered. Within this model the functioning of information system as a sequence of failures and recovery actions that appear in response to security threats is described. A detailed investigation of the model is provided, and its important characteristic called the relaxation time is introduced. A permissible range of security parameters is constructed by using the relaxation time. The problem of selection of information security remedies as a problem of non-linear optimization with boolean variables is stated and discussed.

Game theory based complex analysis for nuclear security using non-zero sum algorithm

The non-linear complex algorithm is applied to the nuclear security where the non-zero sum quantifications of the game theory is applied for simulations. In the results, the values are described as the integers, because the Boolean values are calculated in the modeling. There are several interested factors as Nuclear Fuel, Safety System, Security System, Operator, and Government. In the simulations, the positive values show the possibility of terror incidents which are obtained as dynamical manner in the Boolean numbers of 1.0 or −1.0. The cumulative values show the five nuclear security factors are summed up. For the aging effect, the graph gives the highest value as 18 at 715th month. The analysis of payoff graph shows the result of the payoff of each factor where there are meeting points around 360th month and 450th month. Therefore, the possibility of the terrorism increases as time goes on.

Binary Representation of Natural Numbers

Summary Binary representation of integers [5], [3] and arithmetic operations on them have already been introduced in Mizar Mathematical Library [8, 7, 6, 4]. However, these articles formalize the notion of integers as mapped into a certain length tuple of boolean values. In this article we formalize, by means of Mizar system [2], [1], the binary representation of natural numbers which maps ℕ into bitstreams.

Fluidic gates simulated with lattice Boltzmann method under different Reynolds numbers

Fluidic devices use fluid as a medium for information transfer and computation. Boolean values are represented by the presence of fluid jets in the input and output channels. Velocity of a fluid is one of the parameters determining Reynolds number of the flow. Reynolds number is a parameter that characterizes the behaviour of the flow: laminar, transient or turbulent. Using lattice Boltzmann method we study the behaviour of fluidic gates for various Reynolds numbers. On the designs of and and or gates we show the fluidic gates remain functional even for low Reynolds numbers, like 100. The gates designed can be cascaded into functional logical circuits.