Programming Problem Research Articles

Size Constrained Clustering With MILP Formulation

Clustering is one of the essential tools for data mining since it reveals the natural structures of the unlabeled data. Many clustering algorithms have been proposed in the last decades. However, few of them are designed to adapt prior knowledge that is available in many real applications, such as the sizes of clusters. In this paper, we propose a novel iterative clustering algorithm that can impose the constraints on the sizes of clusters. Given an unordered set of cluster size constraints, the proposed method minimizes the mean squared error (MSE) while simultaneously considers the size constraints. Each iteration of the proposed method consists of two steps, namely an assignment step and an update step. In the assignment step, the observations are assigned into clusters under the size constraints. The assignment task is modeled as an integer linear programming (ILP) problem. We prove that part of the constraint matrix of this ILP problem is total unimodular. Therefore, the integer constraints on most of the variables can be omitted so that the problem would become a mixed integer programming (MILP) problem which is much easier to solve. In the update step, new cluster centroids will be updated as the centers of the observations in the corresponding clusters. Experiments on UCI data sets indicate that (1) imposing the size constraints as proposed could improve the clustering performance; (2) compared with the state-of-the-art size constrained clustering methods, the proposed method could efficiently derive better clustering results.

On Robust Fractional 0-1 Programming

We study single- and multiple-ratio robust fractional 0-1 programming problems (RFPs). In particular, this work considers RFPs under a wide range of disjoint and joint uncertainty sets, where the former implies separate uncertainty sets for each numerator and denominator and the latter accounts for different forms of interrelatedness between them. We first demonstrate that unlike the deterministic case, a single-ratio RFP is nondeterministic polynomial-time hard under general polyhedral uncertainty sets. However, if the uncertainty sets are imbued with a certain structure, variants of the well-known budgeted uncertainty, the disjoint and joint single-ratio RFPs are polynomially solvable when the deterministic counterpart is. We also propose mixed-integer linear programming (MILP) formulations for multiple-ratio RFPs. We conduct extensive computational experiments using test instances based on real and synthetic data sets to evaluate the performance of our MILP reformulations as well as to compare the disjoint and joint uncertainty sets. Finally, we demonstrate the value of the robust approach by examining the robust solution in a deterministic setting and vice versa.

Secure Wireless Transmission for Intelligent Reflecting Surface-Aided Millimeter-Wave Systems

Due to the broadcast nature of millimeter wave (mmWave) communications, physical layer security has always been a fundamental but challenging concern. Fortunately, the recent advance of intelligent reflecting surface (IRS) introduces another dimension for mmWave secure communications by reconfiguring the transmission environments. In this article, we investigate the physical layer security issue for IRS-aided mmWave communications. Specifically, two scenarios are considered, i.e., with and without the knowledge of the eavesdropper’s channel. When the eavesdropper’s channel is known, under the unit modulus constraints at the IRS and the transmit power constraint at the access point (AP), the secrecy rate is maximized by jointly designing the beamforming vector of the AP and the phase shifts of the IRS. We propose an alternating optimization algorithm for improving the secrecy rate to solve the non-convex optimization problem. In particular, the phase shift matrix of the IRS is firstly optimized based on the manifold optimization algorithm. Under the given phase shift matrix of the IRS, the original problem is transformed into a difference of convex (DC) programming problem. To solve this problem, we use the successive convex approximation (SCA)-based method to transform the original problem into a convex approximation problem, and the transmit beamforming vector is obtained by solving the convex approximation problem. In addition, when the eavesdropper’s channel is unknown, under the transmit power constraint and the minimum user rate constraint, an artificial-noise (AN)-aided scheme is proposed to jam the eavesdropper by maximizing the AN power. Numerical results evaluate that the performance of our proposed schemes is better than that of the conventional scheme in terms of secrecy rate. Moreover, simulations also demonstrate that the secrecy behaviors of the IRS-aided mmWave communication system are superior to the mmWave communications without IRS.

Wide band time optimal spectrum sensing

Conventional methods for spectrum sensing do not consider historical traffic data. Equal amount of time is allocated to each channel of interest for sensing. In this research paper, we formulate the time optimization problem for spectrum sensing keeping historical traffic data into account. We have solved the problem for interesting constraints. For the solution of these constraints stochastic programming formulation has been done. The problem is also formulated as a quadratic/hybrid programming problem where the variance of discrete random variable constitutes a quadratic form associated with a laplacian like matrix. Using this result, time optimal spectrum sensing is formulated as a multi-linear objective function optimization problem.

Multicast-Oriented Task Offloading for Vehicle Edge Computing

Vehicle edge computing (VEC) is expected to be widely used in 5G wireless network in the future owing to its low latency, high reliability, and easy deployment. Unfortunately, the computation resources of roadside units (RSUs) equipped with computing ability are limited, which makes us need to seek other computing nodes. In this article, we explore an offloading model to meet this challenge. Future vehicles equipped with computing abilities can provide VEC services in vehicular fog networks (VeFN), which greatly reduces task delay and improves the efficiency of transportation system. We consider that a package consisting of several tasks is offloaded to vehicles with different computing abilities via multicast, and these vehicles process tasks at the same time. First, we use the mathematical method to construct the system utility function, aiming to obtain low delay and low computing cost, and produce a 0–1 programming problem with inequality constraints. We then solve the slack form of the primary problem based on the interior point method. Finally, a low-complexity algorithm is proposed to optimize the task delay and cost. Numerical results show that the algorithm has fast convergence speed and superior performance.

Particle Swarm Based Service Migration Scheme in the Edge Computing Environment

With the development of Mobile Edge Computing (MEC), it has become a key technology to realize the vision of the Internet of Things. In MEC, users can upload tasks to edge nodes for faster processing speed and lower local energy consumption. However, as the mobility of users and the limited resources of the edge nodes, some edge nodes cannot provide high-quality services. In this case, we study service migration strategy in the MEC system to migrate services from the initial nodes to other edge nodes that can provide services to meet the needs of users. By making service migration decision and allocating computation resource, our work minimizes the delay and the energy consumption caused by finishing tasks. Specifically, we set up an efficient service migration model and formulate the service migration problem as a non-linear 0-1 programming problem. To solve this problem, we design a Particle Swarm based Service Migration scheme (PSSM) which includes Queuing Delay Prediction algorithm (QDP), Delay-aware Computation Resource Allocation algorithm (DCRA), and Modified Quantum Particle Swarm algorithm (MQPS). For evaluating the performance of the proposed PSSM, we conduct simulation in a practical scenario. The results demonstrate that our scheme not only can effectively reduce delay and energy consumption, but also improve the processing capability of servers.

ОПЫТ БРАЗИЛИИ И НЕКОТОРЫЕ ОСОБЕННОСТИ РАЗВИТИЯ ГОСУДАРСТВЕННО-ЧАСТНОГО ПАРТНЕРСТВА В СТРАНАХ БРИКС

The article is devoted to the study of the development of public-private partnerships (PPP) in Brazil. Interest in Brazil is due, on the one hand, to the fact that it is one of the largest economies in the Latin American region with prospects for increasing trade and economic cooperation, and on the other hand, the development of PPPs in the country has a longer history than in Russia, but similar problems . The article analyzes the stages of PPP development and measures taken to intensify the program. The analysis showed that the key problems in the PPP program are the low level of cooperation of various government departments involved in the preparation and implementation of projects, as well as the low quality of the projects themselves, which does not allow involving the private sector in their implementation. In the conclusion, information is provided on the regulatory requirements for PPP projects in accordance with the current legislation, such as the period, amount and obligations arising from the conclusion of PPP agreements. In addition, information is provided on some of the completed projects and the key factors that influenced their implementation and future operation.

Условия минимума гладкой функции на границе квазидифференцируемого множества

In this paper, we consider problems of mathematical programming with nonsmoothconstraints of equality type given by quasidifferentiable functions. By using thetechnique of upper convex approximations, developed by B. N. Pshenichy, necessary conditionsof extremum for such problems are established. The Lagrange multipliers signsare specified by virtue of the fact that one can construct whole familers of upper convexapproximations for quasidifferentiable function and thus the minimum points in such extremalproblems are characterized more precisely. Also the simplest problem of calculusof variations with free right hand side is considered, where the left end of the trajectorystarts on the boundary of the convex set. The transversality condition at the left end of thetrajectory is improved provided sertain sufficient conditons hold

Efficiency of solar and wind energy use in the countries of Central and North-East Asia

This paper investigates the effectiveness of renewable energy sources using solar and wind energy in the countries of Central and North-East Asia. The analysis was carried out in two stages. At the first stage, the efficiency of wind and solar installations in different climatic conditions was compared by the criterion of the cost of electricity. At the next stage of analysis, an optimization mathematical model was used to study the system that simultaneously includes wind and solar installations, backup energy sources and batteries. The model takes into account system effects caused by the interaction of the system elements between themselves and with the environment. It solves the problem of mathematical programming — the search for the minimum of the objective function (total costs) at some constrains. The model is used to study the economic efficiency of the large-scale construction of solar power plants in the Gobi Desert. It is shown that the joint use of solar and wind energy gives a positive economic effect, i.e. energy cost are less than with separate use of these energy sources. Under suitable wind conditions such systems reduces the cost of electricity by more than a quarter compared to the option of using solar energy only.

Recurrent Neural Networks-Based Collision-Free Motion Planning for Dual Manipulators Under Multiple Constraints

Dual robotic manipulators are robotic systems that are developed to imitate human arms, which shows great potential in performing complex tasks. Collision-free motion planning in real time is still a challenging problem for controlling a dual robotic manipulator because of the overlap workspace. In this paper, a novel planning strategy under physical constraints of dual manipulators using dynamic neural networks is proposed, which can satisfy the collision avoidance and trajectory tracking. Particularly, the problem of collision avoidance is first formulated into a set of inequality formulas, whereas the robotic trajectory is then transformed into an equality constraint by introducing negative feedback in outer loop. The planning problem subsequently becomes a Quadratic Programming (QP) problem by considering the redundancy, the boundaries of joint angles and velocities of the system. The QP is solved using a convergent provable recurrent neural network that without calculating the pseudo-inversion of the Jacobian. Consequently, numerical experiments on 8-DoF modular robot and 14-DoF Baxter robot are conducted to show the superiority of the proposed strategy.

An Extended Multi-Objective Capacitated Transportation Problem with Mixed Constraints in Fuzzy Environment

In this paper, we study a multi-objective capacitated transportation problem (MOCTP) with mixed constraints. This paper is comprised of the modelling and optimisation of an MOCTP in a fuzzy environment in which some goals are fractional and some are linear. In real life application of the fuzzy goal programming (FGP) problem with multiple objectives, it is difficult for the decision maker(s) to determine the goal value of each objective precisely as the goal values are imprecise or uncertain. Also, we developed the concept of linearisation of fractional goal for solving the MOCTP. In this paper imprecision of the parameter is handled by the concept of fuzzy set theory by considering these parameters as a trapezoidal fuzzy number. α-cut approach is used to get the crisp value of the parameters. Numerical examples are used to illustrate the method for solving MOCTP.

Energy-Efficient Channel Estimation

We investigate the energy-efficient channel estimation in wireless networks, where one pilot is inserted for every several data slots to estimate the channel coefficients. Both the channel state information estimation error and the time-varying model are considered. We first formulate the energy-efficient channel estimation problem into a mixed integer nonlinear programming (MINLP) problem, where the variables include the transmitted power and the number of data slots. Due to the NP-hard nature, we degenerate the MINLP problem into a series of non-concave optimization problems without integer variables. Then we solve these problems using successive convex approximation, geometric programming, and the Dinkelbach algorithm to obtain a point satisfying the Karush-Kuhn-Tucker (KKT) conditions. Furthermore, we develop a low-complexity sub-optimal scheme through binary variable relaxation to obtain a solution, and the convergence point satisfies the KKT conditions of the relaxed non-concave problem. Simulation results demonstrate the convergence and effectiveness of our proposed schemes.

Uplink Low Power Based Radio Resource Management in Wireless Heterogeneous Networks

Due to the rapid rise of energy consumption and limited battery power of wireless user equipment (UE), low power communication becomes very important. Heterogeneous network deployment can significantly reduce regional power consumption. For heterogeneous network scenarios, this paper proposes an uplink low-power resource allocation scheme considering battery power limitation and user QoS requirements. Based on the assumption that each user has access to at most one base station (BS), the scheme is modeled as a mixed integer nonlinear programming (MINLP) problem. Since each user has access to one BS at most, the transmitting power matrix from the UE to the BSs (UE-to-BS matrix) is a sparse matrix. The MINLP problem can be transformed into an optimization problem searching sparse solution. In this paper, the reweighted L1 norm is introduced as a penalty function to remove the integer constraint and to regulate the sparsity of the UE-to-BS transmitting power matrix. In order to obtain the optimal resource allocation scheme, a reweighted L1 norm penalty based radio resource management (RRM) algorithm is proposed. Simulation results show that the reweighted L1 norm penalty based RRM algorithm has good convergence performance and the results are very close to optimal solutions. The proposed resource management scheme can prolong the working time of low-energy users and guarantee the QoS requirements of UE in the system.

Coordination and Profit Optimization by Producer-Distributor System of Agricultural Products in Bangladesh

This study, presents three different mathematical models: Producer, Distributor and Coordination modelwhich negotiate with a Producer-Distributor system for producing and distributing ofagricultural products in Bangladesh. In this paper, we investigated supply chain network (SCN) are two distinct freelance supply organizations. SCN management has the difficulties for the disconnected and freelance economic people. Further, fast technological changes and high fight build SCN a lot of complicated. The problem of locating distribution centers (DCs) is one among the foremost necessary problems in design of SCN. Current study, SCN was modeled using a formulation in mixed integer linear programming (MILP) problem, in which the facilities are coordinated by mutually sharing information with each other between producer and wholesaler. We think, this research presents a real life coordination optimization problem. The formulated MILP model is solved by using a mathematical programming language (AMPL) and results obtained by appropriate solver MINOS.

Sparsity-Aware Noise Subspace Fitting for DOA Estimation.

We propose a sparsity-aware noise subspace fitting (SANSF) algorithm for direction-of-arrival (DOA) estimation using an array of sensors. The proposed SANSF algorithm is developed from the optimally weighted noise subspace fitting criterion. Our formulation leads to a convex linearly constrained quadratic programming (LCQP) problem that enjoys global convergence without the need of accurate initialization and can be easily solved by existing LCQP solvers. Combining the weighted quadratic objective function, the norm, and the non-negative constraints, the proposed SANSF algorithm can enhance the sparsity of the solution. Numerical results based on simulations, using real measured ultrasonic, and radar data, show that, compared to existing sparsity-aware methods, the proposed SANSF can provide enhanced resolution with a lower computational burden.

System Optimum Fuzzy Traffic Assignment Problem

This paper focuses on converting the system optimum traffic assignment problem (SO-TAP) to system optimum fuzzy traffic assignment problem (SO-FTAP). The SO-TAP aims to minimize the total system travel time on road network between the specified origin and destination points. Link travel time is taken as a linear function of fuzzy link flow; thus each link travel time is constructed as a triangular fuzzy number. The objective function is expressed in terms of link flows and link travel times in a non-linear form while satisfying the flow conservation constraints. The parameters of the problem are path lengths, number of lanes, average speed of a vehicle, vehicle length, clearance, spacing, link capacity and free flow travel time. Considering a road network, the path lengths and number of lanes are taken as crisp numbers. The average speed of a vehicle and vehicle length are imprecise in nature, so these are taken as triangular fuzzy numbers. Since the remaining parameters, that are clearance, spacing, link capacity and free flow travel time are determined by the average speed of a vehicle and vehicle length, they will be triangular fuzzy numbers. Finally, the original SO-TAP is converted to a fuzzy quadratic programming (FQP) problem, and it is solved using an existing approach from literature. A numerical experiment is illustrated.

Solving the fair electric load shedding problem in developing countries

Often because of limitations in generation capacity of power stations, many developing countries frequently resort to disconnecting large parts of the power grid from supply, a process termed load shedding. This leaves households in disconnected parts without electricity, causing them inconvenience and discomfort. Without fairness being taken into due consideration during load shedding, some households may suffer more than others. In this paper, we solve the fair load shedding problem (FLSP) by creating solutions which connect households to supply based on some fairness criteria (i.e., to fairly connect homes to supply in terms of duration, their electricity needs, and their demand), which we model as their utilities. First, we briefly describe some state-of-art household-level load shedding heuristics which meet the first criteria. Second, we model the FLSP as a resource allocation problem, which we formulate into two Mixed Integer Programming (MIP) problems based on the Multiple Knapsack Problem. In so doing, we use the utilitarian, egalitarian and envy-freeness social welfare metrics to develop objectives and constraints that ensure our FLSP solutions results in fair allocations that consider the utilities of agents. Then, we solve the FLSP and show that our MIP models maximize the groupwise and individual utilities of agents, and minimize the differences between their pairwise utilities under a number of experiments. When taken together, our endeavour establishes a set of benchmarks for fair load shedding schemes, and provide insights for designing fair allocation solutions for other scarce resources.

Duality Gap in Interval Linear Programming

This paper deals with the problem of linear programming with inexact data represented by real intervals. We introduce the concept of duality gap to interval linear programming. We give characterizations of strongly and weakly zero duality gap in interval linear programming and its special case where the matrix of coefficients is real. We show computational complexity of testing weakly- and strongly zero duality gap for commonly used types of interval linear programming.

Класифікація метаданих великих даних

Now there are a lot of data of different structure (or not structured at all) and origin, their volumes are growing ex­ponentially. The problem is the existing software and hardware are not able to cope with so many dif­fe­rent types of data appearing with great speed. Big Data has become too complex and dynamic to pro­cess, store, analyze and manage with traditional tools. It caused the appearance of new platforms and ap­pro­a­ches for working with data, and at the same time, an understanding of the fact that to solve big data prob­lems, these raw data must be supplemented with me­ta­data. Metadata in this case is a means of classifying, organizing, and characterizing data and its content. Their main advantage is an ordered structure. Due to it, metadata is readable not only by a person, but also by a computer. Thus, they can be pro­ces­sed auto­ma­ti­cal­ly and used for indexing, searching, com­bining, auto­mated processing, classification of big data, etc. The creation of effective metadata management sys­tems, first of all, requires their coordinated general classification that take into account the types of data sour­ces (methods of their obtaining) that form the con­tent, tasks solved at different stages of the life cycle, existing formats of data presentation, principles of re­a­sonable efficiency, since often metadata size sig­ni­fi­can­tly exceeds the amount of described data (even big). Therefore, the aim of this work is to analyze exis­ting sources of big data, methods for creating and processing the corresponding metadata, as well as software products that allow them to be processed in a certain way, and building the classification of me­ta­da­ta on the basis of the analysis. Problems in programming 2019; 4: 53-74

Підхід до побудови та використання моделі предметної області ризиків стратегічних рішень організації

A Conceptual Model is proposed for Problem Area of Strategic Decisions’ Risks within Organizational Management Systems (OS) being a result of selection, addition and interpretation operations caused by the proper Risk Object specifics and applied to the elements of regular conceptual basis for risk treatment within the other domains. The Model includes such the Concepts: Decision , Consequences for both Decision and OS ; Source , Factor, Aspect and Event of Risk , Vulnerability, Hazard , Affected Property and their interrelations. Based on the Model proposed for Strategic Decision life cycle and integration of well-known Strategic Management practices the System of Strategic Decisions Risks Management Measures is considered being represented as actions with hazards, threats, vulnerabilities, risk objects and consequences. The Usage of Conceptual Model proposed is demonstrated for the Method elaboration of knowledge ambiguity- caused Risks Assessment for the decisions of Expertise using different business groups and «Value Tree» model. The Method is based on the model, where the set of knowledge ambiguity-caused Risk Factors is formalized. The Factors’ Sources are the elements of expert problem statement. Factors‘ types are the types of non-coherent knowledge interrelations, Vulnerabilities relate to experts activity nature, Hazards are caused by the systems of expert estimates in use producing Risk Events during the process of decision life cycle. Each Risk Aspect is specialized with decision Properties being Risk targets due to Risk Events. The Method produces Risk estimates to conclude about expertise satisfactoriness and to enable selection the least risky form of its process organization. Enhancing and using of Conceptual Model proposed for Strategic Decisions Risks is advantageous for tools elaboration to support Defense Planning processes with the mechanisms of ontology based experience operation concerning with Problem Situations and Anti-crisis Measures. Problems in programming 2019; 4: 75-91