Programming Problem Research Articles

About a regional development model that takes into account environmental problems with budgeting uncertainty

Raw-materials base (hereinafter RMB) is one of the largest industries for financial investments in Russia. There are various mathematical descriptions for the development of regions with resource-based economy. Earlier in [1] the researchers considered the model based on bilevel integer stochastic programming problems with Boolean variables. This paper proposes a new approach to public-private partnership modelling, including a bilevel linear stochastic programming problem. This model assumes that budget constraints of the state and the investor can vary in a random manner with a specific probability distribution. We put forward two methods to solve this problem: problem’s reduction to the deterministic bilevel one and formulation of deterministic problems sequence with help of Monte Carlo methods. In order to solve deterministic problems of integer programming, we suggest two approaches: direct enumeration and heuristic “Game” approach. The numerical experiments for proposed algorithms validation are conducted on the basis of actual data of Zabaykalsky Krai development. Multiple input parameters of the model vary in these experiments. Finally, we present a brief analysis of the obtained solutions to the stochastic linear programming problems with Boolean variables.

Математична задача диверсифікації банківських активів

In article we consider a problem of optimal investment strategy by a commercial bank building. This task is actual and the development of a procedure to solve it can help in making investment banking decisions. The general formulation of the problem consists of two criteria. The first one is to maximize the expected return, and the second is to minimize the risk of the investment transaction. Mathematical formulation of the problem is considered as a problem of nonlinear programming under constraints. The procedure for solving such a two-criteria optimization problem allows to obtain many solutions, which requires further steps to make a single optimal solution. According to the algorithm proposed in the work, the problem is divided into two separate problems of single-criteria optimization. Each of these tasks allows to obtain the optimal values of the investment vector both in terms of its expected return and in terms of investment risk. Additional constraints in the mathematical formulation of the problem, make it possible to take into account factors that, from the point of view of the investor, may influence decision-making. The procedures presented in this work allow to obtain analytical representations of formulas that describe the optimal values of the investment distribution vector for both mathematical formulations of the problem.

COMPARISON OF THE RESULTS OF APPLICATION OF METHODS FOR SOLVING THE TRANSPORTATION PROBLEM OF LINEAR PROGRAMMING

COMPARISON OF THE RESULTS OF APPLICATION OF METHODS FOR SOLVING THE TRANSPORTATION PROBLEM OF LINEAR PROGRAMMING

Розв’язання багатокритеріальної задачі оптимізації системи автосервісу на прикладі «АНТ-АВТО-СЕРВІС», м. Черкаси

The paper investigates the problem of determining the rational modes of operation of the car service system at the macro level in the process of solving the multicriteria problem of optimizing the technological processes of the system to achieve the maximum level of socio-economic efficiency of the car service and minimum losses of customers taking into account the characteristics and limitations of its functional elements. Mathematical dependences have been developed to calculate the efficiency function of the car service system in general, which takes into account nineteen morphological features of the system and the annual costs of customers who are consumers of the offered car service. In order to solve this problem, a mathematical formulation and implementation of the problem of nonlinear programming, multicriteria model of which takes into account constraints imposed on the seven basic parameters. A method for determining the feasibility of implementing optimization measures has been developed and a block diagram of the algorithm according to its stages has been constructed. Indicators of socio-economic efficiency before and after optimization of technological processes are determined and the criterion of expediency of realization of optimization programs on the example of specialized system of car service "ANT-AUTO-SERVICE", Cherkasy is calculated. During the calculations of the predicted values of socio-economic efficiency, the values for the previous periods were used and the optimal values of the system parameters were calculated. The results of testing indicate the feasibility of optimizing the work of this enterprise. It is projected that the annual efficiency of the specialized car service system will increase by UAH 2,486,465. The results of the study can be used in the decision-making process on the feasibility of optimizing the car service system at the macro level. Further research will focus on the formulation and implementation of mathematical models for the optimization of car service systems at the micro and meta levels.

Клієнтоорієнтована оптимізація кадрового складу закладів охорони здоров’я

The problem of developing information technology for customer-oriented optimization of healthcare facilities staff is considered. It is determined that the key tasks in the development of personnel decisions in the formation of personnel policy in medical institutions are assessing such current characteristics of staff as to regulatory and actual workload and the task of forecasting needs for medical services in future periods. To effectively perform such a forecast, it is proposed to consistently solve clustering, identification, and forecasting problems. A mathematical model of the multicriteria optimization problem for the formation of many variants of solutions for the formation of personnel policy in health care facilities is built. The model of search of optimum distribution of services between employees of establishment in the form of a problem of integer linear programming is executed. Production rules have been developed to analyze the results of solving the formulated problem. A model for developing variants of decisions on changes in the staff of a medical institution to ensure the completeness of medical services is proposed. To assess the effectiveness of the options made, the customer orientation index is used, which is calculated by the principles of egalitarianism. Experimental verification of the developed models and methods is performed.

Progress and problems in literacy programmes in Central Nigeria

Central Nigeria is a region of great linguistic diversity where there were no pre-colonial orthographies in use. The expansion of population and modern education has created a strong demand for local literacy programmes for the Plateau languages of Central Nigeria. For people to be able to develop themselves intellectually, it is important that they have a system of writing that is truly their own. Initially, demand for literacy has been in relation to programmes for Bible translation, and this is largely where funding is sought. However, these programmes are frustratingly long-term and some have been quite ineffective due to poor (or no) initial planning and ill-designed orthographies.
 However, in the decade since 2010, demand is increasingly coming from non-denominational organisations whose concern is cultural maintenance, and thus the use of vernacular languages in education. This paper examines the progress achieved and problems faced by some of the Plateau languages in the area of literacy development with a more detailed case study of the Mada Literacy Programme, as well as offering some practical solutions to assist the spread of literacy.

Power and Resourse Efficient Envoronmentally Safe Technology for Processing Dumps of Technogenic Waste From Ore-Dressing and Processing Enterprises


 
 
 This research proposes a systematic approach for the analysis of volumes, physicochemical, granulometric, lithologic and thermal characteristics of waste from ore-dressing and processing enterprises stored in the dumps (tailing dumps) of ore-dressing and processing plants to assess the economic potential of its use in the system of complex power and resource efficient environmentally safe processing including palletizing machines, conveyor indurating machines and ore–thermal furnaces. The obtained results allow the authors to formulate the basic engineering, technological, economic and environmental requirements for complex chemical and power engineering systems of processing technogenic waste from ore-dressing and processing plants, these results make it also possible to define the degree of variability for the characteristics of the waste lots from various dumps. The paper describes the developed intensional and mathematical formulations for the multiscale problem of optimizing chemical and power engineering processes of technogenic raw materials processing in a complex chemical and power engineering system as a problem for discrete dynamic programming. The distinctive feature of this problem is to take into account the spatio-temporal multistage processing in a moving multilayer mass of pelletized raw material, the intensity of the process of internal moisture transfer and the variables for the control flow of the heat carrier gas. It allows increasing power efficiency by intensifying heat and mass transfer processes of multilayer drying, calcination and sintering. The criterion of the efficiency is the minimum cost of electric and thermal energy spent on processing. The obtained results were used to calculate power efficient environmentally safe processing of technogenic waste from ore-dressing and processing enterprises dumps. It was defined that heat and mass transfer processes are intensified, power consumption is reduced and the quality of the finished product is increased in the conditions of optimal power and resource efficient operation for the processing system.
 
 
 
 Keywords: tecnhogenic waste, waste processing, ore-dressing and processing plant, power and resource efficiency, optimization, system analysis, environmentally safety
 
 
 
 
 

Suppressing Range Ambiguity by Pattern Synthesis for SAR via Semidefinite Relaxation

Range ambiguities severely degrade the performance of the synthetic aperture radar (SAR) system. To make an improvement without increasing the system complexity, antenna pattern synthesis is a feasible method. To this end, a novel algorithm that can shape the mainlobe and suppress the range ambiguities simultaneously by relaxing the problem as a semidefinite relaxation (SDR) programming problem is proposed here for the first time. Compared to the algorithm with global optimization, the presented algorithm could find the desired pattern without the large occupation of computing resources and has great potential in raising the performance of SAR system. In addition, some simulations are carried out, and the results prove that the proposed algorithm has the superior ability to suppress the range ambiguities while controlling the beamwidth and dynamic range ratio (DRR).

Adaptive Panoramic Video Multicast Streaming with Limited FoV Feedback

Virtual reality (VR) provides an immersive 360-degree viewing experience and has been widely used in many areas. However, the transmission of panoramic video usually places a large demand on bandwidth; thus, it is difficult to ensure a reliable quality of experience (QoE) under a limited bandwidth. In this paper, we propose a field-of-view (FoV) prediction methodology based on limited FoV feedback that can fuse the heat map and FoV information to generate a user view. The former is obtained through saliency detection, while the latter is extracted from some user perspectives randomly, and it contains the FoV information of all users. Then, we design a QoE-driven panoramic video streaming system with a client/server (C/S) architecture, in which the server performs rate adaptation based on the bandwidth and the predicted FoV. We then formulate it as a nonlinear integer programming (NLP) problem and propose an optimal algorithm that combines the Karush–Kuhn–Tucker (KKT) conditions with the branch-and-bound method to solve this problem. Finally, we evaluate our system in a simulation environment, and the results show that the system performs better than the baseline.

Mathematical Model of Object Classifier based on Bayesian Approach

The paper claims that the primary importance in solving the classification problem is to find the conditions for dividing the General complexity into classes, determine the quality of such a bundle, and verify the classifier model. We consider a mathematical model of a non-randomized classifier of features obtained without a teacher, when the number of classes is not set a priori, but only its upper bound is set. The mathematical model is presented in the form of a statement of a minimax conditional extreme task, and it is a problem of searching for the matrix of belonging of objects to a class, and representative (reference) elements within each class. The development of the feature classifier is based on the synthesis of two-dimensional probability density in the coordinate space: classes-objects. Using generalized functions, the probabilistic problem of finding the minimum Bayesian risk is reduced to a deterministic problem on a set of non-randomized classifiers. At the same time, the use of specially introduced constraints fixes non-randomized decision rules and plunges the integer problem of nonlinear programming into a General continuous nonlinear problem. For correct synthesis of the classifier, the dispersion curve of the isotropic sample is necessary. It is necessary to use the total intra-class and inter-class variance to characterize the quality of classification. The classification problem can be interpreted as a particular problem of the theory of catastrophes. Under the conditions of limited initial data, a minimax functional was found that reflects the quality of classification for a quadratic loss function. The developed mathematical model is classified as an integer nonlinear programming problem. The model is given using polynomial constraints to the form of a General problem of nonlinear continuous programming. The necessary conditions for the bundle into classes are found. These conditions can be used as sufficient when testing the hypothesis about the existence of classes.

A modified exchange algorithm for distributional robust optimization and applications in risk management

AbstractConvex semi‐definite semi‐infinite programming problems (SDSIP) represent a special class of distributionally robust optimization (DRO) problems with a wide range of applications in engineering and economics. In this paper, we propose a modified exchange algorithm for convex SDSIP that arises from DRO with matrix moment constraints. We first explore the convergence results of the modified exchange algorithm and perform the efficiency analysis based on a set of benchmark tests. In addition, we apply the SDSIP framework to investigate an optimized certainty bound risk with an ambiguity uncertainty set and implement the algorithm to solve a practical risk minimization problem in portfolio selection. The empirical results show both the efficiency of the algorithm and the robustness of the risk measure.

PREDICTIVE CONTROL METHODS IN TASKS OF SEARCHING SADDLE POINTS

The article presents new methods for searching critical points of a function of several variables, including saddle points. Such problems are found in various fields of theoretical and practical science, for example, saddle-point construction lens design, machine and deep learning, problems of convex optimization and nonlinear programming (necessary and sufficient conditions for the solution are formulated using saddle points of the Lagrange function and proved in the Kuhn-Tucker theorem. When training neural networks, it is necessary to repeat the training process on large clusters and check the network's trainability at different loss functions and different network depth. Which means that thousands of new calculations are run, where each time the loss function is optimized on large amounts of data. So any acceleration in the process of finding critical points is a major advantage and saves computing resources. Many modern methods of searching saddle points are based on calculating the Hessian matrix, inverting this matrix, the scalar product of the gradient vector and the current vector, finding the full Lagrangian, etc. However, all these operations are computationally “expensive” and it would make sense to bypass such complex calculations. The idea of modifying the standard gradient methods used in the article is to apply fixed-point search schemes for nonlinear discrete dynamical systems for gradient descent problems. It is assumed that these fixed points correspond to unstable equilibrium positions, and there are large units among the multipliers of each equilibrium position. The averaged predictive control methods are used. Results of numerical modeling and visualization are presented in the form of two tables, which indicate basins of attraction for each critical point in each scheme, and statistical data by the convergence rates.

Alternative formulations for the obnoxious p-median problem

The problem of locating obnoxious facilities has gained attention, as do environmental issues. Particularly, in view of the impacts of facilities on their clients, Labbé et al. formulated a model, called the obnoxious p-median problem, to locate obnoxious facilities away from the clients. However, this model is a difficult 0–1 programming problem, involving a large number of 0–1 variables. Actually, many of the 0–1 variables can be relieved in some alternative formulations. This paper presents three alternative formulations for the obnoxious p-median problem. Numerical examples show that the formulation based on distance-sorting appeared to be the most efficient one.

A stochastic programming approach for heterogeneous variable message sign location problem for freeway networks

Variable message signs (VMS) are electronic signage systems that display real-time traffic information to drivers to mitigate congestion and reduce travel time. We propose a heterogeneous VMS location problem based on a stochastic model of accidents on a freeway network. We consider both gantry and cantilever mounted VMS that displays both passive and active real-time messages. The problem is formulated as a two-stage stochastic programming model. The first-stage model determines the location and type of VMS installation. The second stage evaluates the performance of VMS location solutions by minimizing travelers’ travel time and the penalty for misleading guidance. The model is formulated as a mixed-integer linear programming (MILP) problem that can be solved using the Benders decomposition (BD) algorithm. The Nguyen-Dupuis and Sioux-Fall networks are used to verify the effectiveness of the proposed models. We believe this study will provide practical guidance to freeway administrators.

Existence and sensitivity analysis for nonconvex cubic optimization problems

In this paper, we propose necessary/sufficient conditions for existence of minimizers of nonconvex cubic programming problems via an Eaves type theorem. Directional differentiability of the optimal value function under total perturbation are characterized. Among our proposed assumptions, there are some weaker than the existing assumptions (applied to cubic programming).

Robust control of vehicle multi‐target adaptive cruise based on model prediction

On the issue of low utilisation and acceptance of current adaptive cruise control (ACC), a multi-objective adaptive cruise control (MO-ACC) algorithm is developed in this study. Based on model predictive control theory, comprehensively considering the coordination among various conflicting objectives, the decision of desired longitudinal acceleration is transformed into online quadratic programming (QP) problem. In order to compensate for prediction error caused by modelling mismatch, the robustness of control system is improved by introducing an error feedback correction mechanism. Meanwhile, vector management method is adopted to deal with the non-feasible solution owing to hard constraints during the process of optimisation. Further, under different work conditions, the focusing performance index along with constraint space varies, and therefore different ACC modes are established to meet the demand of skilled driving groups by means of slightly adjusting performance index, constraint space as well as slack relaxation. The simulations show that under the combined work conditions of the preceding vehicle, the following vehicle can realise seamless switching among various working modes, and also is able to achieve the good expectation during vehicle following, which will help to enhance the adaptability of the ACC system to the complex road traffic environment.

On decomposition and multiobjective-based column and disjunctive cut generation for MINLP

Most industrial optimization problems are sparse and can be formulated as block-separable mixed-integer nonlinear programming (MINLP) problems, defined by linking low-dimensional sub-problems by (linear) coupling constraints. This paper investigates the potential of using decomposition and a novel multiobjective-based column and cut generation approach for solving nonconvex block-separable MINLPs, based on the so-called resource-constrained reformulation. Based on this approach, two decomposition-based inner- and outer-refinement algorithms are presented and preliminary numerical results with nonconvex MINLP instances are reported.

PROBLEMS IN COMMUNITY DEVELOPMENT FIELD INSTRUCTION PROGRAM AMONG SOCIAL WORK STUDENTS IN HANOI, VIETNAM

Social work students are coping with challenges in the community development field instruction (CDFI) program. Therefore, this study aims to find out problems in CDFI program among social work students in Hanoi, Vietnam. The total number of quantitative study participants was 30, and eight (8) social work students participated in in-depth interviews. Our results showed that problems in the CDFI program include personal, community, and supervision problems. These problems posed a challenge to social work students. We had suggestions to stakeholders to improve CDFI program.

Legal Status of The Social Security Administrator (BPJS) As A Public Legal Entity

The Social Security Administrator (BPJS) as an independent public legal entity has its legal position and authority. Because of the regulation issued by the Ministry of Health, the independence of BPJS is interfered with. The relationship that has not been well organized and elegant between BPJS and the Ministry of Health has caused many program problems in the field. Therefore, we need to figure out where the position of BPJS is as a state institution with a public legal entity. The BPJS forms the basis of the Welfare State, through which the government carries out its role of providing basic citizens’ rights to life. Based on Article 28 H and 34 of the 1945 Constitution, the National Social Security System (SJSN) law was established. The Social Security Administrator for Health (BPJS Kesehatan), a legal entity established by the law to administer social security programs, was then formed. Based on those bases, the relationship between BPJS of Health and the Ministry of Health is functional so that the BPJS as a state institution responsible to the President has complete independence. Keywords: Social Security Administrator for Health; Public Legal Entity; Legal Position.

Non-Monotone Projected Gradient Method in Linear Elasticity Contact Problems with Given Friction

We are focusing on the algorithms for solving the large-scale convex optimization problem in linear elasticity contact problems discretized by Finite Element method (FEM). The unknowns of the problem are the displacements of the FEM nodes, the corresponding objective function is defined as a convex quadratic function with symmetric positive definite stiffness matrix and additional non-linear term representing the friction in contact. The feasible set constraints the displacement subject to non-penetration conditions. The dual formulation of this optimization problem is well-known as a Quadratic Programming (QP) problem and can be considered as a most basic non-linear optimization problem. Understanding these problems and the development of efficient algorithms for solving them play the crucial role in the large-scale problems in practical applications. We shortly review the theory and examine the behavior and the efficiency of Spectral Projected Gradient method modified for QP problems (SPG-QP) on the solution of a toy example in MATLAB environment.