Problem Of Optimal Choice Research Articles

Математическое моделирование, оптимизация структуры и режима работы оборудования конденсационных котлов

One of the priority areas of the development of science, technology, and engineering in the Russian Federation is energy saving issues. One of the promising areas to solve the problem of energy saving is to reduce waste heat losses of power plants. The designs of condensing heat exchangers used in industry and energy sector allow both to reduce waste heat losses and to significantly reduce moisture losses. Despite the substantial number of scientific publications on this issue and the positive experience of using the developed designs of condensing heat exchangers, most gas boiler houses and thermal power plants currently continue to operate without deep heat recovery units. To a great extent, it is due to the lack of the universal methods to calculate and optimize heat exchanger modes. Thus, to effective selection of the optimal structure and operating mode of the equipment, the development of mathematical models of power plants with condensing heat exchangers and software packages for their computer implementation is an urgent task. To design a model of a condensing boiler, equations of energy and mass balances are used. To solve the problem of optimal choice of structure and operating mode of the equipment, mathematical programming methods are used. A model and a method to solve the problem of choosing the optimal structure and operating mode of condensation heat exchangers have been developed. As a target optimization function, it is proposed to use the amount of fuel required to provide pre-set heat load. A computer program has been developed for optimal distribution of load between operating units. Analysis of the results obtained has showed an adequate description of real equipment model and the possibility to generate computer mode maps. Application of these maps allows significant savings of energy resources due to the optimal choice of mode and load distribution between operating equipment. The proposed approach allows us to formulate and solve inverse problems of diagnosing the state of condensing heat exchangers.

МЕТОДИКА МНОГОКРИТЕРИАЛЬНОЙ СРАВНИТЕЛЬНОЙ ОЦЕНКИ ЭФФЕКТИВНОСТИ ЗАМЕНЫ СРЕДСТВ ИЗМЕРЕНИЙ И АВТОМАТИКИ

Ensuring technological sovereignty requires large-scale and massive replacement of foreign technical means in the control and automation systems of many industrial enterprises. This problem is especially relevant for critical infrastructure facilities, in particular energy supply systems and enterprises. The article presents a methodology that allows for a comparative multi-criteria assessment and selection of control and measuring instruments (measuring-and-recording apparatus) for the comprehensive re-equipment of control and management systems of energy enterprises, heat, electricity and water supply systems, industrial and household consumers. The methodology implements an integrated approach to solving the optimal choice problem based on the Data Envelopment Analysis (DEA) methodology. The global efficiency criterion is formed as a result of the convolution of heterogeneous local efficiency criteria of measuring devices, which makes it possible to take into account specific technological requirements for measuring instruments and methods, the specifics of installation and operating conditions of devices. The method of multi-criteria assessment of the effectiveness of the use of measuring instruments significantly speeds up and simplifies the process of objective selection of optimal technical means and reduces qualification requirements for users. The database and algorithm for calculating global criteria can be used to create a decision support system within the framework of automatic design systems.

Poisk parametrov modeli s nailuchshey lokal'noy upravlyaemost'yu

We study the problem of optimal choice of model parameters with respect to anyfunctional. Locally controllable affine systems and integral functionals depending on the programcontrol are considered. Local controllability of affine systems with nonnegative inputs isproved in the case where the columns multiplying the controls form a positive basis. For suchsystems, we introduce the local controllability coefficient and pose the problem of its maximizationdepending on the choice of model parameters. As an example, we consider a very simplifiedmodel of an underwater vehicle and study the problem of finding an arrangement of its controlpropellers in which the energy consumption of the vehicle is minimal.

Small-sized asset owners’ OCIO selections and evaluations

This study analyzes small-sized asset owners’ optimal choice problems in selecting an outsourced chief investment officer (OCIO). While large-sized asset owners can select OCIOs through procurement auctions, it is difficult for small-sized asset owners to use this method. Instead, they access OCIO services by participating in an investment pool or utilizing OCIO funds. In this study, the authors compare the two OCIO selection methods. The authors construct an agent-based model for OCIO selection to reflect the heterogeneity in production efficiency and preferences. The results of this study imply that when the market has enough investment pools, the utility of all small-sized asset owners increases. To enhance the growth in the OCIO market, the investment pool should represent the preferences of small-sized asset owners and enable individual owners to find an appropriate OCIO.

Dynamic user optimal route choice problem on a signalized transportation network

In this paper, we present a new route-based discrete time variational inequality (VI) ideal dynamic user optimal route choice (DUO) model on a transportation network with fixed signal timing at signalized intersections and a relaxation with gradient projection algorithm to solve the model. The new trait of our study is the queue length in red time and the throughput in green time for each cycle at each intersection can be found when traffic is in DUO status. This is different from other studies, in which either only average queue length or average delay in a period composing of multiple cycles can be found or traffic is not in DUO status. Furthermore, the optimal signal timings can be found by the algorithm. Under optimal signal timing, the total queuing delay of the network reaches minimum when traffic is in DUO status.

Food supply network disruption and mitigation: an integrated perspective of traceability technology and network structure.

The 2019 coronavirus disease (COVID-19) epidemic has caused serious disruptions in food supply networks. Based on the case of the remerging epidemic in China, this paper aims to investigate food supply network disruption and its mitigation from technical and structural perspectives. To solve the optimal policy choice problem that how to improve mitigation capability of food supply networks by using traceability technology and adjusting network structure, the occurrence mechanism of food supply network disruptions is revealed through a case study of the remerging COVID-19 outbreak in Beijing’s Xinfadi market. Five typical traceability solutions are proposed to mitigate network disruptions and their technical attributes are analyzed to establish disruption mitigation models. The structure of food supply networks is also controlled to mitigate disruptions. The structural attributes of three fundamental networks are extracted to adjust the network connections pattern in disruption mitigation models. Next, simulation experiments involving the disruption mitigation models are carried out to explore the independent and joint effects of traceability technology and network structure on mitigation capability. The findings suggest that accuracy makes a more positive effect on the mitigation capability of food supply networks than timeliness due to the various technical compositions behind them; the difference between these effects determines the choice decision of supply networks on traceability solution types. Likewise, betweenness centralization makes a positive effect but degree centralization makes a negative effect on mitigation capability because intermediary firms and focal firms in food supply networks have different behavior characteristics; these effects are both regulated by supply network types and exhibit different sensitivities. As for the joint effect of technical and structural attributes on mitigation capability, the joint effect of accuracy and betweenness centralization is bigger than the independent effects but smaller than their sum; the joint effect of timeliness and betweenness centralization depends on networks type; while the positive effect of accuracy or timeliness on mitigation capability is greater than the negative effect of degree centralization; theses joint effects are caused by the complicated interactive effects between technical composition and behaviors of intermediary firms or focal firms. These findings contribute to disruption management and decision-making theories and practices.

Analysis of Multi-Server Queue with Self-Sustained Servers

A novel multi-server vacation queuing model is considered. The distinguishing feature of the model, compared to the standard queues, is the self-sufficiency of servers. A server can terminate service and go on vacation independently of the system manager and the overall situation in the system. The system manager can make decisions whether to allow the server to start work after vacation completion and when to try returning some server from a vacation to process customers. The arrival flow is defined by a general batch Markov arrival process. The problem of optimal choice of the total number of servers and the thresholds defining decisions of the manager arises. To solve this problem, the behavior of the system is described by the three-dimensional Markov chain with the special block structure of the generator. Conditions for the ergodicity of this chain are derived, the problem of computation of the steady-state distribution of the chain is discussed. Expressions for the key performance indicators of the system in terms of the distribution of the chain states are derived. An illustrative numerical result is presented.

Game with a random second player and its application to the problem of optimal fare choice

The choice of the optimal strategy for a significant number of applied problems can be formalized as a game theory problem, even in conditions of incomplete information. The article deals with a hierarchical game with a random second player, in which the first player chooses a deterministic solution, and the second player is represented by a set of decision makers. The strategies of the players that ensure the Stackelberg equilibrium are studied. The strategy of the second player is formalized as a probabilistic solution to an optimization problem with an objective function depending on a continuously distributed random parameter. In many cases, the choice of optimal strategies takes place in conditions when there are many decision makers, and each of them chooses a decision based on his (her) criterion. The mathematical formalization of such problems leads to the study of probabilistic solutions to problems with an objective function depending on a random parameter. In particular, probabilistic solutions are used for mathematical describing the passenger's choice of a mode of transport. The problem of optimal fare choice for a new route based on a probabilistic model of passenger preferences is considered. In this formalization, the carrier that sets the fare is treated as the first player; the set of passengers is treated as the second player. The second player's strategy is formalized as a probabilistic solution to an optimization problem with a random objective function. A model example is considered.

On generalizations of the optimal choice problem

The article is dedicated to some generalizations of the classical optimal choice problem (the fastidious bride problem, the secretary problem). Let there be a sequence of n identically distributed random variables on the interval [0, 1]. Getting consistently observed values of these variables, we should stop at some moment on one of them, accepting it as the initial point for counting upper or lower record values. In the optimal choice problem and its generalizations, it is needed to make the correct choice of the initial point of counting records, in order to guess the place of the last record (the classical optimal choice problem) or to maximize the expected sum of upper and/or lower record values or the expected total number of upper and/or lower records, obtained by this procedure. A review of results on the uniform distribution of the random variables and some new results concerning the exponential distribution are presented.

On Generalizations of the Optimal Choice Problem

In this paper, we consider generalizations of the optimal choice problem. There is a sequence of n identically distributed random variables on the interval [0, 1]. Sequentially obtaining the observed values of these quantities, it is necessary at some point to stop at one of them, taking it as the starting point for counting the upper or lower record values. In the optimal choice problem and its generalizations, it is required to make the correct choice of the starting point of the records in order to maximize the mathematical expectation of the sum of values or the number of upper, lower, or both record values obtained as a result of such a procedure. A review of the results on the uniform distribution of random variables and new results on the exponential distribution of random variables are presented.

Space-time processing for «range – azimuth – elevation» measurements in non-cooperative systems of radars with phased array antennas

The methods of measuring the three coordinates of an aircraft in the takeoff and landing mode on the runway of airfields based on the use of non - cooperative two-and three-position systems of radars with phased array antennas are considered. For these variants, general analytical expressions are obtained for the complex generalized correlation integral of space – time processing in the function of spatial coordinates, taking into account the individual directional pattern of phased array antennas. On the basis of two – dimensional profiles of the correlation integral modules «range – elevation» and «azimuth – elevation», examples of comparing particular variants of two-position and three-position systems of radars with their location on one straight line parallel runway are given. In conditions of large signal-to-noise ratios, power-law nonlinear transformations of the correlation integral correlation integral module are applied to reduce the level of side lobes in the two – dimensional sections «range – elevation» and «azimuth – elevation». The following results are obtained using examples. Two-dimensional diagrams of the correlation integral module «range – elevation» do not depend on the azimuth of the aircraft in the range of azimuth values β=0…10 ̊ and correctly display the angle of elevation and the range of the aircraft when 2…3 radars of a non-cooperative system are located on the straight line parallel runway. The two-dimensional diagrams of the correlation integral module «azimuth – elevation angle» have an interference structure, and the number and level of their side lobes increase with increasing azimuth of the aircraft. With azimuth β≥10 ̊, this can lead to ambiguity in the measurement of the azimuth and uncertainty in the elevation angle . One of the measures to reduce the side level of the diagrams of the correlation integral module can be the use of a power-law transformation of normalized diagrams exponentiation of degree 3...4. An increase in the number of radars from two to three when they are located on one straight line parallel to the runway led to a decrease in the side lobes level of the «range – elevation angle» and «azimuth – elevation angle» diagrams. In this case, it may be advisable to solve the problem of optimal choice of the position of the intermediate radar on the same straight line. Calculations were also carried out for an additional example of the location of the intermediate radar of a 3-position system with its removal from the base line. At the same time, there was an increase of the side lobes level in the «azimuth – elevation angle» sections, which in the future may require additional research in terms of optimizing the placement of the radars in horizontal plane for such a radar systems.

SUBSTANTIATION OF COSTS MODEL FOR OPERATION OF AIR NAVIGATION EQUIPMENT

The article is devoted to the substantiation of costs model for the operation of electronic navigation equipment. The equipment of air navigation includes a set of ground, near-ground and onboard technical means, the quality and reliability of which largely influences on the safety and regularity of civil aviation. These include ground radio navigation and radar systems, radio communications, and automated air traffic control systems, which generate and provide consumers with information on flight parameters along the entire route from take-off to landing. The tasks of maintaining the required level of efficiency and reliable operation of these equipment are solved in the operation systems. The article considers the issues of obtaining analytical relations and determining mathematical relations for estimating the cost of resources for current repairs. Normative documents usually use such a concept of cost indicator as mathematical expectation, although the efficiency of resource costs for current repairs are objectively random variables and therefore the most complete characteristic is the probability density function or a number of characteristics, not only mathematical expectation but also variance, asymmetry, kurtosis and other moments of a higher order. In this paper, the author considered two options for financing repair procedures. The first option is related to the case when the level of the reserve for repairs is determined at the level of mathematical expectations. The second option is related to the case when the maintenance and repair system has a reserve of resources for repair procedures, which differs from the traditional approach to cost planning. The article analyzes the results of calculations of mathematical expectations of resource costs for different levels of interest rates and different indicators of reserve funds. Analytical relations are obtained to solve the problem of optimal choice of the resource fund for current repairs. At the same time, modeling was performed and histograms were constructed for different values ​​of reserve funds for repairs. Based on theoretical calculations, a nomogram is constructed, which shows that at certain interest rates there is an optimal value of total operating costs. The research results can be used in the process of designing and improving the operation systems of ground-based air navigation equipment.

Time is money: An economic analysis of the optimal pacing problem

Athletes in many sports can potentially earn significant amounts of prize money from taking less time to complete a given distance than their competitors. Time is literally money in these cases. The objective of an athlete is to choose an optimal race strategy that minimizes race time without becoming prematurely exhausted. If the first part of a race is completed too quickly, the fatigue generated makes the second part of the race slow and painful. If completed too slowly, the second part will be fast but it cannot make up for the time lost earlier on. Either way, the total time taken to complete the entire distance will not be as fast as it could otherwise have been. This optimal decision problem has long been debated by athletes, coaches, and more recently by physicists and applied mathematicians. We show that this optimal choice problem can be solved with solutions that are both simple enough for them to be of practical use but flexible enough for them to be personalized for an athlete. We use the 800 m running race to demonstrate how our technique works since it is a well known ideal example of an event that combines both the elements of speed and endurance.

Optimal consumption and portfolio decision with stochastic covariance in incomplete markets

Abstract This paper investigates finite and infinite horizon optimal consumption and portfolio choice problems in incomplete markets with stochastic covariance among stock returns. The stock price dynamics are assumed to follow a multivariate stochastic volatility process. The Hamilton-Jacobi-Bellman (HJB) equation is derived by using dynamic programming method and the closed-form expressions for portfolio–consumption strategies are derived in the case of logarithmic utility. In the case of infinite time horizon, we prove the existence of a classical solution and provide a verification theorem. The closed form approximate solutions to the optimal consumption and portfolio polices for a power utility investor are obtained by solving the same utility maximization problem in two fictitious complete markets. Moreover, we verify the existence and optimality of the solution of the original incomplete market and also provide the upper bound of the utility loss of approximate rules. Finally, a numerical application to an incomplete market with stochastic factors show that the utility loss of the approximation rules is small and the performance of the approximate rules is close to optimal.

HYBRID NEURON NETWORKS BASED ON RADIAL BASIS NETWORK WITH DIFFERENT RADIAL BASIS FUNCTION

It is considered the problem of structural-parametric synthesis of a hybrid neural networks based on the use of radial basis network. Hybridization is achieved through the use of various radial basis functions: Gaussian, multivariate, inverse quadratic, inverse multivariate, thin plate spline, linear, cubic, wavelet functions. The problem of structural-parametric synthesis of hybrid neural network consists in the optimal choice of the number of layers, the number of neurons in the layers, the order of alternation of layers with different neurons. The problem of optimal choice of the number of network cascades and the type of radial basis function in each cascade of the number of layers is solved. Examples of a hybrid neural network synthesis using this methodology for classification and prediction tasks solution are given.

Generalized Euler Equation Errors for Discrete Time Dynamic Portfolio Choice Models

The solution to dynamic portfolio choice models can be formulated in terms of a value function by the Bellman principle of optimality, which reduces the multi-period optimal policy choice problem to a sequence of one-period maximization problems. For two adjacent periods, economists compute the error of numerically obtained policies by measuring how much these policies violate the intertemporal first order conditions for the optimal policy choice problem---so-called Euler equation errors. In this paper, we derive generalized Euler equation errors for the solution to a broad class of discrete time dynamic portfolio choice models where the policies are continuous choice variables. Our key precondition is that the gradient of the value function with respect to the state variables can be approximated. This is, for example, the case when a global polynomial basis or B-spline basis functions are used for the approximation of the value function within the discrete time dynamic programming approach. We apply our theoretical results to exemplary, representative dynamic portfolio choice models.

METHODICAL APPROACH OF PROVIDING OF SAFETY AND ACCIDENT PREVENTION OF ROCKET AND SPACE COMPLEX

The analysis of scientific works shows that today there is no generally accepted theory of technical and economic security of the system "personnel-rocket and space complex-environment". However, it should be noted that some elements of this theory are contained in the General theory of risk assessment in combination with the methods of actuarial mathematics, as well as in combination with the methods of assessing the technical and economic costs of the creation and operation of space assets. The known methods of technical and economic assessment of costs for the creation and operation of space objects are based mainly on the cost principle and are focused on the actual costs necessary for the development, production and operation of samples of space technology, space infrastructure with the inclusion of standard profit. At the same time, many of the known methods of technical and economic evaluation of the costs of the creation and operation of space objects can be divided into the following main groups: methods of calculation, normative and parametric methods and methods of expert evaluation. When studying safety issues and preventing accidents at the rocket and space complex, it is necessary to take into account the main features of their functioning, which consist in the mandatory accounting of the properties of maintenance personnel, the actual technical means of the rocket and space complex and the environment. A feature of the system "personnelrocket and space complex-environment" is the presence of a large number of information links that characterize its information efficiency. This scientific and technical article proposes new ways, methods and means to ensure the adoption of optimal (rational) decisions to prevent accidents, taking into account resource constraints on parrying emergencies. Models of some types of resources that are appropriate to use in carrying out technical and economic calculations to solve various problems of the security system “personnel-rocket and space complex-environment”. Core results. The aggregate models of resources which are expedient to use for an assessment of technical and economic indicators of safety are developed. The problem of optimal choice of the level of accident-free SPACECRAFT in the process of flight operation with restrictions on safety using the criterion "efficiency-safety-cost" is solved, nomograms of interrelation of indicators for the criterion "efficiency-safetycost" are received». Practical relevance. The proposed models allow us to estimate the share of costs required to ensure the safety of service personnel, RSC and its components, as well as the environment.

Optimization of Queueing Model with Server Heating and Cooling

The operation of many real-world systems, e.g., servers of data centers, is accompanied by the heating of a server. Correspondingly, certain cooling mechanisms are used. If the server becomes overheated, it interrupts processing of customers and needs to be cooled. A customer is lost when its service is interrupted. To prevent overheating and reduce the customer loss probability, we suggest temporal termination of service of new customers when the temperature of the server reaches the predefined threshold value. Service is resumed after the temperature drops below another threshold value. The problem of optimal choice of the thresholds (with respect to the chosen economical criterion) is numerically solved under quite general assumptions about the parameters of the system (Markovian arrival process, phase-type distribution of service time, and accounting for customers impatience). Numerical examples are presented.

OPTIMAL DISTRIBUTION OF PARALLEL WORKING EQUIPMENT WITH REGARD TO ENVIRONMENTAL TAXES UNDER UNDERSTANDING CONDITIONS

For a case where the compressor station, where the parallel-supplied gas-pumping units operate, has an excess capacity, the problem of optimal choice of the number of aggregates by a certain criterion arises. The prevailing criterion has two components. The first component is the cost of the fuel gas consumed by the compressor station. The second component is the ecological tax charged for the release of nitrogen oxides into the environment. To calculate the second component, an empirical model is synthesized in the form of a polynomial of a given degree which parameters and structure are determined using genetic algorithms. Such a model characterizes the dependence of the power of emissions of nitrogen oxides on the technological parameters that characterize the process of combustion of natural gas in the combustion chamber.
 In the generated problem of power emissions are calculated by the average values of technological parameters, which generates their fuzziness. Each parameter is characterized as the fuzzy value by a triangular membership function that is approximated by the Gaussian function.
 The formalized problem of choosing the optimal number of parallel operating units has in its composition the optimality criterion as fuzzy value and the limitations are determined by the given volume of pumped natural gas by the compressor station and the maximum allowable number of aggregates in each group of superchargers.
 The introduction of fuzziness generates a discrete nonlinear programming problem with linear constraints. For its solution, the method of boundaries and branches is used, on the basis of which algorithms and software are developed. The software is tested on the developed example, where the data used to determine the operation of the compressor station is used.

Portfolio choice, portfolio liquidation, and portfolio transition under drift uncertainty

This paper presents several models addressing optimal portfolio choice, optimal portfolio liquidation, and optimal portfolio transition issues, in which the expected returns of risky assets are unknown. Our approach is based on a coupling between Bayesian learning and dynamic programming techniques that leads to partial differential equations. It enables to recover the well-known results of Karatzas and Zhao in a framework a la Merton, but also to deal with cases where martingale methods are no longer available. In particular, we address optimal portfolio choice, portfolio liquidation, and portfolio transition problems in a framework a la Almgren–Chriss, and we build therefore a model in which the agent takes into account in his decision process both the liquidity of assets and the uncertainty with respect to their expected return.