Nonlinear Mathematical Programming Research Articles

A method for processing the results of thermophysical experiments based on solving two types of problems of nonlinear mathematical programming

A method for processing the results of thermophysical experiments based on solving two types of problems of nonlinear mathematical programming

Simplified evaluation of the N-M-V ultimate domain of R.C. rectangular members with shear reinforcement

This paper describes a simple analytical tool for the calculation of the shear strength of r.c. rectangular members with shear reinforcement and subjected to only truss mechanism. The proposed method considers simplified stress fields and evaluates the shear strength of members subjected to axial force, bending moment and shear force by means of the application of the static theorem of limit analysis. Unlike most of the formulations proposed in codes and in other research studies, the proposed method considers a single physical model to explain the resistance to axial force, bending moment and shear force, and simultaneously satisfies the equilibrium under all the above internal forces. The paper identifies basic points of the N-M-V ultimate domain and reports relations and procedures to calculate the values of the internal forces of these points as well as the internal forces of the points in between. The method is applied to a set of beam and column members and a comparison is drawn between the shear strength resulting from the simplified method and that from a more complex non-linear mathematical program proposed in the past by the same author. Finally, to prove the value of the method and define the field of reliable application, the proposed method is applied to members tested in laboratory by other researchers and characterised by different geometric and mechanical properties. The obtained results are also compared with those deriving from other methods present in the literature.

Upper Bound Analysis of Non-Persistent Jointed Rock Slope Using Rigid Block Element Method

The upper bound method analyzing the stability of the non-persistent jointed rock slopes is proposed by considering rock bridge mechanical effects, which combines the upper bound theorem, the discretization technique of rigid block element and the nonlinear mathematical programming. The kinematically admissible velocity fields of non-persistent jointed rock are constructed. The non-linear mathematical programming models are established for solving the rigorous upper bound solution of ultimate load or safety coefficient by using successive linear programming algorithm. two numerical examples are performed and analyzed. The proposed method is successfully validated by comparing the simulation with those produced by other classical methods. The method has the following advantages: (1) it can simultaneously simulate the discontinuous mechanism properties of the rigid rock blocks and the continuous medium mechanism properties of the rock bridge failures. Both the tensile and shear mechanism effects of the rock bridges can be considered simultaneously; (2) comparing with the exiting numerical methods such as finite element method or discrete element method, this method can not only consider the tensile and shear effects of the rock bridges simultaneously, but also avoid the complex constitutive relationship between the rock masses and the joints. The safety factor and its corresponding failure mechanism can be obtained simultaneously; (3) comparing with the traditional rigid limit equilibrium method, this method does not need to make any assumption of the failure surfaces. The final critical failure mechanism can be directly obtained through mathematically programming method; (4) this method has the characteristics of clear concept, simple in the program composition and high computational efficiency.

Application of linear and nonlinear mathematical programming to retrofit hydrogen networks

Hydrogen network management has economic appeal due to its importance in oil refineries. It has become genuinely relevant due to the restrictions of sulfur content in fuels, which need hydrogen to be removed. Mathematical programming can be used as a tool for optimizing hydrogen networks, and the efficient management of hydrogen within the refineries can be achieved through a material balance of the units that make up the hydrogen network. In this work, an optimization model Mixed-Integer Linear Programming (MILP) and Mixed-Integer Nonlinear Programming (MINLP) for hydrogen networks was applied to minimize the operating costs. The optimization model was developed in GAMS, and it was validated using a literature case study and a real case study from a Brazilian Refinery. The operation cost was reduced by 10% and 19.6% with MILP and 9.7% and 31.5% with MINLP, for example 1 and 2, respectively. Comparing the results, both achieve significant savings in operating costs. The MILP model, which is easier to solve, has proved to be an efficient tool for optimizing hydrogen networks. However, optimization via MINLP, although not guaranteeing the optimal solution, resulted in lower operating and capital costs. The design of the optimized hydrogen networks was also detailed, and other extra restrictions were imposed on the problem.

Optimization of a multi-generation power, desalination, refrigeration and heating system

The optimization of a multi-generation system which represents the integrated dual-purpose desalination plant and a low-scale absorption refrigeration system is addressed. A nonlinear mathematical programming optimization model that integrates a natural gas combined-cycle, a multi-effect distillation desalination plant, a series flow double-effect water-lithium bromide absorption refrigeration system, and a water heater, is developed based on first-principle models. The model is implemented in General Algebraic Modelling System and a generalized gradient-based optimization algorithm is used.Given design specifications for electricity generation (around 37 MW), freshwater production (100 kg/s), refrigeration capacity (2 MW), and thermal load for heating (around 0.7 MW of hot water), the integrated system is optimized by minimizing two objective functions by single-objective optimization: total heat transfer area and total annual cost. As a result, minimum total heat transfer area values of 39148 m2, 36002 m2, and 35161 m2 are obtained when 4, 5, and 6 distillation effects were considered in the multi-effect distillation system, respectively. Also, a minimum annual cost of around 24 MM$/yr. is obtained for 5 distillation effects.The influence of the number of effects in the multi-effect distillation subsystem on the optimal solutions is analyzed. Cost-effective optimal solutions are developed for the studied multi-generation system.

MATLAB Implementation of Direct and Indirect Shooting Methods to Solve an Optimal Control Problem With State Constraints

The paper presents a general procedure to solve numerically optimal control problems with state constraints. Itis used in the case, when the simple time discretization of the state equations and expressing the optimal control problem as a nonlinear mathematical programming problem is too coarse. It is based on using in turn two multiple shooting BVP approaches: direct and indirect.The paper is supplementary to the earlier author’s paper on direct and indirect shooting methods, presenting the theory underlying both approaches. The same example is considered here and brought to an end, that is two full listings of two Matlab codes are shown.

Profit maximization in an inventory system with time-varying demand, partial backordering and discrete inventory cycle

In this paper, an inventory problem where the inventory cycle must be an integer multiple of a known basic period is considered. Furthermore, the demand rate in each basic period is a power time-dependent function. Shortages are allowed but, taking necessities or interests of the customers into account, only a fixed proportion of the demand during the stock-out period is satisfied with the arrival of the next replenishment. The costs related to the management of the inventory system are the ordering cost, the purchasing cost, the holding cost, the backordering cost and the lost sale cost. The problem is to determine the best inventory policy that maximizes the profit per unit time, which is the difference between the income obtained from the sales of the product and the sum of the previous costs. The modeling of the inventory problem leads to an integer nonlinear mathematical programming problem. To solve this problem, a new and efficient algorithm to calculate the optimal inventory cycle and the economic order quantity is proposed. Numerical examples are presented to illustrate how the algorithm works to determine the best inventory policies. A sensitivity analysis of the optimal policy with respect to some parameters of the inventory system is developed. Finally, conclusions and suggestions for future research lines are given.

Optimization of supply chain finance based on Stackelberg model

In recent years, the relationship between the concepts of operations management and finance management has been an attractive area of research among researchers. One of the emerging areas at the beginning of the 21st century in the literature of operations and supply chain management is the topic of supply chain finance (SCF). SCF is a new concept that provides efficient financing of the supply chain, where all parties can balance the working capital and improve cash flow at a reduced cost by utilizing the buyer's or other parties' credit rating. Hence, in this study, an approach to optimize financing based on the Stackelberg model in a three-level supply chain, considering the circumstances in which the supplier is financially constrained for fulfillment the buyer's order and funded by the bank as another member of the supply chain based on the purchase order financing (POF) is discussed. For this purpose, a nonlinear mathematical programming model has been developed to maximize the payoff function of the partners.

A New Mathematical Model for Redesigning the Reverse Supply Chain with Social Sustainability

The flow of goods in the supply chain is divided into two types of direct and reverse flows. Recently, more attention has been paid to the reverse supply chain because it can create benefit in waste products. In this paper, a nonlinear integer mixed integer multi-objective mathematical programming model for inverse and sustainable supply chain is presented. The objective functions of this model are economic, social and environmental goals. In addition, this model covers four levels including suppliers, collection centers, recycling centers and consumers. The purpose of this article is to assist managers in making decisions at strategic and tactical levels such as choosing a suitable location for the establishment of collection and recycling centers, selecting production technology, determining the amount of production in each recycling center and the use of available vehicles. To solve this mathematical model, a method based on linearization as well as foal planning is developed. Finally, in order to validate and evaluate the performance, the model is examined using a numerical example and sensitivity analysis is performed on its various parameters.

Strategic planning of power to gas energy storage facilities in electricity market

This paper proposes an approach for optimal planning of the power to gas energy storage facilities faced by a strategic investor in an electricity market while considering the network constraints. The proposed approach relies on a bi-level programming model whose upper-level problem determines both investment and bidding decisions to maximize the expected profit of the investor and the lower-level problem corresponds to the electricity market clearing. The bi-level model is transferred into a mathematical program with equilibrium constraints through replacing the lower-level problem by its optimality conditions. The resulting nonlinear mathematical program with equilibrium constraints is linearized by using the duality theory and Karush-Kuhn-Tucker optimality conditions. The mixed-integer linear programming problem is solved using GAMS with CPLEX solver. Results pertaining to an illustrative example and a case study are reported and discussed, which validate the proposed approach.

Digital design of heat-resistant dimensionally stable carbon laminate (CFRP) structures

Special features of designing heat-resistant dimensionally stable structures are considered. A new design procedure is proposed, in which finite elements are used as a language for describing the load-bearing structure of a construction and the distribution of material in it considering the possibility of setting the desired structure of a composite material. The design task is formulated in terms of nonlinear mathematical programming. A sequence of digital models is used for its approximate solution in the interactive mode. The specific features of finite element modeling of thin-walled structures made of laminated composite material are discussed. The technique is demonstrated using the example of the development of a large-size space telescope body.

პროპორციულ-ინტეგრალური რეგულატორის პარამეტრების ოპტიმალური მნიშვნელობების გაანგარიშება ინტეგრალური კვადრატული კრიტერიუმის მინიმუმის მიხედვით და გარდამავალი პროცესის რხევის ჩაქრობის კოეფიციენტის მნიშვნელობის გათვალისწინებით

The problem of determining the optimal the values of the parameters of the PI controller by the quadratic integral criterion taking into account the coefficient of attenuation of the transition process. The problem is presented as a nonlinear mathematical problem programming. Finding the global minimum of the objective function carried out by random search, and to determine the parameters of the PI controller used the expanded amplitude-phase frequency response of the system. An attempt is made to provide designers with an effective tool for solving the above problem. The given graphs and tables facilitate the selection of parameters. To compile a computer program, the visual programming system VBA (Visual Basic for Application) is used. Concrete examples are given.

ავტომატური მართვის სისტემის წრფივი მაკორექტირებელი მოწყობილობის პარამეტრების ოპტიმალური მნიშვნელობების განსაზღვრა ინტეგრალური კვადრატული კრიტერიუმის მიხედვით

When designing an automatic control system (ACS), it is important to determine the optimal values of the parameters of the correcting device according to any of the criteria. Recently, more and more publications have appeared on the use of the method of nonlinear mathematical programming for solving problems of synthesis of an automated control system. The article discusses a method for determining the optimal parameters of linear correcting devices according to the quadratic integral criterion. The novelty is the presentation of the above mentioned problem in the form of a nonlinear mathematical programming problem. To find a multiparametric, multiextremal, i.e. complex, objective function, a random search method is used. Also, a class of automatic control systems having one extreme objective function is highlighted. For this case, the theorems are proved, and the formula for determining extreme points is given in an analytical form. Numerical examples are also considered. Programs have been developed for implementing the corresponding algorithms on a computer in VBA language. The graphs of the corresponding transients are given.

Integrated disassembly line balancing and routing problem with mobile additive manufacturing

This paper introduces the integrated disassembly line balancing and routing problem with mobile additive manufacturing (I-DLB-RP-MAM). In the I-DLB-RP-MAM, end-of-life products are first disassembled in a single disassembly center, and a vehicle equipped with a 3D printer then dispatches both recycled and 3D printed components to the customers, i.e. remanufacturing centers. Several demanded components are obtained in disassembly center and the remaining amounts are produced by 3D printer en-route. We formulate a non-linear mathematical programming model for the I-DLB-RP-MAM. We conduct experiments on a numerical example-based on a real product. Scenario analysis is conducted and results show that additive manufacturing technology can be successfully incorporated into the supply chain. We obtain significant improvements such as reduction in inventory and total cost.

An Optimal Task Assignment Strategy in Cloud-Fog Computing Environment

With the advent of the Internet of Things era, more and more emerging applications need to provide real-time interactive services. Although cloud computing has many advantages, the massive expansion of the Internet of Things devices and the explosive growth of data may induce network congestion and add network latency. Cloud-fog computing processes some data locally on edge devices to reduce the network delay. This paper investigates the optimal task assignment strategy by considering the execution time and operating costs in a cloud-fog computing environment. Linear transformation techniques are used to solve the nonlinear mathematical programming model of the task assignment problem in cloud-fog computing systems. The proposed method can determine the globally optimal solution for the task assignment problem based on the requirements of the tasks, the processing speed of nodes, and the resource usage cost of nodes in cloud-fog computing systems.

THE FINANCIAL COMPONENT OF THE COMMUNICATION MANAGEMENT STRATEGY IN HIGHER EDUCATION INSTITUTIONS

Abstract. The article defines the role of the financial component of the communication management strategy in HEIs based on the construction of the algorithm for optimizing the distribution of costs for communication processes and the construction of the financial mechanism of communication management. Communication processes in HEIs have a number of specific features due to the fact that a large number of people and groups of people with different levels of education, level of intelligence, age, upbringing and interests take part in the communication process. That is, effective communication management of HEIs requires from the management of institutions to develop a management strategy that would satisfy the interests of all groups of communication process participants. It has been emphasized that the communication management strategy in HEIs should be developed for the long term taking into account the conditions of the changing external environment, and have the goal to continuously transmit information to employers, applicants, their parents, and the whole society in order to make the services of institutions attractive to the target audience and have feedback which would allow monitoring the quality of communication processes and have an economic effect from their implementation. It has been noted that one of the main components of the communication management strategy in HEIs is finance. An algorithm has been built to optimize the costs of managing communication in HEIs based on the use of the classical method of mathematical nonlinear programming problems optimization. A financial mechanism for managing communication in HEIs has been built, which is a system of measures aimed at achieving a certain level of communication processes management while maintaining a certain level of financial stability and independence. It has been concluded that the financial component of the communication management strategy in HEIs is one of its main elements, which allows constant increasing the level of institutions competitiveness and the quality of education as well as scientific and technical potential. Keywords: financial component, communication, management strategy, costs, algorithm, mechanism, higher education institutions. Formulas: 11; fig.: 2; tabl.:1; bibl.: 15.

Optimal electricity supply system under Iranian framework limitations to meet its emission pledge under the Paris climate agreement

As part of its Paris Agreement commitment, Iran pledged to decrease 4 percent of its carbon dioxide (CO2) emissions from 2020 to 2030. About 29% of total emission in Iran belongs to electricity supply while energy consumption in other sectors (transport, household, and industry) have a lower share in CO2 emission. The main concern here is finding the optimal mix of power plants in the electricity supply system that should be deployed to meet Iran’s mentioned respective targets. So, we developed a non-linear mathematical programming model for Iran’s electricity system to address this concern. Results show that a 10-20% diffusion of renewable energy and converting gas turbine power plants to gas combined cycle technology with 5% annual rate can satisfy Iran’s emissions pledge under the Paris Climate Accord. Finally, this model has been run for years between 2017-2030. Four scenarios have also been prepared based on different Iranian Five-Year Development Plans.

Network Slicing with MEC and Deep Reinforcement Learning for the Internet of Vehicles

The interconnection of vehicles in the future fifth generation (5G) wireless ecosystem forms the so-called Internet of Vehicles (IoV). IoV offers new kinds of applications requiring delay-sensitive, compute-intensive, and bandwidth-hungry services. Mobile edge computing (MEC) and network slicing are two of the key enabler technologies in 5G networks that can be used to optimize the allocation of the network resources and guarantee the diverse requirements of IoV applications. As traditional model-based optimization techniques generally end up with NP-hard and strongly non-convex and nonlinear mathematical programming formulations, in this article, we introduce a model-free approach based on deep reinforcement learning (DRL) to solve the resource allocation problem in MEC-enabled IoV networks based on network slicing. Furthermore, the solution uses non-orthogonal multiple access (NOMA) to enable better exploitation of the scarce channel resources. The considered problem addresses jointly the channel and power allocation, the slice selection, and the vehicle selection (vehicle grouping). We model the problem as a single-agent Markov decision process. Then we solve it using DRL with the well-known deep Q learning (DQL) algorithm. We show that our approach is robust and effective under different network conditions compared to benchmark solutions.

Data Center Network Design for Internet-Related Services and Cloud Computing

We study an integrated data center network design problem for Internet-related services and cloud computing, of which the objective is to minimize total operating cost and service delay penalty by optimizing data center location, footprint allocation, and resource provisioning decisions, while incorporating essential features such as latency, power, multiple resources, configuration limits, and interdependent footprints. We formulate the optimal design problem as a nonlinear mathematical program. We analyze a queueing model to approximate the service latency and provide tractable reformulations. We further develop Lagrangian relaxation methods and generate strengthening cuts by exploiting the structural properties of the problem to enhance computational efficiency for large-scale problems. Our numerical studies demonstrate that the proposed integrated model, which jointly optimizes location, allocation, and resource provisioning, can significantly reduce cost and improve quality-of-service when compared with a hierarchical approach that optimizes these decisions sequentially. Moreover, our proposed solution methods outperform state-of-the-art commercial software in computational performance. Based on real-world data sets, the proposed model selects data centers that have been chosen by major cloud computing infrastructure providers. We also draw managerial insights that can be used as design guidelines in practice.

A Stochastic Flight Problem Simulation to Minimize Cost of Refuelling

Commercial airline companies are continuously seeking to implement strategies for minimizing costs of fuel for their flight routes as acquiring jet fuel represents a significant part of operating and managing expenses for airline activities. A nonlinear mixed binary mathematical programming model for the airline fuel task is presented to minimize the total cost of refueling in an entire flight route problem. The model is enhanced to include possible discounts in fuel prices, which are performed by adding dummy variables and some restrictive constraints, or by fitting a suitable distribution function that relates prices to purchased quantities. The obtained fuel plan explains exactly the amounts of fuel in gallons to be purchased from each airport considering tankering strategy while minimizing the pertinent cost of the whole flight route. The relation between the amount of extra burnt fuel taken through tinkering strategy and the total flight time is also considered. A case study is introduced for a certain flight rotation in domestic US air transport route. The mathematical model including stepped discounted fuel prices is formulated. The problem has a stochastic nature as the total flight time is a random variable, the stochastic nature of the problem is realistic and more appropriate than the deterministic case. The stochastic style of the problem is simulated by introducing a suitable probability distribution for the flight time duration and generating enough number of runs to mimic the probabilistic real situation. Many similar real application problems are modelled as nonlinear mixed binary ones that are difficult to handle by exact methods. Therefore, metaheuristic approaches are widely used in treating such different optimization tasks. In this paper, a gaining sharing knowledge-based procedure is used to handle the mathematical model. The algorithm basically based on the process of gaining and sharing knowledge throughout the human lifetime. The generated simulation runs of the example are solved using the proposed algorithm, and the resulting distribution outputs for the optimum purchased fuel amounts from each airport and for the total cost and are obtained.