Mathematical Programming Methods Research Articles

Enhancing the passive design of buildings: A mixed integer non-linear programming approach for the selection of building materials and construction building systems

Consumption of energy in buildings accounts for a considerable proportion of worldwide energy use. There is a dire need for enhancing the energy efficiency of building to limit their demand for operating energy as this leads to enhanced reductions in environmental impacts. Of particular relevance to the amount of energy utilised in a building during the operation phase is the nature of material and size of components utilised in the building. In this work, a mathematical programming framework is presented to optimise a number of building design objective functions, including heat gain, daylight and economic cost of material utilised. The variables that are focussed on in this study are the sizes of windows, type of material adopted for the building, embodied in the construction building systems used for various building components, and the type of lighting adopted. To validate the framework, two realistic case studies obtained from an industry partner are adopted and solved via the use of the proposed mathematical programming method. Results indicate that compared to the solutions proposed by an experienced engineer, the daylight, heating and cost of the building is enhanced by up to 39%, 43% and 23% respectively. The framework is hoped to help policy makers introduce more streamlined guidance for the building sector when it comes to optimised material choice and window sizing to result in energy-efficient and economical buildings.

Throughput of distributed queueing-based LoRa for long-distance communication

LoRa, due to its advantage of long-range communication capability, is promising for Internet of Things (IoT) and space-air-ground communications. However, the conventional MAC protocol used with LoRa is classified as an Aloha-based algorithm, which leads to drastic decrease in throughput when a huge amount of end-devices try to access the network. To achieve stable and high throughput of LoRa, we propose a design to combine the distributed queueing (DQ) and in-band-full-duplex (IBFD) technologies. The usage of DQ mechanism is benefit for fast collision resolution, while the IBFD-enabled gateway helps to reduce the heavy control overhead of DQ. The designs of access procedure and frame structure are discussed in detail. The outage probability and average throughput are evaluated under imperfect self-interference cancelation. Also, a mathematical programming method is developed to optimize the spreading factor and code rate. Numerical results show that our proposal gains an extra enhancement of 1.83-fold in throughput.

The Growth of E-Commerce Due to COVID-19 and the Need for Urban Logistics Centers Using Electric Vehicles: Bratislava Case Study

Before the COVID-19 pandemic there had already been an increase in individual shipment transportation including inner-city areas. During the pandemic and implementation of adopted preventive measures, it has increased by more than 100% in some cities. This presents an unsustainable development, particularly in terms of urban environment. The above-mentioned development has accelerated the research related to optimal allocation of logistics centres considering the last-mile distribution. Unfortunately, the theoretical mathematical model that finds an optimal urban logistics centre location based on the matrix of distance, number, and weight of shipments is not applicable in most cities. Therefore, the following research methodology was chosen in accordance with the approved territorial plan. The authors considered those locations in Bratislava—the capital of Slovak Republic—which are designated, or suitable for building up of an urban logistics centre. These localities were afterwards evaluated in a real-world case study employing methods of mathematical programming (linear programming), the nearest neighbour method, and the Clarke-Wright method. The presented methodology can be applied not only when deciding on the appropriate location of the city logistics centre, but also at optimizing the vehicle routing problem. Taking into account the urban logistics sustainability and the e-commerce growth, it was analysed whether the suggested location of urban logistics centre is feasible to provision examined facilities using electric vehicles. The range of considered electric vehicles of N2 category present in the market tends to be at the limits of distribution routes length for the given case study. Therefore, the article also deals with the fast-charging possibilities of vehicles during handling operations and the use of hybrid freight vehicles in city logistics.

An axiomatic design-based mathematical programming method for heterogeneous multi-criteria group decision making with linguistic fuzzy truth degrees

This paper aims to develop a new axiomatic design-based mathematical programming method for heterogeneous multi-criteria group decision making (HMCGDM) problems with linguistic fuzzy truth degrees (LFTDs). The main contributions of this paper are summarized in five aspects: (1) The information content definitions for six types of fuzzy numbers are initially provided according to axiomatic design . (2) Considering the authority of experts on different criteria and group consensus, a bi-objective programming model is constructed to derive experts’ weights by maximizing individual deviation and minimizing group discordance. (3) Each alternative is assessed on the basis of its information content to a fuzzy positive ideal solution. Information content is firstly used to define the linguistic fuzzy consistency and inconsistency indices. (4) A bi-objective linguistic fuzzy mathematic programming model is built to determine the criteria weights, which considers consistency and inconsistency indices simultaneously. This model can be dexterously transformed into a crisp linear programming model for resolution by the linguistic scale function. (5) The group information content of each alternative to fuzzy positive ideal solution is calculated to determine the ranking order of alternatives. Finally, an example of blockchain service provider selection is given to validate the proposed method.

Projection-operator optimization of controls of dynamic objects

The principles of application of projection-operator methods of mathematical programming for calculating optimal controls based on “immersion of control problems” in problems of finite-dimensional mathematical programming are formulated. The results obtained illustrate the technique of qualitative study of the stability of systems with optimizing feedback based on the contraction mapping principle of functional analysis. The considered technique allows one to synthesize locally optimal systems with nonlinear control objects. In this case, nonlinear models of objects are taken into account in the right-hand sides of linear manifolds, and the projection operator forms nonlinear optimal controls with feedback taking into account the operators of nonlinearities of the object.

Matrix method to solve the inverse problem of heat transfer in heat exchangers

Along with verification calculations of known designs of heat exchangers, in design engineering and when we develop new technologies, design calculations are necessary to solve the inverse problems of choosing the optimal designs and operating modes of equipment. Previously, the formulation and solution of inverse problems of classification and unsteady heat conduction have been considered, while the inverse problems of heat transfer in the design of heat exchange equipment are poorly presented in the literature. The development of methods to solve inverse problems in the design of heat exchange equipment is an urgent task of power industry. Matrix models of heat transfer based on mass and energy balance equations are used to formulate and solve inverse problems of heat exchange systems. Methods of mathematical programming are applied to solve inverse and optimization problems. For design calculations, a matrix method to solve inverse problems for choosing the design of devices and parameters of heat carriers that ensure the effective operation of the system is proposed. The inverse problem is formulated for the case of the sliding boundary of the beginning of the phase transition with the countercurrent type of movement of heat carriers. The obtained results can be used in power energy, chemical and food industries to improve the efficiency of designing resource-and energy-saving technologies. The solutions obtained can be implemented when developing measures to improve resource and energy saving technologies.

A Framework for Design and Operation Optimization for Utilizing Low-Grade Industrial Waste Heat in District Heating and Cooling

In the process industry, a large amount of low-grade waste heat is discharged into the environment. Furthermore, district heating and cooling systems require considerable low-grade energy. The integration of the two systems has great significance for energy saving. Because the energy demand of consumers varies in periods, the design and operation of an industrial waste heat recovery system need to match with the fluctuations of district energy demand. However, the impact of the periodic changes on the integration schemes are not considered enough in existing research. In this study, a framework method for solving above problem is proposed. Industrial waste heat was integrated with a district heating and cooling system through a heat recovery loop. A three-step mathematical programming method was used in design and operation optimization for multiperiod integration. A case study was conducted, and the results show that the multiperiod optimization method can bring significant benefits to the system. By solving the mixed integer nonlinear programming model, the optimal operation plans of the integration in different periods can be obtained.

The Current State Of The Use Of Lalmi Crop Land And The Main Directions Of Their Improvement

The article analyzes the current state of lalmi crop lands using the methods of variability, mathematical programming and scientific observation, evaluates and develops the ratio of land and crop species to their location, natural-geographic, socio-economic and environmental conditions of these regions.

Secondary wastewater treatment processes optimization

Introduction. The level of water pollution in Ukraine continues to grow, despite the strengthening of requirements for the treated water, so the existing approaches to the water treatment processes control need to be revised and improved.
 Materials and methods. Mathematical Programming methods for formalization and solving the optimization problem are used. Computer simulation research using the program developed by the authors are applied to verify the compliance of the obtained results with the normative values and data of normal operation.
 Results and discussion. The optimization of processes control was performed on the example of a typical process of secondary wastewater treatment, which is used for wastewater treatment in Kyiv and nearby settlements. The secondary treatment unit consists of an aeration tank, into which air is forcibly supplied and evenly distributed, and a secondary settling tank with recycling. The problem of optimization of biological wastewater treatment control process is formalized: minimization of pollutant concentration in treated water is chosen as the main aim of optimization, air flow to aeration tank is chosen as control parameter, quadratic deviation of current concentration values from normative ones is chosen for target function. To solve the optimization task, a software module in JavaScript was developed using a client-server architecture that works in real time and allows to obtain such values of oxygen consumption in the aeration tank, which provide a minimum deviation of the concentration of pollutants from the normative values. The simulations showed that the calculated control values provide a reduction in the concentration of pollutants to the normative values within 6-10 hours, which corresponds to the data of normal operation, and the difference between the calculated and actual data does not exceed 5%.
 Conclusions. The obtained results allow to find a set of technological influences to ensure optimal control according to the selected criterion, and are also the basis for calculating the control system. The results of calculations can be used for short-term - up to 8 hours - forecasting of water quality indicators.

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.

A novel primal‐dual eigenstress‐driven method for shakedown analysis of structures

AbstractThe shakedown load of elastoplastic structures under multiple variable loading is an important factor in structural design and integrity analysis. In classical plasticity shakedown analysis is an essential and challenging problem. Most existing methods are based on the solution of super large‐scale mathematical programming, basis reduction or mechanics insight method which have their own limitations in practical engineering problem. In the present study, the proposed method explores the Karush–Kuhn–Tucker (KKT) conditions and the physical reinterpretation of its primal‐dual variables of the Melan's lower bound theorem, and establishes the relation of the primal‐dual variables in finite element formulation. Based on the primal‐dual theory, the primal‐dual eigenstress‐driven method is proposed which is a two‐level nested algorithm: the inner level is the eigenstress‐driven incremental algorithm for constructing the beneficial residual stress field and calculating the safe multiplier and the outer level is the load multiplier descent algorithm for searching the shakedown multiplier. For the purpose of algorithm's universality, the proposed algorithm is fully integrated with the commercial finite element software ANSYS APDL without special optimization solvers, which is well suited for large‐scale practical engineering structures. Several numerical examples are provided to demonstrate the accuracy and efficiency of the proposed algorithm.

On Methodological Approaches to Modeling the Quality of Life

In recent decades, it has become obvious that an ecological catastrophe is rapidly approaching civilization and the continued existence and development of mankind depends on it. It has long been understood in society that environmental factors affect the standard and quality of life of the population. Modeling the relationship of this influence is an interdisciplinary task that requires the removal of a number of methodological restrictions. Among them: effective data collection and monitoring, the choice of a measurement system, "noisiness" of data. The purpose of the work is to analyze the current state of methodological foundations and choose a method for building a model of the relationship of quality of life with components of the structure of quality of life of the population. Today, various systems of formalized description of the quality of life are proposed at the global level: the human development index, the environmental-economic accounting system, the real progress index and the sustainable economic well-being index, the happiness index, the quality of life index according to the Economist Intelligence Unit, the Sustainable Society Index. The modern stage of research on the problem of modeling the level and quality of life is represented by intercountry and interregional comparisons using a developed mathematical apparatus. The work presents general and methodological problems of quality of life research; analysis and selection of methods for solving problems of modeling the relationship of components and indicators of the level and quality of life of the population. The following are considered: methods of multicriterial evaluation, methods of multipurpose mathematical programming, statistical methods, methods of dynamic modeling, methods of simulation modeling. It is shown that in order to solve the applied problems of building a model of level and quality of life, it is advisable to use multidimensional statistical methods, where the initial necessary stage is the procedure of data conversion by standardizing (normalizing) data, namely, bringing all variables involved in the construction of an integral indicator to a single unified scale.

The bilevel optimisation of a multi-agent project scheduling and staffing problem

In this paper, we study a multi-agent project staffing problem involving a single project, which has to be scheduled under resource constraints. We consider a functional organisational structure where a team leader and a project manager are together responsible for the operational execution of a project. The team leader, which has the formal authority over the resources, is standing at the top of the hierarchy and determines the number and mix of (additional) employees and tries to level the workload over the planning period in order to avoid idle resource times. The project manager is responsible for the scheduling of the project activities and his/her objective is to minimise the project duration. The interaction between both agents in the decision-making process is, on the one hand, hierarchical, i.e. the team leader imposes his/her decision on the project manager. On the other hand, the decision taken by the team leader should comply to the objective of the project manager such that the staffing plan and project schedule is agreed by both parties. We propose a bilevel optimisation model that embeds a nested inner optimisation problem, i.e. the project manager decision problem, as a constraint in the outer optimisation problem, i.e. the decision problem of the team leader. The algorithm is a mathematical programming method thriving on the generation of additional lazy constraints via feasibility callbacks so that the team leader problem has to respect the requirements formulated in the project manager problem. In the computational experiments, we compare this solution approach to alternative classical optimisation approaches and we validate the design choices related to the proposed speed-up mechanisms and parameter settings.

Time Coordination of Periodic Passenger Train Connections in Conditions of Single-Track Lines

The article addresses creation of a mathematical model for a real problem regarding time coordination of periodic train connections operated on single-track lines. The individual train connections are dispatched with a predefined tact, and their arrivals at and departures to predefined railway stations (transfer nodes) need to be coordinated one another. In addition, because the train connections are operated on single-track lines, trains that pass each other in a predefined railway stations must be also coordinated. To optimize the process, mathematical programming methods are used. The presented article includes a mathematical model of the given task, and the proposed model is tested with real data. The calculation experiments were implemented using optimization software Xpress-IVE.

Study of the functional properties of dough

The paper presents the studies of gluten - free types of unleavened dough, it shows the effect of hydrocolloids on the structure of the dough. The aim of the work is to study the functional and technological properties of the dough depending on the type and concentration of the flour and hydrocolloids. The tasks of the research are the following: to determine the concentration of colloids that makes dough plastic and strong dough; to identify the dependence of the concentration of flour on the type and properties of hydrocolloids; to study organoleptic quality indicators. The dynamic viscosity of the dough was determined by using a Brookfield viscometer. The methods of mathematical experiment planning were used to design the recipes of the unleavened dough. To define the reference dependency of viscosity on shear rate, the coefficients of nonlinear model equations have been estimated by using the methods of regression analysis in the program Statistica v6. For the experimental samples, the equation of the viscosity dependence is determined as a model of non-linear multiple regression. The graphs of the viscosity dependence on the shear rate compared to the reference rate are made. The methods of mathematical programming have been used to find the optimal ratio of flour and each type of structure-forming agents (soy protein isolate, xanthan gum, and potato starch) in the dough to maximize the approximation of the viscosity curve to the reference one. For this purpose, an objective function with limits on the shear rate is compiled. Using the MathCAD v15, the optimal values of the content of the components such as rice flour - 27.78%, soy protein isolate - 7.22%, potato starch - 32.22%. xanthan gum - 0.28 % are found. The results of the control measurement of the viscosity of the sample with the optimal composition indicate that the selected mathematical model corresponds to the elastoviscoplastic properties of this dough and the curve changes depending on the composition of the dry dough mixture. The description of the mathematical model and the regression analysis make it possible to select the ratio of the prescription components so that the resulting product has rheological characteristics close to the control sample.

Assessment of the impacts of climate change and variability on water resources and use, food security, and economic welfare in Iran

Climate change influences the agricultural sector by reducing available water resources, thereby influencing income, consumer and producer surplus, and crop prices. So, it is necessary to have a comprehensive integrated method to measure the effects of these changes on natural resources and social conditions. The present study aims to use the positive mathematical programming method to discover the trend and conditions of groundwater resources, agricultural water use, food security, and economic welfare of the agricultural sector in Iran. To this end, data for the period 2000–2015 was used under four different scenarios of normal climate change, climate change, climate variability, and concurrent climate change The results showed that the mean agricultural water use will amount to 35,103.6, 26,533.8, 35,216, and 26,510.7 million m3 and the mean decline in the reserves of aquifers will amount to 4422.22, 11,165.6, 4438.25, and 11,267.4 million m3 under the scenarios, respectively. With respect to food security, the net farm revenue will be 314,560, 248,753, 315,427, and 248,574 billion IRR, respectively. The mean crop price per ton will reach 905.3, 1141.8, 904, and 1142.8 million IRR, respectively. The mean consumer surplus will be 172,107.7, 166,450, 172,024, and 166,403 billion IRR and the mean producer surplus will be 419,959.2, 395,380, 419,751, and 395,204 billion IRR, respectively. Based on the results, to reduce the adverse impacts of climate change on different studied aspects, it is necessary to change policymaking in the water and agricultural sectors, especially regarding the shift from traditional agricultural water allocation to its market-based allocation and to change planting pattern.

Strength analysis of the roller bearing with a crowning and misalignment error

This article aims to present a reliable method that can conduct loading-capacity calculations and strength analyses of roller bearings. A new algorithm and mathematical model are proposed in this paper to realize the purposes through building deformation compatibility relationships and load equilibrium relationships among the outer ring, rollers and the inner ring using mathematical programming method and three-dimensional, finite element method. Special software is developed through many years of efforts to realize the analysis procedures. Contact analysis of a roller bearing is conducted successfully by the developed software. It is found that edge-loads of the roller bearing are analyzed successfully by the developed software when the rollers are not crowned. It is also found that the edge-loads are disappeared and the contact pressure on roller surface becomes a uniform distribution when the rollers are crowned. The effect of quantity of roller-crowning on the contact pressure distribution of rollers is also investigated. It is found that the maximum contact pressure can be reduced about 11% if the quantity of roller-crowning is determined by the maximum roller load. Shear stresses inside the rollers are also analyzed. It is found that the maximum shear stresses exist at the two ends of rollers and near the contact boundaries of the rollers. This means that the roller bearing shall have a fatigue failure at the two ends and near the contact boundaries of the rollers, not at the center of the contact area of the rollers. Finally, contact pressure distribution is analyzed successfully for the roller bearing with a misalignment error.

A group decision making approach for supplier selection with multi-period fuzzy information and opinion interaction among decision makers

Since the performances of suppliers usually fluctuate over time and are affected by environmental changes, enterprises need to evaluate suppliers in the past several periods, rather than a single period. As the environment changes, decision makers will exchange their views and influence each other. In addition, multiple decision makers are not always knowledgeable and sometimes express their preferences about suppliers using fuzzy numbers. To meet the different evaluation requirements of decision makers and analyze the influence of time factors and opinion interaction between decision makers, this paper develops a group decision making approach considering multi-period fuzzy information and opinion interaction of decision makers for supplier selection. In this approach, decision makers provide their preferences in multiple periods using generalised fuzzy numbers and the weights of different periods are determined by a mathematical programming method. The effects of opinion interaction are considered by assigning various weights to different decision makers. Fuzzy Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) method is used to rank potential suppliers. The results of a supplier selection example show the proposed approach can select suitable suppliers by considering multi-period fuzzy information and opinion interaction.

Evaluation of Agricultural Sustainability Indicators and Determination of Cropping Patterns with Emphasis on Deficit Irrigation Strategy: the Case of the Qazvin Irrigation Network, Iran

The purpose of this study was to evaluate the effect of different levels of water consumption reduction in different growing stages as deficit-irrigation scenarios based on economic, social, and environmental criteria in line with agricultural sustainability of the Qazvin irrigation network. In order to maximize farm income, the positive mathematical programming (PMP) method along with the maximum entropy (ME) were used on the basis of crop yield response functions comparing to water in the space of other constraints. Then, the analytical hierarchy process (AHP) method was hired to calculate the weight of the major indices and their sub-indices, and in the final stage, the best-ranked scenarios were selected using Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) approach. The information required for this study was obtained via two-stage cluster sampling method by completing 144 questionnaires. The results showed that applying different deficit-irrigation scenarios on crop growth stages that yield formation was of less susceptibility to water stress, leads to a cropping pattern in favor of crops that generate more revenue (such as Alfalfa) for less water use. Also, the results of weights for the economic (43.4), social (18.1), and environmental (38.5) indices showed that economic indicator is of great importance. Five scenarios used in this study. The scenario ranking process showed that the S1 scenario (5% reduction of deficit-irrigation at ripening stage for wheat, barley, fodder maize, grain corn and beet, and 5% decrease at vegetative growth stage of Alfalfa) was selected as the best and also the most desirable state of sustainability in agriculture scenarios.

A Fuzzy-MOP-Based Competence Set Expansion Method for Technology Roadmap Definitions

Technology roadmaps have been widely adopted as an important management tool during the past three decades after their invention by Motorola in the 1980s. Technology roadmapping processes can be integrated with a firm’s competence sets and play dominant roles in strategy definitions. Although the issue of how multiple objectives can be dealt with in technology roadmaps by including the uncertainties of the modern management environment is important, it has seldom been addressed. To remedy this, we aim in this research to propose a competence set expansion method based on fuzzy multiple objective programming (FMOP). An empirical study based on the roadmapping of silicon intellectual properties (SIPs) of automotive applications will be used to demonstrate the feasibility of the proposed roadmapping method. In the future, the proposed analytic technique can be integrated with the data mining results of academic research database, patent libraries, etc. The well-verified mathematical programming method can serve as a basis for research and development (R&D) strategy definitions by managers of high-technology firms as well as policy makers of governments.