Mathematical Programming Methods Research Articles

A novel hybrid clonal selection algorithm for the corridor allocation problem with irregular material handling positions

As an essential influencing factor in the facility layout, the reasonable setting of material handling positions plays a vital role in improving operational efficiency and reducing material handling costs. In this paper, a corridor allocation problem (CAP) that allows irregular logistics material handling positions (IMHPCAP) is proposed. Compared with previous CAP studies, IMHPCAP allows facilities to set irregular material handling positions according to their characteristics to increase material handling flexibility. However, the IMHPCAP is more challenging than the traditional CAP finding the best layout solution. In order to solve this problem, a mixed-integer programming model of IMHPCAP is established. A clonal selection algorithm with social engineering optimiser based on a two-stage solution was proposed to obtain the best layout for large-scale problems. In the first stage of this algorithm, the rows in which facilities are placed, and the arrangement sequence of the facilities are established. In the second stage, the precise coordinates of the MHPs are obtained using a mathematical programming method. Finally, some benchmark instances of the CAP and IMHPCAP were solved to verify the performance of the algorithm. Furthermore, an actual case of a baby plastic product processing plant was considered to validate the IMHPCAP. The results showed that the hybrid clone algorithm performed well in solving the CAP and IMHPCAP, thereby exhibiting practical significance.

On Solving a Class of Continuous Traffic Equilibrium Problems and Planning Facility Location Under Congestion

This paper presents methods to obtain analytical solutions to a class of continuous traffic equilibrium problems, where continuously distributed customers from a bounded two-dimensional service region seek service from one of several discretely located facilities via the least congested travel path. We show that under certain conditions, the traffic flux at equilibrium, which is governed by a set of partial differential equations, can be decomposed with respect to each facility and solved analytically. This finding paves the foundation for an efficient solution scheme. Closed-form solution to the equilibrium problem can be obtained readily when the service region has a certain regular shape, or through an additional conformal mapping if the service region has an arbitrary simply connected shape. These results shed light on some interesting properties of traffic equilibrium in a continuous space. This paper also discusses how service facility locations can be easily optimized by incorporating analytical formulas for the total generalized cost of spatially distributed customers under congestion. Examples of application contexts include gates or booths for pedestrian traffic, as well as launching sites for air vehicles. Numerical examples are used to show the superiority of the proposed optimization framework, in terms of both solution quality and computation time, as compared with traditional approaches based on discrete mathematical programming and partial differential equation solution methods. An example with the metro station entrances at the Beijing Railway Station is also presented to illustrate the usefulness of the proposed traffic equilibrium and location design models.

A Comparative Study of Multi-Stage Approaches for Wind Farm Layout Optimization

Abstract The wind farm layout optimization (WFLO) problem is a complex and nonconvex optimization problem. Even though many different heuristic algorithms and mathematical programming methods have been tested and discussed, there is no consensus about which algorithm is the most suitable approach for solving WFLO problems. Every algorithm presents its own advantages and disadvantages in solving different optimization problems; thus, multi-stage approaches may combine the advantages of multiple algorithms and offer superior performance. One multi-stage approach used for solving WFLO problems is to apply an algorithm in the first stage to produce an optimized layout which serves as the initial condition for a second-stage algorithm to perform further refinement. This paper presents a comparison between two types of multi-stage methods: the Heuristic-Gradient-based (H-G) model which consists of a heuristic algorithm in stage 1 and a gradient-based algorithm in stage 2 and the Discrete-Continuous (D-C) model which consists of a heuristic algorithm in the discrete scheme in stage 1 and an algorithm in the continuous scheme in stage 2. Annual energy production (AEP) is used as the objective function while the computational time associated with each approach is documented. Three scenarios are investigated in this paper with different complexity in the wind conditions. It was observed that the D-C models provide the optimal solutions with an average of 0.67% higher AEP and an average of 6.2% lower computational time in comparison with the H-G models. The results from this study provide a basis for selecting a proper optimization algorithm for solving WFLO problems which can lead to a significant increase in the overall annual energy production and a large reduction in computational time.

Axial compression behaviour of cruciform cold-formed steel built-up columns: Shape optimization and experimental study

In this paper, the cruciform CFS built-up cross sections are formed through four identical multi-roll lipped channels connected at their webs with high-strength bolts and filler plates. An optimization algorithm is primarily proposed that integrates sequential quadratic mathematical programming methods and finite strip analysis. It is desirable to effectively improve the buckling behaviour of cruciform CFS built-up columns without increasing the material volume. Eight different areas of built-up sections were optimized, each built-up open section was formed by fold-lines of the steel plate, and the width and angle of the constituent elements of the built-up section were selected as the main design variables. To simplify the optimization task and provide more practical structural components, usage constraints and practical manufacturing limits were imposed on the selected built-up sections during the optimization process. The results show that the adopted optimization process significantly increased the critical local buckling stress of the cruciform CFS built-up columns by 26.2%–58.9%. The design strength calculated according to the AISI standard was increased by 2.76%–18.15%. The axial compression bearing capacity tests with two different optimized cross sections were conducted, and the test loading capacities and failure modes of each specimen were obtained. The test results show that the failure modes were mainly driven from local and distortional buckling to torsional and flexural buckling with increasing slenderness, and the deformations were concentrated in the region near the end of column. Finally, the axial compression strengths of such cruciform CFS built-up columns obtained from the tests were used to assess the applicability of AISI standards. For columns failed by local and distortional buckling, AISI standard were un-conservative, whereas for torsional and flexural, AISI standard were conservative.

A Data-Driven Genetic Algorithm for Power Flow Optimization in the Power System With Phase Shifting Transformer

Phase-shifting transformer (PST) is one of the flexible AC transmission technologies to solve the problem of uneven power transmission. Considering that PST can also be used as a regulation means for the economic operation of the system, it is necessary to study the power flow optimization of power systems with PST. In order to find a more efficient power flow optimization method, an improved genetic algorithm including a data-driven module is proposed. This method uses the deep belief network (DBN) to train the sample set of the power flow and obtains a high-precision proxy model. Then, the calculation of the DBN model replaces the traditional adaptation function calculation link which is very time-consuming due to a great quantity of AC power flow solution work. In addition, the sectional power flow reversal elimination mechanism in the genetic algorithm is introduced and appropriately co-designed with DBN to avoid an unreasonable power flow distribution of the grid section with PST. Finally, by comparing with the traditional model-driven genetic algorithm and traditional mathematical programming method, the feasibility and the validity of the method proposed in this paper are verified on the IEEE 39-node system.

Sequential Linearization Method for Bound-Constrained Mathematical Programs with Complementarity Constraints

Sequential Linearization Method for Bound-Constrained Mathematical Programs with Complementarity Constraints

Fleet Management and Charging Scheduling for Shared Mobility-on-Demand System: A Systematic Review

Challenged by urbanization and increasing travel needs, existing transportation systems call for new mobility paradigms. In this article, we present the fleet management and charging scheduling of a shared mobility-on-demand system, whereby electric vehicle fleets are operated by a centralized platform to provide customers with mobility service. We provide a comprehensive review of system operation based on the operational objectives. The fleet scheduling strategies are categorized into four types: i) order dispatching, ii) order-dispatching and rebalancing, iii) order-dispatching, rebalancing and charging, and iv) extended. Specifically, we first identify mathematical modeling techniques implemented in the transportation network, then analyze and summarize the solution approaches including mathematical programming, reinforcement learning, and hybrid methods. The advantages and disadvantages of different models and solution approaches are compared. Finally, we present research outlook in various directions.

Regulation of biological balance between pests and their entomophages in biological protection of cotton

The issues of regulation of biological balance between the main pests of cotton and their entomophages in biological protection are considered. The ways and methods of developing optimal work plans of biological factories for the production of useful entomofauna (trichogram, brackon, golden-eyed) against cotton pests (cotton and winter scoops) for various zones of the republic using mathematical modeling and programming methods are determined.

SQP Methods for Mathematical Programs With Switching Constraints

The mathematical program with switching constraint (MPSC) problem makes a new-type optimization issue in recent years. Due to the existence of switching constraints, the common constraint specification is not satisfied, so that the convergence results of existing algorithms can not be directly applied to this problem. The sequential quadratic programming (SQP) method was applied to solve the problem, and to prove that the clustering point of the solution sequence of the subproblem is the Karush-Kuhn-Tucker point of the original problem under the linear independent constraint specification with the switching constraint. At the same time, in order to improve the relationship between stationary points, the equivalence between the strong stationary point and the KKT point was proved. Finally, the numerical results show that, the sequential quadratic programming method is feasible to deal with this type of problems.

Systems Theory and Evidence‐Based Decision‐Making as Keys for Arbitrating between Optimal Production and Efficient Maintenance: A Case Study

Organizations in the 21st century operate in evolving and highly competitive environments—such environments are catalysts for deviation in organization‐planned operations, including production and maintenance. The differences between maintenance and production, in general, are well known, given the several studies found in the literature regarding industrial engineering. However, the differences between maintenance and production are becoming less significant as a result of increased understanding of the systemic approach to organizations where the whole matters more than the sum of the parts. The aim of this study was to maximize the productivity of a manufacturing factory by applying mathematical programming methods while simultaneously considering the requirements of efficient maintenance. A case study is used to show how systems theory can be used as the basis for evidence‐based decision‐making in a factory manufacturing line in Morocco. Despite the potential for conflict between optimal production objectives and efficient maintenance in high‐performance factories, the four‐month case application suggests that systems theory is a key for arbitration. Research implications are presented along with future research directions.

Examining Farmers’ Adoption Decisions towards Precision-Agricultural Practices in Greek Dairy Cattle Farms

Nowadays, the sustainability of Greek dairy cattle farms is questionable due to low competitiveness and high GHG emissions. In this context, the BIOCIRCULAR project, funded by the EYDE ETAK, developed a series of alternative practices focusing on precision agriculture principles. However, the adoption of any practice from farmers is not a given, and depends on several determinants. Hence, the objective of this study is to examine farmers’ adoption decisions regarding precision-agricultural practices in Greek dairy production systems, as well as the economic and environmental impacts of this adoption. In order to achieve this, a bio-economic model was developed based on mathematical programming methods. The proposed model simulates a large number of dairy cattle farms with or without crop production, including different management strategies and their relevant costs, and provides an environmental assessment of the adopted practices based on GHG emissions. Moreover, in order to analyze farmers’ adoption decisions, different policy measures, linked to various environmental outcomes, were examined. The results highlighted that the adoption of precision-agricultural practices led to significantly better economic and environmental outcomes. Furthermore, it was found that different levels of incentives can be efficiently targeted to encourage the adoption of new feeds and, more broadly, to secure the sustainability of the sector.

Development of a model of selecting cloud software for a road construction organization under interval information

The object of research is the management processes of a road construction organization. The research is based on the principles of systems analysis for structuring design processes; methods of mathematical modeling, fuzzy mathematics, discrete programming, multicriteria assessment and optimization for the selection of cloud software for road construction organizations in terms of interval information. The information system of a road construction organization includes planning, reporting, regulatory and technical documentation that characterizes the state and movement of information in the enterprise. It is important to use systems that speed up the generation, processing and preparation of documents, as well as improve the storage and retrieval of information. The introduction of cloud technologies has become a necessary condition for increasing the mobility, flexibility and efficiency of the management system of a road construction organization. Formalized processes of information collection and internal distribution can better predict the dynamics of market trends and act more quickly, make decisions confidently and reasonably. In the final stages of selection for assessment, it is convenient to apply the criteria in conditions of interval uncertainty. The study was aimed at improving the efficiency of transport management by developing a model for choosing the cloud software of a road construction organization in terms of interval information. The following criteria of partial optimization were used in the developed model: maximum speed of execution of functions by cloud software; minimum cloud software requirements for internet connection speed; minimum cost of cloud software. The scope of permissible solutions is determined by restrictions:
 – execution of all functions must be provided by cloud software;
 – the minimum speed of execution of functions by the cloud software should be not lower than set;
 – cloud software requirements for Internet connection speed should not exceed the specified;
 – the cost of cloud software should be no more than specified.
 The developed model will reduce the cost of purchasing cloud software and increase the efficiency of transport management of a road construction organization.

Application of intelligently controlled technologies in designing of technological processes for explosive forming of shell parts

The object of research is the processes of pulse metalworking (hydroexplosive, magnetic pulse, electrohydraulic, gas detonation forming, etc.). Among these methods of forming for the production of aircrafts engines parts from cylindrical and conical blanks, the most efficient in terms of its energy capabilities and overall dimensions is explosive. The modern level of theory and practice of metal forming processes allows, on the basis of a systematic approach and control theory, to determine the optimal parameters of plastic forming processes, select the best technical solutions, and create a precondition for the transition to complex automation. The most difficult task of metals forming methods optimizing is to find the best solution among many potentially possible ones, considering the introduced restrictions and efficiency criteria, environmental, economic, technical, ergonomic, and other requirements. The most problematic is that it is impossible to optimize the process of forming post-factum (finishing works, elimination of defects in shape and size, welding of cracks, etc. are required), therefore, when solving optimization problems, the implementation of the feedback principle is required - comparison of the value of the controlled variable, determined by the control program, with the desired value. In general, the processes of metal forming by pressure are characterized by a variety of problems of the theory of optimal control, the solution of which is carried out by methods of mathematical programming. And, although the equipment for pulse processing can have a different design, it necessarily includes structural elements that make it possible to convert the energy of the source and with its help (through the action of a solid body, transmitting medium, or field) to deform the metal of the workpiece. Due to this, in this work, it is proposed to control the quality of the obtained parts by varying the degree of deformation of the workpiece in the process of forming. The result of the work is the development of an integrated intelligent system, with the help of which it is possible to carry out the computer-aided design of almost all pulse-action processes based on the intelligent selection of suitable forming parameters.

Innovative Control of the Development of an Ergatic Electric Power System Based on Fuzzy Logic

This article deals with the search for a palliative optimal solution to the optimization of the electric power problem. A mathematical model of planning by the development of a hierarchical ergatic electric power system is proposed to be presented as an optimization problem of minimizing vectors. An innovative direction in modeling the control system of an ergatic electric power system based on artificial neural networks is also considered. It is noted that intelligent control systems for power supply systems are robust. The innovative concept of a smart power system is due to the integration into a hierarchical power system of renewable energy sources based on modern computer technologies. It is noted that during the operation of an intelligent electric power system, control systems must provide adaptive qualities in relation to the topology of the power supply system. It is proposed to investigate the solution to the optimization of electric power problems using methods of fuzzy mathematical programming.

Optimal Allocation and Scale Operation of Agricultural Machinery Based on Mathematical Planning Method

Background: To study the application of the mathematical programming method in agricultural machinery operation optimal allocation and scale management, this paper adopts the nonlinear programming method to establish the relevant mathematical model. Methodology: This paper investigates the crop planting area, mechanization level, and agronomic direction requirements, production situation, and technological process of corn planting mode. Results: The structure of agricultural machinery equipment is relatively reasonable, and the production efficiency is high. In the whole process of corn production, 11.195 million yuan of maize production value was optimized. The proper harvest time of corn was 5 days, the planting time of wheat was 26 days, and the harvest time of wheat was 10 days. Conclusion: The optimal allocation quantity of agricultural machinery system is calculated by lingo software, and the mathematical model is established by combining non-linear programming.

Flow modeling of high-viscosity fluids in pipeline infrastructure of oil and gas enterprises

Today, the issues related to solving the problem of finding an effective distribution of oil flows through the system of oil pipelines in order to reduce the total energy consumption are relevant. The solution to this problem is connected with selection of rational pumping modes for various technological sections of oil pipelines using modern methods of mathematical programming or new techniques for improving the energy and transport characteristics of oil.Reducing energy consumption during pumping of crude through oil trunk pipelines can be achieved by various methods. Numerous investigations in this direction are mainly carried out to save energy on separate single-line pipelines. However, due to the development of the network of trunk oil pipelines in the world over the past decades, the issues of energy efficient management of oil flows throughout the entire oil pipeline system of oil and gas enterprises become urgent.This paper analyses parameters for pipeline transport of high-viscosity and heavy oils. The article proposes a method for assessing the rheological properties of oil for further planning of pumping taking into account the preservation of oil quality and an increase in energy and transport characteristics. The proposed solutions and tasks for predicting changes in the viscosity-temperature characteristics of the flow for blends of different oil types are especially relevant in the current conditions of an increase in the share of oil production with complex rheological characteristics. Results of the presented investigations may be used for planning the measures of efficient transportation of high-viscosity and heavy oils.

A decision support model for handling customer orders in business chain

One of the elements of the modern trade and services market is a business chain solution (chain store/retail chain). An example of a business chain is, e.g., a restaurant chain, where each restaurant in the chain has the same decor, organization, menu, and delivery method. Although such solutions have been known for decades, the rapid development of IT technology, the widespread access to the Internet as well as the development of mobile technologies have changed and modernized their formula. Many customers place orders remotely with the option of delivery to their door. This method of ordering and fulfilling orders is becoming more and more popular and ever more common in the recent period due to the pandemic and the resulting restrictions and limitations on the functioning of trade and services. The following key questions arise in relation to customer order processing for chain business managers: How to allocate individual customer orders to selected branches so that the cost of their processing (production and delivery) is the lowest?, How to deliver on time?, etc. To answer these questions, a decision support model has been developed, which combines routing, allocation and planning problems for restaurant/store chains. Two ways to implement the model have been proposed. The first one uses the methods of mathematical modeling and programming, and the other, which is a proprietary approach that integrates the mechanisms of evolution (specialized representations, repair mechanisms, genetic operators, etc.), uses constraint logic programming and dedicated heuristics. In addition, procedures for constraint handling and presolving have been developed.

Experimental simulation and a reliable calibration method of rockfill microscopic parameters by considering flexible boundary

The discrete element method (DEM) is an important method to study the mechanical properties of rockfill materials, in which model parameters are critical to the accuracy of simulation results. This paper presented a reliable calibration method considering a flexible boundary to calibrate the microscopic parameters in the DEM. Firstly, the sensitivity of microscopic parameters to macroscopic responses was analyzed through the orthogonal test to narrow down the value ranges of microscopic parameters. Secondly, the nonlinear relationship between macroscopic responses and microscopic parameters was obtained using the response surface method (RSM). Thirdly, the optimal solution was derived by applying the mathematical programming method to obtain the specific microscopic parameters. Finally, the calibrated macroscopic parameters were used to study rockfill materials' micro- and macro- mechanical behaviors under different confining pressure conditions. It was showed that DEM can accurately simulate the rockfill compression process, and the parameter calibration method is reliable.

Research of Methods of Optimal Design of Special Electric Drives

Problems of optimization of special electrical and electromechanical systems in modeling, creation and design are solved mainly by methods of mathematical programming. The task of mathematical programming is to find extremes of the function of many variables in the presence of restrictions on variables, which creates fundamental difficulties. To solve such problems, the number of methods for solving the general problem of mathematical programming is currently expanding significantly. In this regard, the trend in the development of mathematical programming is following the path of highlighting and studying various subclasses of problems. The use of certain specific features of the tasks of the selected subclass creates opportunities for their more effective investigation and solution. Examples of such subclasses give convex, quadratic, linear programming problems, transport-type problems, and others. Geometric programming is also a section of mathematical programming that research a certain class of optimization problems. However, when using geometric programming, you have to apply linear, nonlinear programming, the concept of convex programming. Using optimization methods will allow you to correctly investigate, design and create special electric drives.

Акустический сенсор для оценки состояния производственного оборудования

An important trend in the development of industry is the development of digital models of industrial facilities, the work of which is based on information coming from sensors. This allows you to optimize functionality, predict the technical condition of objects, which is especially important, for example, in the field of metallurgical production, where forced stops are accompanied by huge losses. The sensors themselves are also modeling objects, because they need to adapt to rigid production conditions in which their own shortcomings are manifested, while the correct introduction of corrections for environmental conditions, diagnostics and self-diagnostics, which are impossible without building various types of sensor models, is important. The purpose of the work is to deve¬lop a universal discrete model of an acoustic sensor suitable for receiving and emitting acoustic signals. Methods. The work used methods of classical mechanics and mathematics, vibration theory, generalized functions, distributed systems, and mathematical programming methods were used to provide calculations. Results. The main result is a universal discrete model of a sensor with a working element in the form of a round plate, which by choosing parameters can be transformed into a model of a unidirectional dynamic microphone with a flat membrane or a radiator with a focusing spherical element. It is shown that on the basis of the model it is possible to synthesize narrow-directional radiation diagrams and thereby obtain the necessary spatial selectivity and noise immunity of measurements. Conclusion. Calculations made using the proposed model correspond to the known results of acoustics. Verification of the discrete model using a natural sample showed a high accuracy in determining the resonant frequencies and forms of oscillation of the sensor.