Nonlinear Programming Method Research Articles

The Method for Distribution of Aircrafts of Joint Aviation Groups Depending on Importance of Targets and Probability of their Defeat

This study considers the approach for the distribution of a limited number of combat means - unmanned aerial vehicles during preparation for their application at objects (targets) of impact, taking into account the importance of targets and the state of their protection (probability of defeat). The approach is based on one of the non-linear programming methods, but is reduced to an algorithm available for practical use among practitioners who prepare data for decision making in headquarters, control points, support services. It is noted that such an approach can be useful in case of limited quantity of combat means, when there is a need to direct them primarily to priority targets for implementing a general ultimate task set by the highest authority. It is shown that the proposed approach can be extended to the distribution of any material and technical resources, with importance of the limited amount of resource, the priority of resource distribution objects and the resource provision level of these objects at the time of decision on distribution. Technically, unmanned aerial vehicles control, distribution of unmanned aerial vehicles to objects (targets) is carried out by UAV operators. Keywords— Maximal element method, objects of impact, objective function, distribution algorithm, optimization process.

A novel mathematical model for integrating the hydrogen network of refinery with compressor allocation considered

The allocation and cost of compressors have significant influence on hydrogen network. A novel mixed integer nonlinear programming method is proposed for optimizing hydrogen network with the allocation of compressors considered. This model considers the streams compressed stage by stage with multiple compressors and all possible compression paths. The compression power cost of multiple compressors is deduced to optimize the number of compressors in each compression process. The trade-off between the power loss and capital cost of compression is analyzed for different compression paths. The superstructure and mathematical model are built to optimize the hydrogen network in terms of minimizing the total annual cost. The proposed model is flexible and efficient. Three literature cases are studied by the proposed method, and the optimal flowsheets are identified. Compared with previous methods, the computing time is significantly reduced and the total cost of compressors is reduced by 3.38%–8.46%.

On the exactness of the ε-constraint method for biobjective nonlinear integer programming

The ε-constraint method is a well-known scalarization technique used for multiobjective optimization. We explore how to properly define the step size parameter of the method in order to guarantee its exactness when dealing with biobjective nonlinear integer problems. Under specific assumptions, we prove that the number of subproblems that the method needs to address to detect the complete Pareto front is finite. We report numerical results on portfolio optimization instances built on real-world data and show a comparison with an existing criterion space algorithm.

Selected Mathematical Optimization Methods for Solving Problems of Engineering Practice

Engineering optimization is the subject of interest for many scientific research teams on a global scale; it is a part of today’s mathematical modelling and control of processes and systems. The attention in this article is focused on optimization modelling of technological processes of surface treatment. To date, a multitude of articles are devoted to the applications of mathematical optimization methods to control technological processes, but the situation is different for surface treatment processes, especially for anodizing. We perceive their lack more, so this state has stimulated our interest, and the article contributes to filling the gap in scientific research in this area. The article deals with the application of non-linear programming (NLP) methods to optimise the process of anodic oxidation of aluminium using MATLAB toolboxes. The implementation of optimization methods is illustrated by solving a specific problem from engineering practice. The novelty of this article lies in the selection of effective approaches to the statement of optimal process conditions for anodizing. To solve this complex problem, a solving strategy based on the design of experiments approach (for five factors), exploratory data analysis, confirmatory analysis, and optimization modelling is proposed. The original results have been obtained through the experiment (performed by using the DOE approach), statistical analysis, and optimization procedure. The main contribution of this study is the developed mathematical-statistical computational (MSC) model predicting the thickness of the resulting aluminium anodic oxide layer (AOL). Based on the MSC model, the main goal has been achieved—the statement of optimal values of factors acting during the anodizing process to achieve the thickness of the protective layer required by clients, namely, for 5, 7, 10, and 15 [μm].

Hybrid methods for reservoir operation rule curve determination considering uncertain future condition

In this research, simple and practical methods have been proposed to determine the reservoir operation rule curves considering uncertain water inflow values at future conditions based on the concept of comparative reservoirs management. For this purpose, two methods are proposed. In the first method named His-Inf, by considering the historical water inflow values, a mathematical optimization model is proposed for defining the reservoir operation rule curves determination problem and solved using nonlinear programming (NLP) method. However, in the second method, three different approaches named Pre-Inf1, Pre-Inf2 and Pre-Inf3 are proposed. In the Pre-Inf1 method, at first, water inflow values into the dam reservoir are predicted using neural network (ANN) model. Then, the predicted water inflow values are used to determine and update the reservoir operation rule curves using NLP method. In the Pre-Inf2 method, the ANN model is used to simulate and update the constant coefficients of the reservoir operation rule curves considering the water demand, water inflow values into the reservoir, water release values form reservoir and time index (T) as data set. For this purpose, two different framework and structure are proposed for sorting and providing data set leading to two different cases. Finally, in the Pre-Inf3 method, at first, water inflow values, reservoir storage volumes, water demand values and time index (T) are used to simulate and predict water releases values from the reservoir. Then, the linear regression method is used to determine the reservoir operation rule curves and policies. Here, both static and dynamic ANN models are used for simulating and predicting the water inflow values and reservoir operation rule curves and policies. In order to investigate the performance of proposed methods, here, the Sefidrood dam reservoir is considered as a case study in which it is located at the intersection of the QezelOzan River and Shahroud River near the city of Manjil in the north of Iran. Finally, the obtained results are presented and compared by calculating the reliability, residency, vulnerability and sustainability indexes. Comparison of the result indicates the superiority of the proposed Pre-Inf3 method for determining the reservoir operation rule curves at uncertain future condition in which the results of the His-Inf, Pre-Inf1 and Pre-Inf2 methods are almost similar. In other words, the sustainability index of His-Inf, Pre-Inf1, Pre-Inf2 and Pre-Inf3 are 63%, 63%, 63% and 74%, respectively, in which the corresponding value of Pre-Inf3 is 17.5% bigger than other proposed methods.

A Smoothing SAA Method for Solving a Nonconvex Multisource Supply Chain Stochastic Optimization Model

We construct a new multisource supply chain stochastic optimization model when the supply and demand are both uncertain. This model is nonconvex because the decision variables are truncated by the random variable in the objective function. It is a common technical challenge encountered in many operations management models. To address this challenge, we adopt a novel transformation technique to transform the nonconvex problem into an equivalent convex optimization problem. Then, we provide a smoothing sample average approximation (SAA) method to solve the transformed problem. The SAA model is a good approximation for the expected value function in the objective function when the number of samples is large enough. The smoothing technique can transfer the nonsmooth plus function into a smoothing function in the model, and thus, we can use the numerical methods for the common nonlinear integer programming to solve the transformed model. Numerical tests verify the effectiveness of the new model and the smoothing SAA method.

Data-Driven Dynamic Neural Programming for Network Media Nonlinear Visual Communication Design

As network media data gradually enters the field of visual communication design as information, more scholars have begun to rationally study the relationship between visual communication and network media. This paper mainly studies how to use data-driven nonlinear dynamic neural programming method to realize visual communication design in network media environment. The study constructs a network media visual communication design system from three aspects: data-driven, design process realization, and system flow establishment. The network media visual communication design is realized through the five process stages of data: analysis, definition, integration, visual presentation, and rendering. Based on the optimal control of visual communication design, the evaluation of visual communication realization and the dissemination of visual communication information are further analyzed, and the following three conclusions are drawn: firstly, each factor does not exist alone; they influence each other. The system digs out the association rules of different factors that affect the visual communication design under the standard of 10% support and 85% confidence; secondly, comparison of the output value of the system with the real output value of the object is found that they are very close, which shows that the dynamic neural programming method is more complex and nonlinear. Finally, through the simulation of the relationship between the continuous dissemination of information and the number of tourists, on the first day, there was the first burst of new customers. The first outbreak occurred on the fifth day of the first week. In the first month, as the number of tourists increased, the dissemination of tourist information by tourists also gradually increased. This fully shows that there is always a long-term relationship between information dissemination and audiences.

Stochastic coordination of the wind and solar energy using energy storage system based on real-time pricing

In this paper, stochastic synchronization of the wind and solar energy using energy storage system based on real-time pricing in the day-ahead market along with taking advantage of the potential of demand response programming has been analyzed. Since renewable energies, loads and prices are uncertain, and planning is based on real-time pricing, the optimal biding proposition considers the wind power, solar system, and energy storage system. Uncertainty is addressed to solve the bidding strategy in a day-ahead market for optimal wind and PV power and optimal charging for energy storage. Batteries are the most promising device to compensate for the fluctuations of wind and photovoltaic power plants to mitigate their uncertainty. In general, using MILP is a suitable approach to address uncertainty as long as a linear formulation is acceptable for modeling either with continuous variables or integer ones. By setting some scenarios to formulate market prices, imbalance of energy, wind and solar system, the uncertainty problems could be easily solved by MILP solver. The model created enables the retailer to realize the potentials of the demand response program and exploit high technical and economic advantages. To ensure fair prices, a set of regulating constraints is considered for sales prices imposed by the regulation committees. A model is presented to optimize the electricity trading strategy in the electricity market, considering the uncertainty in the wholesale market price and the demand level. The retailer considered in this paper is a distribution company that is the owner and operator of the networks and operates under real-time pricing regulations. To model demand response, the elasticity coefficient is used. The proposed solution is implemented on a standard 144-bus sample network using a nonlinear integer programming method. The presented method results provide helpful and valuable information based on the optimal method proposed by the retailers considering the demand response program and real-time pricing system.

A 1D linearization–based MILP–NLP method for short-term hydrothermal operation

Abstract The scheduling and optimization of short-term hydrothermal operation utilize the water resources efficiently and magnify the benefits of hydro energy while reducing the fuel and operation cost of thermal power plants. Short-term hydrothermal operation is a complex non-linear and non-convex optimization problem, which reflects thermal valve point effects, load balances, generation bounds and water transport delay. It is highly important and significant to figure out these problems to maximize the benefits of hydrothermal joint operation for energy saving, emission reduction and efficient resources management. This article presents a 1D linearization technique to deal with the non-linear function of two variables, a combined mixed-integer linear programming (MILP) and non-linear programming (NLP) method to solve this problem. The applied method introduces integer variables to linearize the original model into a MILP one; the solution by MILP is then corrected and re-optimized to formulate a feasible solution to warm start NLP. The 1D linearization method is efficient for MILP as it avoids the coupled relationships of integer variables, and the NLP local search is used to correct the influence of linearization errors and search further. The case studies show that the result derived by the 1D linearization–based MILP–NLP method is superior to that of previous works. The method is tested with different linearization accuracy, and the results demonstrate that the method is stable. The presented technique is promising for real-world hydrothermal operation and related problems.

Multi-objective robust energy management for environment powered unmanned surface vehicles

The environment powered unmanned surface vehicle (EPUSV) is capable of achieving large-range and long-term marine operations by harvesting abundant environment energy. However, considering the intermittency of environment energy, limitation on battery capacity and varieties of loads, it is necessary to control and coordinate the electric devices of EPUSV to exploit energy efficiently. To address this issue, an optimization-based energy management strategy (EMS) is proposed in this paper to achieve optimal management for the devices of EPUSV. The operation constraints and relevant objectives of different types of devices are firstly modeled through mix-integer nonlinear programming (MINLP) method. The uncertainty parameters in the model are addressed by robust optimization method. Then various task modes are defined based on the preference for different objectives. Simulations indicate that the proposed method is able to achieve optimal scheduling for each device while satisfying the underlying operation constraints. Besides, the adaptability for different kinds of tasks and the robustness to the fluctuation of uncertainty parameters of the proposed EMS is analyzed and discussed.

Methodology for Rationalising the Distribution of Limited Material Resources Considering the Importance and Initial Adequate Supply of Facilities

The organisation of resource support for the needs of the Armed Forces of Ukraine is an important daily task related to the distribution of material resources for their intended purpose. If there is a sufficient resource base and the factors of time, speed, and priority of delivery of funds are secondary, resource support is carried out according to the principles “if necessary” and “if possible”. However, the practices of resource support for the needs of the Armed Forces of Ukraine considering the limited resource capabilities of the national economy and other similar tasks, as a rule, demonstrates the necessity of acting in the conditions of quantitative and qualitative restrictions of the resource base. Moreover, in the conditions of requirements for reducing the time of implementation of resource support, considering the priority of resource assignment objects and different levels of their initial resource provision. The purpose of this study is to find the best, rational, and even optimal distribution of resources for certain characteristics in three types of business conditions: certainty, uncertainty, and risk in managerial decision-making. Based on the analysis of available methods of nonlinear programming in distribution problems, proceeding from the condition of maintaining mathematical correctness and accessibility to practical use, the study presents the procedure for applying the maximum element method. The proposed approach to optimising the distribution problem is considered on the example of possible distribution options for equally efficient resource supply between the resource supply facilities. The options differ in the values of the importance of objects and the levels of initial supply in relative units at the time of decision-making on the allocation of resources upon providing resources for a certain final management task. The methodology of this study can be used in planning and decision-making related to the distribution of resources in organisational systems of military and civil administration, considering the importance and initial state of adequate supply of destination facilities in case of limited capabilities of the resource manager

Evaluation of energy efficiency of wastewater treatment plants: The influence of the technology and aging factors

Wastewater treatment is an energy-intensive process and therefore, improving the energy efficiency of wastewater treatment plants (WWTPs) is relevant from an economic and environmental perspective. Water companies managing WWTPs operate under monopolistic conditions and thus, benchmarking their performance using robust methods is fundamental for regulation. This study evaluates the energy efficiency of a sample of Chilean WWTPs using a newly developed technique, called stochastic non-parametric envelopment of data (StoNED). This technique integrates non-parametric (non-linear programming) methods with stochastic noise (parametric techniques) and therefore, it overcomes the limitations of both methodological approaches. Moreover, it allows exploring the influence of operating environment on the energy performance of WWTPs. Results evidenced that the Chilean WWTPs were considerably inefficient (average score was 0.433) presenting therefore significant opportunities to save energy (average savings were 203,413 MWh/year). Only 8 out of 203 facilities reported an average energy efficiency score which was greater than 0.81. It was also found that the age of the facilities negatively affected energy efficiency. Recently built WWTPs showed an average energy efficiency score of 0.489, whereas older facilities were found to be considerably inefficient, 0.340 on average. WWTPs using suspended-growth processes, i.e., conventional activated sludge and extended aeration, as secondary treatment were those with the lowest levels of energy efficiency on average. The results and conclusions of this study are useful for policy makers and WWTP operators who want to reduce energy consumption of WWTPs and therefore, their operational costs and environmental impacts.

Optimal dispatch for reversible solid oxide cell-based hydrogen/electric vehicle aggregator via stimuli-responsive charging decision estimation

The ongoing growth of green vehicles had led to an increase in demand of cost-effective and driver-satisfactory hydrogen/electric vehicle aggregators (HEVAs). However, existing approaches for cost minimization of HEVA can lead to poor performance due to the inaccurate modelling of power–gas exchange system and neglection of schedulable characteristics of loads. Furthermore, the behaviour of drivers was rarely considered from a psychological perspective. To resolve these limitations, the optimal dispatch scheme of HEVA, equipped with reversible solid oxide cell (rSOC), is investigated by quantifying drivers’ charging decision response toward pricing stimuli. As the core of the bi-directional energy conversion, rSOC is modelled by considering the climbing power constraints and time-dependent restart-up cost. At the driver side, EVs are aggregated as clusters for efficient computation. Two charging modes are designed for drivers with incentive discounts. To measure the relationship between external factors and charging decision response, the stimuli-responsive charging decision estimation is proposed by introducing Weber–Fechner law (W–F Law). To minimum operation cost, a mixed integer nonlinear programming (MINP) method is presented. The results validate that the operation cost of HEVA can be decreased by 19.37%, and the maximum utilization of energy is realised in the proposed scheme. Additionally, the impacts of sizes of power–gas exchange devices are investigated for practical reference. Under a given charging demand, the proposed dispatch scheme can realise installation of smaller devices, and thereby, resulting in lower construction cost.

Evaluation of Correlation Between Surface Diaphragm Electromyography and Airflow Using Fixed Sample Entropy in Healthy Subjects.

In clinic, the acquisition of airflow with nasal prongs, masks, thermistor to monitor respiratory function is more uncomfortable and inconvenience than surface diaphragm electromyography (EMGdi) using electrode pads. The EMGdi with strong electrocardiograph (ECG) interference affect the extraction of its characteristic information. In this work, surface EMGdi and airflow signals of 20 subjects were collected under 5 incremental inspiratory threshold loading protocols from quiet breathing to maximum forced breathing. First, we filtered out the ECG interference in EMGdi based on the combination of stationary wavelet transform and the positioning of ECG to obtain pure EMGdi (EMGdip). Second, the Spearman's rank correlation coefficients between EMGdi and EMGdip quantified by time series fixed sample entropy (fSampEn), root mean square (RMS), and envelope were compared to verify the robustness of the fSampEn to ECG. A comparative analysis of correlation between fSampEn of EMGdi and inspiratory airflow and the correlation between envelope of EMGdip (EMGdie) and inspiratory airflow found that there was no significant difference between the two, indicating the feasibility of using fSampEn to predict airflow. Moreover, fSampEn of EMGdi was used as characteristic parameter to build a quantitative relationship with the airflow by polynomial regression analysis. Mean coefficient of determination of all subjects in any breathing state is greater than 0.88. Finally, nonlinear programming method was used to solve a universal fitting coefficient between fSampEn of EMGdi and airflow for each subject to further evaluate the possibility of using surface EMGdi to monitor and control respiratory activity.

ОПТИМАЛЬНЕ ТРАСУВАННЯ ТРАЄКТОРІЙ ГЛИБОКИХ СВЕРДЛОВИН МЕТОДАМИ НЕЛІНІЙНОГО ПРОГРАМУВАННЯ

The issues of rational (optimal) trajectory trajectory of oil and gas wells are apparently one of the few areas of the oil and gas industry that still does not use optimal control and nonlinear programming methods. 133 At the same time, the use of these methods makes it possible to design smoother and shorter trajectories with less risk of emergency situations occurring in them, leading to resonant vibrations of the system, buckling of the drill string and its sticking. In addition, in such columns, the conditions for the hydrodynamic and aerodynamic flow of the working fluid are improved, and the likelihood of the formation of blood clots and plugs is reduced. In this paper, a new approach for the optimal design of curved well trajectories based on the application of the anti-gradient descent method is proposed, resolving equations are formulated, algorithms for their solution are developed, a practical example is considered, and it is shown that solving this problem leads to a decrease in the total curvature of the well and its length. KEYWORDS: DEEP BOREHOLE, BOREHOLE TRAJECTORY OPTIMIZATION, ANTIGRADIENT RUNING METHOD, OBJECTIVE FUNCTIONS, NONLINEAR PROGRAMMING.

Linear and nonlinear shelf space allocation problemswith vertical and horizontal bands

Aim/purpose – Shelf space is one of the most important tools for attracting customers’ attention in a retail store. This paper aims to develop a practical shelf space allocation model with visible vertical and horizontal categories. and formulate it in linear and non- -linear forms. Design/methodology/approach – The research is mainly based on operational research. Simulation, mathematical optimization, and linear and nonlinear programming methods are mainly used. Special attention is given to the decision variables and constraints. Changing the dimensioning of the decision variables results in an improvement in the formulation of the problem, which in turn allows for obtaining an optimal solution. Findings – A comparison of the developed shelf space allocation models with visible vertical and horizontal categories in linear and nonlinear forms is presented. The compu- tational experiments were performed with the help of CPLEX solver, which shows that the optimal solution of the linear problem formulation was obtained within a couple of seconds. However, a nonlinear form of this problem found the optimal solution only in 19 out of 45 instances. An increase in the time limits slightly improves the performance of the solutions of the nonlinear form. Research implications/limitations – The main implication of research results for sci- ence is related to the possibility of determining an optimal solution to the initially formu- lated nonlinear shelf space allocation problem. The main implication for practice is to take into consideration the practical constraints based on customers’ requirements. The main limitations are the lack of storage conditions and holding time constraints. Originality/value/contribution – The main contribution is related to developing math- ematical models that consider simultaneous categorization of products vertically, based on one characteristic, and horizontally, based on another characteristic. Contribution is also related to extending the shelf space allocation theory with the shelf space allocation problem model in relation to four sets of constraints: shelf constraints, product con- straints, orientation constraints, and band constraints. Keywords: Retailing, decision making/process, merchandising, shelf space allocation, planogram. JEL Classification: C61, L81.

Optimization of Data Distributed Network System under Uncertainty

The major network design or data distributed problems may be described as constrained optimization problems. Constrained optimization problems include restrictions imposed by the system designers. These limitations are basically due to the system design’s physical limitations or functional requirements of the network system. Constrained optimization is a computationally challenging job whenever the constraints/limitations are nonlinear and nonconvex. Furthermore, nonlinear programming methods can easily deal same optimization problem if somehow the constraints are nonlinear and convex. In this paper, we have addressed a distributed network design problem involving uncertainty that transmits data across a parallel router. This distributed network design problem is a Jackson open‐type network design problem that has been formulated based on the M/M/1 queueing system. Because our network design problem is a nonlinear, convex optimization problem, we have employed a well‐known Kuhn–Tucker (K‐T) optimality algorithm to solve the same. Here, we have used triangular fuzzy numbers to express uncertain traffic rates and data processing rates. Then, by applying α‐level interval of fuzzy numbers and their corresponding parametric representation of α‐level intervals, the associated network design problem has been transformed to its parametric form and later has been solved. To obtain the optimal data stream rate in terms of interval and to illustrate the applicability of the entire approach, a hypothetical numerical example has been exhibited. Finally, the most important results have been reported.

Bridging the Gap between Trust–Region Methods (TRMs) and Linesearch Based Methods (LBMs) for Nonlinear Programming: Quadratic Sub–Problems

Bridging the Gap between Trust–Region Methods (TRMs) and Linesearch Based Methods (LBMs) for Nonlinear Programming: Quadratic Sub–Problems

МЕТОДИКА СИНТЕЗУ РОЗВІДУВАЛЬНО-ВОГНЕВИХ СИСТЕМ

The article proposes an algorithm for the synthesis of reconnaissance and fire systems. Which allows you to justify the need for weapons samples for the completion of subsystems of fire damage and reconnaissance of the specified systems. The essence of the algorithm is to organize the stages of determining the need for weapons samples to ensure the effective functioning of reconnaissance and fire systems. The advantage of the algorithm is that it allows you to take into account the stability of functioning and the capabilities of each type of weapon based on the tasks that rely on the reconnaissance and fire system. This ensures the optimal distribution of weapons and prevents overspending of resources. At the same time, the algorithm is universal and ensures work with all types of means of fire damage and reconnaissance that are in service in the missile forces and artillery of the Armed Forces of Ukraine, taking into account those that are being modernized or developed, as well as those that come as aid from Western countries - partners. In addition to the fact that the proposed algorithm determines the need for weapons when creating new reconnaissance and fire systems, taking into account the given degree of task performance, it also allows determining the degree of performance of assigned tasks, taking into account the available forces and means. The algorithm is based on an improved method of nonlinear programming (two functions), which allows you to take into account both the heterogeneity of types of weapons and military equipment, and the heterogeneity of targets. The improvement consists in determining the "weight" of the types of fire weapons depending on the "weight" of the targets to be hit they are involved. And in the future, normalized fractions of this "weight" are used as weighting coefficients. This makes it possible to justify the need for weapons samples taking into account the given level of performance of the assigned tasks. The defined algorithm allows taking into account the nonlinearity of the functions that describe different types of weapons and targets.

Reliability optimization using hybrid genetic and particle swarm optimization algorithm

Redundancy-allocation problem i.e. RAP is among the reliability optimization problems which make use of non-linear programming method to improve the reliability of complex system. The objective of this research paper is reliability optimization through the application of Genetic Algorithm i.e. GA and Hybrid Genetic & Particle Swarm Optimization (H-GAPSO) on a RAP. Certain shortcomings have been seen when results are obtained by application of single algorithms. In order to get rid of these shortcomings, HGA-PSO is introduced where attractive properties of GA and PSO are combined. This hybrid method makes use of iterative process of GA after obtaining initial best population from PSO. Comparative Analysis of results of GA and H-GAPSO is done with respect to reliability and computation (CPU) time and it is observed that H-GAPSO improved system reliability up to maximum by 63.10%. MATLprogramming has been used for computation of results from GA and HGA-PSO algorithms.