Optimization Of Multiple Variables Research Articles

Utilization of Multivariate Optimization for Preconcentration and Determination of Lead in Different Water and Food Samples Using Functionalized Activated Carbon

In this study, apricot-pit-based activated carbon was functionalized and used as a sorbent for the preconcentration of lead (Pb2+) in different water and food samples. The activated sorbent was modified with ethylenediaminetetraacetic acid (EDTA) to enhance its selectivity for the efficient removal of Pb2+ ions. The modified activated sorbent was characterized using FTIR, an SEM, BET, and TGA. The column adsorption method was used to study the adsorption capacity of synthesized and modified activated carbon and analyzed using atomic absorption spectrophotometry. A multivariate procedure, i.e., Plackett–Burman design (PBD) and central composite design (CCD), was studied for optimizing the adsorption process, which allows the optimization of multiple variables at the same time. An interference study was conducted to ascertain the selectivity of the developed method. The developed method was validated by assessing certified reference materials and additional standards for Pb2+ detection in real samples. To assess the precision of the proposed procedure, repeatability (RSDr) and reproducibility (RSDR) were calculated, which were determined to be <3.0 (n = 7) and <7.5 (n = 15), respectively. The obtained results revealed that the modified AC is a suitable and efficient sorbent for the preconcentration of Pb2+ in real water and food samples.

An efficient and random synthesis method for mass exchange networks with multi-component using a node-based vertical non-structural model

Mass exchange network (MEN) synthesis is an important technique to ensure efficient purification of industrial waste gas sources and water streams. However, most existing models for MEN synthesis are not capable of dealing with multi-component problems and achieving optimal designs. In this study, an innovative process integration strategy based on a node-based vertical non-structural model (NV-NSM) is proposed. The developed strategy allows for a more random representation of process configuration and aids in handling both single- and multi-component problems. The NV-NSM arranges several groups of main nodes in the process streams and the sub-nodes in their branches and results in design configurations by connecting any two sub-nodes on the rich and lean streams at the same main node number. When dealing with multi-component synthesis, the number of tray column is directly optimized to balance the mass transfer needs of different components. As part of the current investigation, the random walk algorithm with compulsive evolution (RWCE) is established to realize the simultaneous optimization of multiple variables, including the mass transfer loads, the number of trays, the stream split ratios, and the flowrates of lean streams. Furthermore, the fine-search strategy based on the RWCE is applied to improve global and local optimization performance. Finally, the proposed method is applied to four MEN cases featuring different exchanger specifications and considering both single and multiple components. The implementation and analysis result in more optimal solutions compared to those published in the literature, demonstrating the feasibility and effectiveness of the proposed method in analyzing and evaluating different MEN problems, including multi-component ones.

Optimización simultánea de variables operativas y de diseño de una celda de iones de litio para procesos simples de carga y descarga

En este trabajo se resumen los principales resultados obtenidos de la aplicación de un modelo fenomenológico de celda de iones de litio en diferentes esquemas de optimización mediante un enfoque de programación matemática. Durante los procesos de carga y descarga de una batería de iones de litio se dan diferentes fenómenos, además, mientras que el proceso de carga se puede predefinir y controlar, los procesos de descarga están sujetos al perfil demandado por determinada aplicación. Debido a esto, se distinguen los esquemas de optimización para cada uno de estos procesos, y a su vez, cada esquema (o problema de optimización) se diferencia principalmente por la función objetivo. Para el proceso de descarga se propone maximizar la energía específica total para un conjunto de valores de tiempo de descarga dados con el objetivo de relacionar energía y potencia entregadas. Para el proceso de carga se consideran tres objetivos distintos basados en los requerimientos de aplicaciones reales; estos son: minimización del tiempo de carga, maximización de la capacidad de carga y minimización de la energía consumida. En ambos esquemas generales (carga y descarga) se plantea la optimización del diseño de celda en diferentes condiciones operativas. Por lo tanto, el enfoque propuesto permite la optimización simultánea de múltiples variables y se obtienen mejoras considerables no sólo en los objetivos evaluados sino también en el desempeño global del sistema.

Input-Decoupled Q-Learning for Optimal Control

A design of optimal controllers based on a reinforcement learning method called Q-Learning is presented. Central to Q-Learning is the Q-function which is a function of the state and all input variables. This paper shows that decoupled-in-the-inputs Q-functions exist, and can be used to find the optimal controllers for each input individually. The method thus converts a multiple-variable optimization problem into much simpler single-variable optimization problems while achieving optimality. An explicit model of the system is not required to learn these decoupled Q-functions, but rather the method relies on the ability to probe the system and observe its state transition. Derived within the framework of modern control theory, the method is applicable to both linear and non-linear systems.

Simultaneous determination and validation of emtricitabine, rilpivirine and tenofovir from biological samples using LC and CE methods.

A combination of antiretroviral agents is frequently used in effective treatment of the human immunodeficiency virus infection. In this study, two different separation methods are presented for the simultaneous determination of emtricitabine, rilpivirine and tenofovir from raw materials and urine samples. Developed liquid chromatography and capillary electrophoresis methods were thoroughly optimized for high analytical performances. Optimization of multiple variables at the same time by performing a minimum number of experiments was achieved by the Box-Behnken design, which is an experimental design in response surface methodology, in capillary electrophoresis. The results of the experimental design ensure minimum analysis time with well-separated analytes. Separation conditions, such as different stationary phases, pH level, organic modifiers and temperatures in liquid chromatography method, were also optimized. In particular, among stationary phases, the core-shell column especially enhanced the effectiveness of separation in liquid chromatography. Both methods were fully validated and applied to real samples. The main advantage of the developed methods is the separation of the drug combination in a short time with high efficiency and without any time-consuming steps.

Simultaneous optimization of heat transfer and reciprocation intensity for thermal processing of liquid particulate mixtures undergoing reciprocating agitation

Abstract Simultaneous optimization of heat transfer and reciprocation intensity (RI) was carried out for reciprocating agitation thermal processing (RA-TP) of liquid-particulate foods. Heat transfer data under various processing conditions (temperature, frequency, and headspace) and product properties (liquid viscosity, particle concentration, and particle density) during RA-TP were utilized to develop a composite model using quadratic stepwise regression analysis. Heat transfer coefficients were maximized individually and simultaneously with minimal RI using multiple-variable optimization. High RI (37–45 ms − 2 ) was recommended to maximize heat transfer alone, whereas lower RI (16–19 ms − 2 ) was found optimal for simultaneous optimization of heat transfer & RI. Product formulations containing low viscosity liquids filled with 23–27% volume of particles with density of 1130–1350 kg/m 3 were found most desirable for maintaining good quality under RA-TP. Optimal conditions were also reported for applying RA-TP under different operating temperatures, liquid viscosities, particle concentrations and particle densities. Industrial significance Reciprocating agitation of containers is receiving interest from thermal processing industry for enhancing product quality. The aim of this study was to optimize the use of reciprocating agitation thermal processing for processing particulate liquid foods. This study attempts to predict optimal conditions of processing conditions and product compositions for reciprocating agitation thermal processing. Multi-variable optimization based on data from multiple experimental designs is conducted in this study, which will be directly relevant to be used by industry seeking to employ reciprocating agitation thermal processing.

Mean-field-type optimization for demand-supply management under operational constraints in smart grid

The electricity business depends significantly on continuous, cost-effective sources of electricity, the efficient reaction to the demand and storage cost. But the increasing demands and alternative renewable energy sources on the power grid are causing instability and price volatility. Smart grid technology and programs are emerging to address these problems. In this paper we study demand-supply management under operational constraints and outage scheduling. We consider a model of an electricity market in which finite number of suppliers offer electricity. Each supplier has several power plants with different maximum capacity of production and different cost depending on the operational constraints. The response of the market to these offers is the quantities bought from the suppliers. The objective of the market is to satisfy the electricity demand at minimal cost. We develop a theoretical framework for cooperative production strategies between electricity producers. We formulate the problem as an optimal control problem under constraints. Using maximum principle techniques, we provide closed-form expressions of the joint production efforts between the electricity producers. Applying inf-convolution technique to the Hamiltonian we transform the multiple variable optimization problem into a single-variable optimization problem, reducing significantly the curse of dimensionality. In order to capture the random nature of most of the renewable energy sources, we introduce stochastic demand and stochastic production variabilities. We derive closed-form expressions using mean-field-type optimization techniques. The framework is shown to be flexible enough to include both risk-neutral and risk-sensitive behavior of a decision-maker when facing uncertainties.

Control of TAME reactive distillation using Non-Dominated Sorting Genetic Algorithm-II

The control system performs poor in characteristics and even it becomes unstable, if improper values of the controller tuning constants are used. So it becomes necessary to tune the controller parameters to achieve good control performance with the proper choice of tuning constants. Many control problems involve simultaneous optimization of multiple variables that competing with each other. In this paper, the Non-Dominated Sorting Genetic Algorithm-II (NSGA-II) has been successfully applied to optimization of dynamic state of t-amyl-methyl-ether (TAME) reactive distillation process. This paper presents the tuning of Proportional–Integral–Derivative (PID) controllers by minimizing of two objective functions (overshoot and Integral of Absolute Error (IAE)) through the NSGA-II. Results show that genetic algorithm is more suitable method for optimal control of the TAME reactive distillation columns than traditional methods such as Tyreus–Luyben.

Optimal control of amine plant using non-dominated sorting genetic algorithm-II

Many control problems involve simultaneous optimization of multiple variables that competing with each other (such as Integral of Absolute Error (IAE), Overshoot, Undershoot, Response time, and etc). On the other hand, the control system performs poor in characteristics and even it becomes unstable, if improper values of the controller tuning constants are used. So it becomes necessary to tune the controller parameters to achieve good control performance with the proper choice of tuning constants. An optimal control of Amine Plant is studied in this paper utilizing the multiobjective genetic algorithm concept in conjunction of Proportional–Integral–Derivative (PID) controller. This paper presents the tuning of PID controllers by minimizing two objective functions (Overshoot and IAE) through the Non-Dominated Sorting Genetic Algorithm-II (NSGA-II). Numerical results show that NSGA-II based tuning method has excellent ability in optimal control of Amine Plant.

Cell-to-cell mapping method for time-optimal trajectory planning of multiple robot arm systems

This paper presents the results obtained by applying the cell-to-cell mapping method to solve the problem of the time-optimal trajectory planning for coordinated multiple robotic arms handling a common object along a specified geometric path. Based on the structure of the time-optimal trajectory control law, the continuous dynamic model of multiple arms is first approximated by a discrete and finite cell-to-cell mapping on a two-dimensional cell space over a phase plane. The optimal trajectory and the corresponding control are then determined by using the cell-to-cell mapping and a simple search algorithm. To further improve the computational efficiency and to allow for parallel computation, a hierarchical search algorithm consisting of a multiple-variable optimization on the top level and a number of cell-to-cell searches on the bottom level is proposed and implemented in the paper. Besides its simplicity, another distinguishing feature of the cell-to-cell mapping methods is the generation of all optimal trajectories for a given final state and all possible initial states through a single searching process. For most of the existing trajectory planning methods, the planning process can be started only when both the initial and final states have been specified. The cell-to-cell method can be generalized to any optimal trajectory planning problem for a multiple robotic arms system.

Optimization and Industrial Experimentation

Combines new developments in numerical optimization with statistical and experimental methods. Discusses the use of statistical methods to develop mathematical models; search methods for single-variable and multiple-variable optimization as well as classical and numerical techniques directly applicable in response surface methodology; and procedures for optimizing systems experimentally.

Multiple response surface methods in computer simulation

This paper reviews the application of multiple re sponse surfaces to multiple-variable optimization problems and describes how these techniques may be used in analyzing computer simulation experiments. An example with four response surfaces illustrates the method. In it a simulation of a tank duel is analyzed to determine the values of two independent (input) variables that will optimize four dependent (output) variables simultaneously. The problem examined is that of training battle-tank crews, and the optimization procedure used is based on the Geoffrion-Dyer interactive vector maximal algorithm.