Generalized Reduced Gradient Method Research Articles

Performance Index Model of Main Structure (CASE STUDY IN IPDMIP)

Purpose: This research intends to build a performance index model of main stucture by case study in IPDMIP. Theoretical reference: It is important to evaluate the percentage weights of 6 (six) variables in the Irrigation System Performance Index (ISPI) assessment so that irrigation managers get assessment results close to actual conditions in the field, improving the quality of irrigation system management. Method: The methodology or the main structure model in this study was analyzed by using SEM-PLS software and GRG analysis. The selection of a research location in the Central Authority Irrigation Area was by considering the same data availability as previous research. In this research, the author used the Smart-PLS (Partial Least Square) application to analyze and reduce variables, which were then analyzed again using the GRG (Generalized Reduced Gradient) method to calculate non-linear equations. Result and Conclusion: The result shows that in this equation, there is only 1 (one) variable, 3 (three) dimensions, and 13 (thirteen) indicators analyzed. After analyzing with SEM PLS, followed by GRG (Generalized Reduced Gradient) analysis with the solver in Microsoft Excel, changes in variable weights occur, so the new model equation for the main structure performance index (Y) is 0.348, with structure body dimensions of + 0.492 and door & gear to operate of +0.160. Mud Bags and drain doors apply to the Central Authority. Implication of research: Based on the results of previous research, where the assessment weight of the variable of the main irrigation network (with a weight of 0.744) is greater than the tertiary irrigation network (with a weight of 0.256). Originality/ value: the role of the main irrigation network is more dominant in channeling water from the intake to the tertiary irrigation network. However, previous research has not been completed since the main structure still has a level below it and has not been included in the scope of previous research.

Forecasting of stage-discharge in a non-perennial river using machine learning with gamma test

Knowledge of the stage-discharge rating curve is useful in designing and planning flood warnings; thus, developing a reliable stage-discharge rating curve is a fundamental and crucial component of water resource system engineering. Since the continuous measurement is often impossible, the stage-discharge relationship is generally used in natural streams to estimate discharge. This paper aims to optimize the rating curve using a generalized reduced gradient (GRG) solver and the test the accuracy and applicability of the hybridized linear regression (LR) with other machine learning techniques, namely, linear regression-random subspace (LR-RSS), linear regression-reduced error pruning tree (LR-REPTree), linear regression-support vector machine (LR-SVM) and linear regression-M5 pruned (LR-M5P) models. An application of these hybrid models was performed and test to modeling the Gaula Barrage stage-discharge problem. For this, 12-year historical stage-discharge data were collected and analyzed. The 12-year historical daily flow data (m3/s) and stage (m) from during the monsoon season, i.e., June to October only from 03/06/2007 to 31/10/2018, were used for discharge simulation. The best suitable combination of input variables for LR, LR-RSS, LR-REPTree, LR-SVM, and LR-M5P models was identified and decided using the gamma test. GRG-based rating curve equations were found to be as effective and more accurate as conventional rating curve equations. The outcomes from GRG, LR, LR-RSS, LR-REPTree, LR-SVM, and LR-M5P models were compared to observed values of daily discharge based on Nash Sutcliffe model efficiency coefficient (NSE), Willmott Index of Agreement (d), Kling-Gupta efficiency (KGE), mean absolute error (MAE), mean bias error (MBE), relative bias in percent (RE), root mean square error (RMSE) Pearson correlation coefficient (PCC) and coefficient of determination (R2). The LR-REPTree model (combination 1: NSE = 0.993, d = 0.998, KGE = 0.987, PCC(r) = 0.997, and R2 = 0.994 and minimum value of RMSE = 0.109, MAE = 0.041, MBE = −0.010 and RE = −0.1%; combination 2; NSE = 0.941, d = 0.984, KGE = 0. 923, PCC(r) = 0. 973, and R2 = 0. 947 and minimum value of RMSE = 0. 331, MAE = 0.143, MBE = −0.089 and RE = −0.9%) performed superior to the GRG, LR, LR-RSS, LR-SVM, and LR-M5P models in all input combinations during the testing period. It was also noticed that the performance of the alone LR and its hybrid models (i.e., LR-RSS, LR-REPTree, LR-SVM, and LR-M5P) was better than the conventional stage-discharge rating curve, including the GRG method.

Irrigation Performance Index Model (Case Study in IPDMIP)

Each irrigation area has its own unique characteristics, depending on its geographical location, topography, population, climate, soil, and others. Based on government regulation, since 2015, all irrigation schemes in Indonesia have to be measured with the irrigation system performance index (IKSI or Indeks Kinerja Sistem Irigasi) every year. Several studies have been conducted since that year, but the IKSI model has not been evaluated yet, especially for surface irrigation. An increasing value of IKSI indicates an increase in the quality of irrigation system services. Conversely, the decreasing value of IKSI means that the efficiency and effectiveness of irrigation system management need further review and improvement. Therefore, this research aims to develop a mathematical model of the irrigation performance index as an evaluation using six parameters that examine the quality of irrigation system management. The research locations are in 947 Central Government Authorized Irrigation Areas, which was chosen considering that the irrigation performance index model had not been evaluated. The methodology consists of a SmartPLS (partial least square) application to analyze and narrow down the variables in this study, the analysis using the GRG (generalized reduced gradient) method to calculate nonlinear equations. In the initial equation, two variables, 12 dimensions, 24 indicators were analyzed. After analyzing the results using PLS-SEM, three indicators were eliminated so that the composition of the new equation became two variables, 12 dimensions, and 21 indicators that were interrelated with one another. Furthermore, GRG analysis using Microsoft Excel solver showed changes in variable weights so that the new model equation for IKSI-Bakti was 0.744 x primary irrigation network + 0.256 x tertiary irrigation network, which applies to the irrigation area of the Central Authority, especially for surface irrigation. Keywords : irrigation, partial least square, generalized reduced gradient, performance index. https://doi.org/10.55463/issn.1674-2974.50.4.1

Optimization of in-Vehicle Carbon Dioxide Level in a 5-Seat Car

The air quality in a car’s cabin can be five times worse than that of residential and non-residential buildings, resulting in a variety of health issues, such as headache, sore throat, and nausea, which are all symptoms of in-vehicle air pollution. The monitoring of carbon dioxide, which is one of the principal pollutants in car cabins, is required before regulating it. The current research is focused on the recording of carbon dioxide levels for different levels of human load, air speed, and temperature. A statistical analysis and plots were obtained for recorded responses to determine air quality parameters for a minimum value of carbon dioxide level in a five-seat car cabin. Three algorithms (generalized reduced gradient (GRG), response surface methodology (RSM), and Genetic Algorithm (GA)) were successfully used in a 5-seat car to optimize the in-vehicle carbon dioxide level. The GRG method provided the minimum carbon dioxide level of 471.531 ppm for a one-human load at an air speed of 2 m/s and a temperature of 24 °C. For varying human loads of 2,3,4, and 5, the GRG and GA methods provided carbon dioxide levels of 508.785 ppm, 580.722 ppm, 659.839 ppm and 769.016 ppm, respectively. Comparing all three techniques, the RSM provided carbon dioxide levels of 471.876 ppm, 508.865 ppm, 580.79 ppm, 659.905 ppm, and 769.362 ppm for human loads of 1, 2, 3, 4, and 5, respectively. This study will provide a platform for the researchers working on indoor air quality characteristics to apply soft computing techniques effectively for the evaluation of comfortable healthy environments and for the benefit of the passengers in car cabins.

PERFORMANCE INDEX MODEL OF GROUNDWATER IRRIGATION SYSTEMS

This research will develop a groundwater irrigation system performance index model with the aim of identifying the groundwater irrigation system performance index; this information can be used by stakeholders to determine management steps. The research location is in Gunungkidul Regency and includes surrounding areas — acknowledging that the karst aquifer has complex characteristics and non-karst aquifer, namely high heterogeneity as a result of the formation of a groundwater flow system through fractures which eventually becomes completely underground runoff. Screening for the variables was carried out using the smart-PLS (Partial Least Square) tool, which was then analyzed using the GRG (Generalized Reduced Gradient) method which is useful for solving non-linear equations. In this research, it examines the physical aspects, social aspects and management aspects as variables. The groundwater irrigation system performance index model examines 3 (three) variables, namely physical aspects, social aspects, and management aspects, then 11 (eleven) dimensions and 42 (forty two) indicators. The analysis using PLS SEM using smart PLS tools determined that the 3 (three) variables, 11 (eleven) dimensions and 30 (thirty) indicators are interrelated and effective. Whereas by using GRG (Generalized Reduced Gradient) analysis with the solver tool in Microsoft Excel, the most influential weights were obtained from the physical aspects, namely physical infrastructure (0.5782), geological conditions (0.2311), water quality (0.1286) and recharge area conditions (0.0475); the social aspects that obtained the most influential weight are socio-cultural (0.7471) and economy (0.2529); the management aspects that obtained the most influential weights are budgeting (0.2534), plant productivity (0.2270), WUA organizational conditions (0.2090), JIAT management organizational conditions (0.1987) and spatial planning directives (0.0674). In general, the weight of the influence of groundwater irrigation performance for these three aspects is 0.6686 physical aspects, 0.0856 social aspects and 0.2458 management aspects which are formulated into a performance index model for groundwater irrigation systems "Kautsar", namely IL = 0.6686 physical IL + 0.0856 social IL + 0.2458 IL management. For development, further research is needed on the performance index model of the groundwater irrigation system using Geography Information System (GIS) and a software application on android, iOS, or windows operation systems. A groundwater irrigation system performance index that consists of these three aspects is unique and has never been assembled in previous studies; it conveniently allow the user to determine survey results immediately.

Deep seawater as efficiency improver for cogeneration plants of petroleum production units

The oil and gas industry is usually related to environmental problems and high level of CO2 emission. This work aims to evaluate different cogeneration plants usually used in FPSOs using cold deep sea water to improve efficiency of the cogeneration plants. Petroleum production data from a given well is used to size process plant while cogeneration plants are modeled using electrical and thermal demands required by process plant. Off-design operation caused by variation in utilities demand is also considered. Optimization using the GRG (Generalized Reduced Gradient) method is performed to minimize fuel consumption by selecting the best load distribution among equipment yearly. Results reveal that the additional cooling subsystem using deep sea water increases the exergy efficiency in 2.5% for gas turbines (which is the most usual technology) and as a consequence, a reduction of 128585 t in CO2 emissions was noticed. For the steam plant, the increase in exergy efficiency was 2.9%. For reciprocating engine and combined cycle technologies there is no significant benefit. Reciprocating engines plant presented the highest exergy efficiency (∼50%), even though no benefits from the use of the additional cooling system were achieved for this technology.

The fundamentals of crystal orientation.

The method described in this paper improves the old methods of crystal orientation, applies new parametric equations for crystallography, and increases the precision and accuracy of measurements. The method applies to inorganic and organic crystals. A breakthrough in crystal orientation happened about 25 years ago when two equations dependent on the Bragg angle and an arbitrary direction in the crystal were developed. Unfortunately, they were analytically insolvable and their unique solution was found numerically. Finding the numerical solution of crystal orientation is challenging from a mathematical point of view. In these conditions the numerical solution was found using the Newton method. The Newton method required a specific programming that limits the full benefit of the method in the laboratory. In recent years, a new numerical technique called GRG (generalized reduced gradient), which can be run on many inexpensive computers, was found to be a good fit for these equations. The solutions that can be found with the GRG method are now completed with additional parametric equations; they are easy to use with computers in many laboratories. In this way, parametrization of nonlinear equations for X-ray crystal orientation determines the positions of a reference surface of the single crystal relative to its crystallographic system and to a goniometer setting with two perpendicular axes of rotation. This approach was successfully validated and checked for different Si wafers with (111) and (004) orientation. The paper shows an innovative approach through the parametric equations in conjunction with exact solutions found with a GRG subroutine. The results of the method demonstrate the potential for new applications in industry and research.

A Generalized Reduced Gradient Method for the Optimal Control of Very-Large-Scale Robotic Systems

This paper develops a new indirect method for distributed optimal control (DOC) that is applicable to optimal planning for very-large-scale robotic (VLSR) systems in complex environments. The method is inspired by the nested analysis and design method known as generalized reduced gradient (GRG). The computational complexity analysis presented in this paper shows that the GRG method is significantly more efficient than classical optimal control or direct DOC methods. The GRG method is demonstrated for VLSR path planning in obstacle-populated environments in which robots are subject to external forces and disturbances. The results show that the method significantly improves performance compared to the existing direct DOC and stochastic gradient methods.

Comprehensive derivation of bond-valence parameters for ion pairs involving oxygen.

Published two-body bond-valence parameters for cation-oxygen bonds have been evaluated via the root mean-square deviation (RMSD) from the valence-sum rule for 128 cations, using 180,194 filtered bond lengths from 31,489 coordination polyhedra. Values of the RMSD range from 0.033-2.451 v.u. (1.1-40.9% per unit of charge) with a weighted mean of 0.174 v.u. (7.34% per unit of charge). The set of best published parameters has been determined for 128 ions and used as a benchmark for the determination of new bond-valence parameters in this paper. Two common methods for the derivation of bond-valence parameters have been evaluated: (1) fixing B and solving for R(o); (2) the graphical method. On a subset of 90 ions observed in more than one coordination, fixing B at 0.37 Å leads to a mean weighted-RMSD of 0.139 v.u. (6.7% per unit of charge), while graphical derivation gives 0.161 v.u. (8.0% per unit of charge). The advantages and disadvantages of these (and other) methods of derivation have been considered, leading to the conclusion that current methods of derivation of bond-valence parameters are not satisfactory. A new method of derivation is introduced, the GRG (generalized reduced gradient) method, which leads to a mean weighted-RMSD of 0.128 v.u. (6.1% per unit of charge) over the same sample of 90 multiple-coordination ions. The evaluation of 19 two-parameter equations and 7 three-parameter equations to model the bond-valence-bond-length relation indicates that: (1) many equations can adequately describe the relation; (2) a plateau has been reached in the fit for two-parameter equations; (3) the equation of Brown & Altermatt (1985) is sufficiently good that use of any of the other equations tested is not warranted. Improved bond-valence parameters have been derived for 135 ions for the equation of Brown & Altermatt (1985) in terms of both the cation and anion bond-valence sums using the GRG method and our complete data set.

Advertisement Policy, Reliability Dependent Imperfect Production and Environmental Pollution Control Problem in Fuzzy-Rough Environment

In this study, a problem for advertising policy to avoid the depreciation rate of sale, an imperfect production rate and environmental pollution control is formulated with reliability and rework over a finite time horizon. The advertisement and production rates are function of time which are taken as control variables. Also, recent studies indicate that industrial solid waste (ISW) in production period has been an important contributor to greenhouse gas (GHG) emissions. The company has agreed to invest a large amount of money to manage the ISW through technological up gradation, etc that reduce the GHG in environment. The unit production cost is a function of production rate and also dependent on raw material cost, development cost due to technological up gradation and reliability and wear-tear cost. The total profit which consists of the sales proceeds, marginal selling price, production cost, operating cost, pollution cost, inventory holding cost and advertisement cost is formulated as an optimal control problem. The selling price and all inventory costs are fuzzy rough in nature and using expectation of fuzzy rough technique, the problem is converted into equivalent crisp problem and solved using Pontryagin's Maximum Principle and Generalized Reduced Gradient Method (GRG). Finally numerical experiment, sensitivity analysis for marginal selling price, defective parameter, rework and depreciation rate of sale and graphical representation are provided to illustrate the model.

Calibrating Mechanistic–Empirical Pavement Design Guide for North Carolina: Genetic Algorithm and Generalized Reduced Gradient Optimization Methods

The Mechanistic–Empirical Pavement Design Guide (MEPDG) is the state-of-the-practice pavement analysis software developed under NCHRP Project 1–37A. Recently, AASHTO announced the first commercial version of the software, DARWin-ME, to replace the 1993 AASHTO design guide DARWin software. The MEPDG and DARWin-ME use similar models for predicting rutting and bottom-up fatigue cracking. Both distress models were nationally calibrated with measured performance data collected from hundreds of long-term pavement performance sections across the United States and Canada. Verification work indicated that these nationally calibrated models did not reflect North Carolina's local materials, construction practices, and local traffic. Therefore, the performance models must be recalibrated to reflect local conditions. The scope includes rutting and alligator cracking in flexible pavements. The development of rutting and fatigue model coefficients (k-values) is investigated for 12 commonly used hot-mix asphalt (HMA) mixtures in North Carolina, and two approaches for recalibrating the rutting and fatigue cracking model coefficients (β-factors) are compared to reflect local materials and conditions. The two optimization methods evaluated are generalized reduced gradient (GRG) and genetic algorithm (GA) optimization. Results indicate that rutting and fatigue cracking k-values for North Carolina HMA mixtures are generally different from national averages. The GA optimization method does a better job of predicting local distresses than do the GRG method and nationally calibrated models.

Improved GRG method for the optimal synthesis of linkages in function generation problems

This paper presents a novel approach for optimizing the dimensions of linkages for application to function-generation problems. The main goal is to minimize the objective function formulated as the difference between the desired and generated functional parameters using the Generalized Reduced Gradient (GRG) method. Although this optimization approach is well-known by mathematicians and researchers in optimal design, the formulation developed by the author reveals that it has not been sufficiently explored in dimensional synthesis. Indeed, the examples presented in this paper show that it can be easily formulated and applied to obtain the optimal dimensions of complex linkages with large numbers of prescribed positions. The main contribution of this approach is to demonstrate that the suitable formulation of this approach (denominated improved GRG method) leads to an algorithm that is general, robust, accurate and efficient for synthesizing linkages in function generation problems.

Transient security dispatch for the concurrent optimization of plural postulated contingencies

The implementation. of a transient security dispatch (TSD) algorithm for real-time applications is presented. The algorithm, based on the generalized reduced gradient (GRG) method, processes collectively a set of contingencies in order to ensure transient stability for all postulated cases. The massive computation has been decomposed on a cluster of workstations, exploiting the decoupled nature of the GRG method and the benefits of distributed computing. The feasibility of the implementation is shown through tests on a realistic-sized test network.

Power Systems Control Complex Optimization in the New Market Conditions

A generalization and development of the theory and methods for complex optimisation of the performance and development control of an interconnected system (IPS) under new market conditions (mainly multicriterial and game approaches) is given considering the specifics of IPS at the international level in post-socialist countries and in particular in the Baltic states. Therby the kernel of the mathematical apparatus of this theory the Generalized Reduced Gradient Method (GRGM) is further generalised and developed with the application of multicriterial and game methods to meet various market conditions.

AUTOMATIC DIFFERENTIATION FOR MORE EFFICIENT SYSTEM ANALYSIS AND OPTIMIZATION

This paper reports on the benefits of using automatic differentiation (AD) to improve the efficiency of multidisciplinary analysis and optimization processes. Automatic differentiation technology provides researchers with new opportunities to use sensitivities for analysis and optimization. This research confirms that analysis and optimization applications in which the use of sensitivity information had previously been avoided or ruled out, as computationally prohibitive, need to be revisited. In this research, two applications are investigated in which the use of AD is observed to improve efficiency. The efficiency of solution strategies for non-hierarchic (i.e., coupled) system analysis is improved using automatic differentiation generated sensitivities. Calculation of sensitivities via AD allows for efficient application of Newton's method and a modified form of Newton's method to converge non-hierarchic system analyses. The line search strategy employed within a generalized reduced gradient (GRG) optimizer is improved through the use of AD generated sensitivities. Using the AD-based line search strategy within the GRG method results in a significant reduction in the number of system analyses and the CPU time required for optimization

A Comparison of Equality Constraint Formulations for Concurrent Design Optimization

In this research two comparative studies are conducted in application to the concurrent design optimization method of Simulta neous ANalysis and Design (SAND) In one study three different forms of equality constraints referred to as compatibility constraints in the SAND procedure are compared with respect to their impact on algorithm efficiency. Results indicate that the form of the compatibility con straints can have a significant impact on performance in the SAND based procedure. In a second study a Generalized Reduced Gradient (GRG) optimizer and a Sequential Quadratic Programming (SQP) optimizer are compared with respect to their efficacy as the internal opti mizer within the SAND based optimization procedure. Comparative studies indicate that the SQP method is preferred over the GRG method in application of SAND based design. The comparative studies were conducted in application to two Multidisciplinary Design Optimization (MDO) test problems. The method of SAND was originally developed as an optimization strategy for structural design problems. Recent studies have focussed on applying the principles of SAND to multidisciplinary design environments In this research we focus on the concurrency that can be achieved in multidisciplinary design environments using SAND. In a multidisciplinary design environment the SAND approach facilitates each of the seven principles of concurrent engineering as described in Prasad, 1996. The SAND based method provides for: parallel work groups, parallel product decomposition, concurrent resource scheduling, concurrent processing, minimal interfaces, transparent communi cation and quick processing. Application studies confirm that a significant savings in the number of analyses required for design optimiza tion are observed when using the SAND approach of concurrent design. SAND based design delivers on the promise of concurrent engi neering, namely to develop optimal designs, working concurrently, while reducing design cycle time.

A parallel processing algorithm for nonlinear programming problems

Algorithms for solving multiple criteria nonlinear programming problems are frequently based on the use of the generalized reduced gradient (GRG) metod. Since the GRG method gives complex and large size processing for computation, it takes much time to solve large-scale multiple criteria nonlinear programming problems. Therefore, parallel processing dealing with the GRG method is required to solve the problems. We propose a parallel processing algorithm for the GRG method under multiple processors systems.

REGIONAL WATER QUALITY MANAGEMENT BY THE GENERALIZED REDUCED GRADIENT METHOD1

ABSTRACT: A river basin‐wide water quality management system is considered. The river receives thermal as well as organic wastes. At‐source treatment of these pollutants is imposed to control the basin‐wide water quality. The related water quality standards are: the minimum DO concentration, the maximum allowable BOD concentration, the maximum allowable stream temperature, and the allowable rise in stream temperature. The general dynamic mathematical model representing water quality in streams and the thermal effects on BOD and DO concentrations is presented. The model is highly nonlinear in nature. The optimal management problem involving the model is solved by a recently developed nonlinear propgramming technique ‐ the generalized reduced gradient (GRG) method. Comparison of results obtained by the GRG method vs. dynamic programming, and of results using a more realistic mathematical model vs. a simple model are presented. The analysis procedure can be applied to designing new and examining existing water quality programs, and to study the influence of alternate policies and constraints.