Set Of Optimal Points Research Articles

Statistical Optimization of Heavy Metal (Cu2+ and Co2+) Extraction from Printed Circuit Boards and Mobile Batteries Using Chelation Technology

Electronic waste has emerged as one of the fastest growing segments of the solid waste stream in the last two decades because of the greater consumption and obsolescence rates of electronic products. Significant content of metals and polymers present in e-waste may affect the ecosystem and human health if treated inappropriately using primitive recycling methods. Several studies have been reported in the literature for the recovery of metals from e-waste; however, limitations associated with ongoing methods incited this study to move toward modern approaches based on green chemistry principles. The present study is a pioneer effort to employ a novel green technology based on a unique combination of chelation–dechelation concepts to extract metals from printed circuit boards and mobile batteries. The applicability of response surface methodology (RSM) was explored to investigate the mutual interaction effect of process parameters and to provide an improved quality of information. Statistical optimization of the extraction process was performed by coupling of Box–Behnken design and central composite design matrices with RSM. Nearly 85.3% Cu2+ and 86.2% Co2+ recovery was predicted at the center level of design matrices using quadratic regression models for the respective metals. Maximum ±4% deviation was observed between experimental and predicted extraction efficiency. The high values of regression coefficients (R2 = 0.994 for Cu2+ recovery and R2 = 0.998 for Co2+ recovery) indicated that >99% of response variability could be explained by regression models. Relatively lower p-values (<0.0001) and coefficient of variation (<2.8%) indicate the adequacy of the proposed models. The desirability function approach was employed to localize the optimum process parameters, and ramp functions were drawn for the set of optimal points. A well-defined optimal region was identified to maximize the metal extraction with desirability >0.95. Characterization of raw material and residues corroborated the significant extraction of metals. Also, recovered chelating agent was successfully employed in subsequent extraction cycles, which fortifies the concept of a zero-waste technology. The proposed design correlations may prove to be a useful tool in designing pilot and commercial plants for extraction of heavy metals using environmentally friendly chelation technology.

SMGDA: an uncertainty based multi-objective optimization approach. Illustration to an airplane composite material

Progress in structural design often requires the resolution of various conflicting design objectives: decreasing the structure mass while increasing safety, etc. Multi-objective optimization is a powerful numerical tool capable of resolving such objectives. Contrary to the single objective case, there exists a continuous set of parameters which are solutions of a given multi-objective problem in the sense that there exist no other designs that can ameliorate all the objectives at the same time. Such a set of optimal points is called the Pareto frontier. Introducing uncertain parameters in the objective function significantly affects the decision making process, the Pareto frontier becoming itself uncertain. Under a probabilistic framework where uncertainty is introduced through a random variable, a first stage before solving the new optimization problem is to specify the mathematical meaning given to the probabilistic optimization problem and then to develop appropriate numerical procedures leading to the solutions, or the corresponding Pareto frontier. Here we shall consider to solve the stochastic multi-objective problem written in terms of the objective function expectation. We propose a new algorithm based on an extension of the deterministic multi-gradient descent algorithm to the stochastic context together with an extension of the Robbins-Monro algorithm. Mean square and almost sure convergence of the algorithm can be proven. An illustration to an aerospace composite material will be given.

Generating Point Configurations via Hypersingular Riesz Energy with an External Field

For a compact $d$-dimensional rectifiable subset of ${\mathbb R}^{p}$ we study asymptotic properties as $N\to\infty$ of $N$-point configurations minimizing the energy arising from a Riesz $s$-potential $1/r^s$ and an external field in the hypersingular case $s\geq d$. Formulas for the weak$^*$ limit of normalized counting measures of such optimal point sets and the first-order asymptotic values of minimal energy are obtained. As an application, we derive a method for generating configurations whose normalized counting measures converge to a given absolutely continuous measure supported on a rectifiable subset of ${\mathbb R}^{p}$. Results on separation and covering properties of discrete minimizers are given. Our theorems are illustrated with several numerical examples.

Multi-objective optimization of compression refrigeration cycle of Unit 132 South Pars refineries

The purpose of this paper is multi-objective optimization of refrigeration cycle by optimization of all components of the cycle contains heat exchangers, air condenser, evaporator and super-heater. Studied refrigeration cycle is compression refrigeration cycle of unit 132 Third refineries in south pars that provide chilled water for cooling refinery equipment's. Cycle will be performed by the genetic algorithm optimization. Thermodynamic purpose of the cycle Expressed by minimization of Exergy destruction or maximization or coefficient of performance (C.O.P), economic purpose of the cycle Expressed by minimization of cold water production cost by TRR method and environmental purpose of the cycle Expressed by minimization of NOx, CO2 and CO Which is produced by power consumption. Combination of objectives and decision variables with suitable engineering and physical constraints makes a set of the MINLP optimization problem. In EES software. Optimization programming is performed using NSGA-II algorithm. Four optimization scenarios including the thermodynamic single-objective, the economic single-objective, environmental single-objective by power electricity consumption and multi-objective optimizations are performed. The output of the multi-objective optimization is a Pareto frontier that yields a set of optimal points that the final optimal solution has been selected using two decision-making approaches including the LINMAP and TOPSIS methods.. It was shown that the best results in comparison to the simple cycle reduction in Exergy destruction from 264.8 kW to 127.6 kW(Increased coefficient of performance from 3.872 to 7.088), reduction in cold water production cost from 117.5 dollar/hour to 87.19 dollar/hour and reduction in NOx emission from 4958 kg/year to 2645 kg/year.

A Unifying Energy-Based Approach to Stability of Power Grids With Market Dynamics

In this paper, a unifying energy-based approach is provided to the modeling and stability analysis of power systems coupled with market dynamics. We consider a standard model of the power network with a third-order model for the synchronous generators involving voltage dynamics. By applying the primal-dual gradient method to a social welfare optimization, a distributed dynamic pricing algorithm is obtained, which can be naturally formulated in port-Hamiltonian form. By interconnection with the physical model a closed-loop port-Hamiltonian system is obtained, whose properties are exploited to prove asymptotic stability to the set of optimal points. This result is extended to the case that also general nodal power constraints are included into the social welfare problem. Additionally, the case of line congestion and power transmission costs in acyclic networks is covered. Finally, a dynamic pricing algorithm is proposed that does not require knowledge about the power supply and demand.

An Analysis of Solution Point Coordinates for Flux Reconstruction Schemes on Tetrahedral Elements

The flux reconstruction (FR) approach offers an efficient route to high-order accuracy on unstructured grids. In this work we study the effect of solution point placement on the stability and accuracy of FR schemes on tetrahedral grids. To accomplish this we generate a large number of solution point candidates that satisfy various criteria at polynomial orders $$\wp = 3,4,5$$ . We then proceed to assess their properties by using them to solve the non-linear Euler equations on both structured and unstructured meshes. The results demonstrate that the location of the solution points is important in terms of both the stability and accuracy. Across a range of cases it is possible to outperform the solution points of Shunn and Ham for specific problems. However, there appears to be a degree of problem-dependence with regards to the optimal point set, and hence overall it is concluded that the Shunn and Ham points offer a good compromise in terms of practical utility.

Long-term economic analysis and optimization of an HT-PEM fuel cell based micro combined heat and power plant

Multi-objective optimization method using genetic algorithm is employed in order to optimize design and operating parameters of a high temperature proton exchange membrane (HT-PEM) fuel cell based combined heat and power system. Net electrical efficiency of the plant, indicating the system's performance (to be maximized) and the total capital cost (to be minimized) are considered as optimization objectives. Current density (indicating the stack size), steam to carbon ratio, burner outlet temperature and auxiliary to process fuel ratio have been chosen as design parameters. Two different multi-objective optimization approaches have been utilized: steady state (without degradation) and long-term optimization while considering the degradation in fuel cell stack and the fuel processor. The results of the optimization procedures are Pareto frontiers which are a set of optimal points each of which is a trade-off between the considered objective functions. The performance indexes and operating conditions of three points with the maximum cumulative net electrical efficiency, minimum capital cost, and the same fuel cell area as that of the initial design are compared. It can be observed that while attempting to maximize the electrical efficiency, the cumulative net electrical efficiency of 29.96% can be achieved although it results in a total capital cost of 115711 €. On the other hand, the capital cost can be reduced down to 39,929 € which significantly diminishes cumulative net electrical efficiency. Finally, by locating the point on the Pareto frontier in which the fuel cell area is the same as that of the initial design, a cumulative net electrical efficiency of 27.07% was achieved which is 1% higher than the value obtained using the operating conditions of the initial design.

Existence of Optimal Points Via Improvement Sets

According to the recent definition of efficiency via improvement sets, the aim of this paper is to characterize the set of optimal points for a set. New existence results are proved in multicriteria situations, and their novelty is illustrated via several examples. Moreover, the study of an economic model is provided as an example of application of our achievements.

Exergoeconomic analysis and multi-objective optimization of an ejector refrigeration cycle powered by an internal combustion (HCCI) engine

Ejector refrigeration systems powered by low-grade heat sources have been an attractive research subject for a lot of researchers. In the present work the waste heat from exhaust gases of a HCCI (homogeneous charge compression ignition) engine is utilized to drive the ejector refrigeration system. Considering the frictional effects on the ejector wall, a new two-dimensional model is developed for the ejector. Energy, exergy and exergoeconomic analysis performed for the proposed system using the MATLAB software. In addition, considering the exergy efficiency and the product unit cost of the system as objective functions, a multi-objective optimization is performed for the system to find the optimum design variables including the generator, condenser and evaporator temperatures. The product unit cost is minimized while the exergy efficiency is maximized using the genetic algorithm. The optimization results are obtained as a set of optimal points and the Pareto frontier is plotted for multi-objective optimization. The results of the optimization show that ejector refrigeration cycle is operating at optimum state based on exergy efficiency and product unit cost when generator, condenser and evaporator work at 94.54°C, 33.44°C and 0.03°C, respectively.

Port-Hamiltonian Formulation of the Gradient Method Applied to Smart Grids

The gradient method is a well-known tool for solving convex optimization problems. This paper shows that the gradient method admits a Brayton-Moser and a port-Hamiltonian representation. In fact, its dynamics can be interpreted as a interconnection of multiple (port-Hamiltonian) passive systems, which plays a key role in proving asymptotic stability of the method. As an application to smart grids, this paper studies the problem of frequency regulation in power grids, while maximizing the social welfare. By applying the gradient method, we obtain a real-time dynamic pricing model in port-Hamiltonian form. By coupling with the port-Hamiltonian description of the physical network we obtain a closed-loop port-Hamiltonian system, which properties are exploited to prove asymptotic stability to the set of optimal points.

Optimal Measurement Allocation Algorithms for Parametric Model Identification of Power Systems

In this paper, we present an optimization algorithm that selects the optimal sets of points for placing phasor measurement units (PMUs) on the transmission lines of a multimachine power system for the purpose of identifying the best model fit for its wide-area swing dynamics. Alternatively, the method can also be viewed as a way to select the optimal set of points at which phasor values should be computed using measurements available from PMUs such that these computed values, also referred to here as pseudo-measurements, can generate the best estimate of the swing model, especially when the measurements are noisy. We pose the identification problem as an equivalent parameter estimation problem for the admittance of each tie-line and the inertia of each machine using phasor measurements of voltage magnitude, phase angle and frequency, corrupted with high-frequency measurement noise. We then formulate the Cramer-Rao bounds (CRBs) for the estimates of these unknown parameters, and show that the bounds are functions of the PMU locations and of the contribution of each measurement variable in the combined output. We finally state the condition for finding the optimal PMU location that guarantees the tightest CRB, and, therefore, the most accurate swing model for the system.

Total Path Length and Number of Terminal Nodes for Decision Trees

This paper presents a new tool for study of relationships between total path length (average depth) and number of terminal nodes for decision trees. These relationships are important from the point of view of optimization of decision trees. In this particular case of total path length and number of terminal nodes, the relationships between these two cost functions are closely related with space-time trade-off. In addition to algorithm to compute the relationships, the paper also presents results of experiments with datasets from UCI ML Repository1. These experiments show how two cost functions behave for a given decision table and the resulting plots show the Pareto frontier or Pareto set of optimal points. Furthermore, in some cases this Pareto frontier is a singleton showing the total optimality of decision trees for the given decision table.

An Adaptive Method for Choosing Center Sets of RBF Interpolation

Radial basis functions (RBF) provide powerful meshfree methods for multivariate interpolation for scattered data. RBF methods have been praised for their simplicity and ease of implementation in multivariate scattered data approximation. But both the approximation quality and stability depend on the distribution of the center set. It leads immediately to the problem of finding good or even optimal point sets for the reconstruction process. Many methods are constructed for center choosing. In this paper, we give a short overview of these algorithms including thinning algorithm, greedy algorithm, arclength equipartition like algorithm and k-means clustering algorithm. A new adaptive data-dependent method is provided at the end with some numerical examples to show its effectiveness.

Evaluation of a 3D point cloud tetrahedral tomographic reconstruction method

Tomographic reconstruction on an irregular grid may be superior to reconstruction on a regular grid. This is achieved through an appropriate choice of the image space model, the selection of an optimal set of points and the use of any available prior information during the reconstruction process. Accordingly, a number of reconstruction-related parameters must be optimized for best performance. In this work, a 3D point cloud tetrahedral mesh reconstruction method is evaluated for quantitative tasks. A linear image model is employed to obtain the reconstruction system matrix and five point generation strategies are studied. The evaluation is performed using the recovery coefficient, as well as voxel- and template-based estimates of bias and variance measures, computed over specific regions in the reconstructed image. A similar analysis is performed for regular grid reconstructions that use voxel basis functions. The maximum likelihood expectation maximization reconstruction algorithm is used. For the tetrahedral reconstructions, of the five point generation methods that are evaluated, three use image priors. For evaluation purposes, an object consisting of overlapping spheres with varying activity is simulated. The exact parallel projection data of this object are obtained analytically using a parallel projector, and multiple Poisson noise realizations of these exact data are generated and reconstructed using the different point generation strategies. The unconstrained nature of point placement in some of the irregular mesh-based reconstruction strategies has superior activity recovery for small, low-contrast image regions. The results show that, with an appropriately generated set of mesh points, the irregular grid reconstruction methods can out-perform reconstructions on a regular grid for mathematical phantoms, in terms of the performance measures evaluated.

Near-optimal data-independent point locations for radial basis function interpolation

The goal of this paper is to construct data-independent optimal point sets for interpolation by radial basis functions. The interpolation points are chosen to be uniformly good for all functions from the associated native Hilbert space. To this end we collect various results on the power function, which we use to show that good interpolation points are always uniformly distributed in a certain sense. We also prove convergence of two different greedy algorithms for the construction of near-optimal sets which lead to stable interpolation. Finally, we provide several examples.

Special Pair of Dual Parametric Nonlinear Optimization Problems with Common Set of Optimal Points

On the base of a given strictly convex function defined on the Euclidean space E n ( n S 2) we can-without the assumption that it is differentiable - introduce some manifolds in topologic sense. Such manifolds are sets of all optimal points of a certain parametric non-linear optimization problem. This paper presents above all certain generalization of some results of [F. No − i ) ka and L. Grygarová (1991). Some topological questions connected with strictly convex functions. Optimization , 22 , 177-191. Akademie Verlag, Berlin] and [L. Grygarová (1988). Über Lösungsmengen spezieller konvexer parametrischer Optimierungsaufgaben . Optimization 19 , 215-228. Akademie Verlag Berlin], under less strict assumptions. The main results are presented in Sections 3 and 4, in Section 3 the geometrical characterization of the set of optimal points of a certain parametric minimization problem is presented; in Section 4 we study a maximization non-linear parametric problem assigned to it. It seems that it is a certain pair of parametric optimization problems with the same set of their optimal points, so that this pair of problems can be denoted as a pair of dual parametric non-linear optimization problems. This paper presents, most of all in Section 2, a number of interesting geometric facts about strictly convex functions. From the point of view of non-smooth analysis the present article is a certain complement to Chapter 4.3 of the book [B. Bank, J. Guddat, D. Klatte, B. Kummer and K. Tammer (1982). Nonlinear Parametric Optimization . Akademie Verlag, Berlin] where a convex parametric minimization problem is considered under more general and stronger conditions (but without any assumptions concerning strict convexity and without geometrical aspects).

On the set of optimal points to the Weber problem: further results

On the set of optimal points to the Weber problem: further results

On the Set of Optimal Points to the Weber Problem: Further Results

In a recent paper, Z. Drezner and A. J. Goldman address the problem of determining the smallest set among those containing at least one optimal solution to every Weber problem based on a set of demand points in the plane. In the case of arbitrary mixed gauges (i.e., possibly nonsymmetric norms), the authors have shown that the set of strictly efficient points which are also intersection points always meets the set of Weber solutions. As shown by Drezner and Goldman, this set is optimal with the ℓ1 or ℓx distance but is not optimal with the ℓp distance, 1 &lt; p &lt; ∞. In this latter case they identify the smallest one. This paper generalizes these results for any strictly convex norm or any polyhedral norm. An example shows that in the case of an arbitrary norm there may exist an infinity of smallest sets and some of them contain points which are neither strictly efficient nor intersection points. In the ℓp distance case, we disprove a conjecture of Drezner and Goldman about the possibility of extending their result to more than two dimensions. The paper contains a different view of the problem: whereas Drezner and Goldman use algebraic-analytical approach, the authors use a geometrical approach which permits us to obtain more general results and also clarifies the geometric nature of the problem.

Competitive location on a network

Consider a network with a given number of customers at fixed locations (vertices) and where each customer will purchase a commodity from the facility closer to his location more frequently than from a remote one. As a generalization of the Condorcet concept we define an optimal point as a location such that there exists no competitor with higher expected value. We show that the set of optimal points consists entirely of vertices. In general we provide polynomial algorithms to answer the question as to: What is the maximum percentage of customers located on the network prefering some rival point to an existing location? Suboptimal points where the maximal relative rejection by a rival point is minimal are determined in polynomial time.

On the Set of Optimal Points to the Weber Problem

It is known that the planar Weber location problem with lp distances has all its solutions in the convex hull of the demand points. for l1 and l∞ distances, additional conditions are known which reduce the set of possible optimal points to the intersection of that convex hull, the efficient set, and the points defined by a certain grid. In this paper, we determine the smallest set which includes at least one optimal point for every Weber problem based on a given set of demand points. It is shown that for 1&lt;p&lt;∞ a certain part of the convex hull is the smallest possible set, but for p=1 or p=∞ the known conditions do not necessarily yield the correct set. Finally, we find the smallest possible set for p=1 or p=∞.