Search results for: optimal number

Authors: Abdel-Aziz M. Mohamed

Abstract:

This paper presents a state-of-the-art survey of the operations research models developed for internal audit planning. Two alternative approaches have been followed in the literature for audit planning: (1) identifying the optimal audit frequency; and (2) determining the optimal audit resource allocation. The first approach identifies the elapsed time between two successive audits, which can be presented as the optimal number of audits in a given planning horizon, or the optimal number of transactions after which an audit should be performed. It also includes the optimal audit schedule. The second approach determines the optimal allocation of audit frequency among all auditable units in the firm. In our review, we discuss both the deterministic and probabilistic models developed for audit planning. In addition, game theory models are reviewed to find the optimal auditing strategy based on the interactions between the auditors and the clients.

Keywords: operations research applications, audit frequency, audit-staff scheduling, audit planning

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Authors: Lydia Wahid, Mona F. Ahmed, Nevin Darwish

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The vehicle routing problem (VRP) consists of a group of customers that needs to be served. Each customer has a certain demand of goods. A central depot having a fleet of vehicles is responsible for supplying the customers with their demands. The problem is composed of two subproblems: The first subproblem is an assignment problem where the number of vehicles that will be used as well as the customers assigned to each vehicle are determined. The second subproblem is the routing problem in which for each vehicle having a number of customers assigned to it, the order of visits of the customers is determined. Optimal number of vehicles, as well as optimal total distance, should be achieved. In this paper, an approach for solving the first subproblem (the assignment problem) is presented. In the approach, a clustering algorithm is proposed for finding the optimal number of vehicles by grouping the customers into clusters where each cluster is visited by one vehicle. Finding the optimal number of clusters is NP-hard. This work presents a polynomial time clustering algorithm for finding the optimal number of clusters and solving the assignment problem.

Keywords: vehicle routing problems, clustering algorithms, Clarke and Wright Saving Method, agglomerative hierarchical clustering

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Authors: Moulana Mohammed

Abstract:

Topic models are widely used in building clusters of documents for more than a decade, yet problems occurring in choosing optimal number of topics. The main problem is the lack of a stable metric of the quality of topics obtained during the construction of topic models. The authors analyzed from previous works, most of the models used in determining the number of topics are non-parametric and quality of topics determined by using perplexity and coherence measures and concluded that they are not applicable in solving this problem. In this paper, we used the parametric method, which is an extension of the traditional topic model with visual access tendency for visualization of the number of topics (clusters) to complement clustering and to choose optimal number of topics based on results of cluster validity indices. Developed hybrid topic models are demonstrated with different Twitter datasets on various topics in obtaining the optimal number of topics and in measuring the quality of clusters. The experimental results showed that the Visual Non-negative Matrix Factorization (VNMF) topic model performs well in determining the optimal number of topics with interactive visualization and in performance measure of the quality of clusters with validity indices.

Keywords: interactive visualization, visual mon-negative matrix factorization model, optimal number of topics, cluster validity indices, Twitter data clustering

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Authors: Songul Cinaroglu

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Background: Random Forest is an efficient, multi-class machine learning method using for classification, regression and other tasks. This method is operating by constructing each tree using different bootstrap sample of the data. Determining the number of trees in random forests is an open question in the literature for studies about improving classification performance of random forests. Aim: The aim of this study is to analyze whether there is an optimal number of trees in Random Forests and how performance of Random Forests differ according to increase in number of trees using sample health data sets in R programme. Method: In this study we analyzed the performance of Random Forests as the number of trees grows and doubling the number of trees at every iteration using “random forest” package in R programme. For determining minimum and optimal number of trees we performed Mc Nemar test and Area Under ROC Curve respectively. Results: At the end of the analysis it was found that as the number of trees grows, it does not always means that the performance of the forest is better than forests which have fever trees. In other words larger number of trees only increases computational costs but not increases performance results. Conclusion: Despite general practice in using random forests is to generate large number of trees for having high performance results, this study shows that increasing number of trees doesn’t always improves performance. Future studies can compare different kinds of data sets and different performance measures to test whether Random Forest performance results change as number of trees increase or not.

Keywords: classification methods, decision trees, number of trees, random forest

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Authors: V. Makis, L. Jafari

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In this paper, we develop an optimal Bayesian chart to control the expected number of defects per inspection unit in production processes with long production runs. We formulate this control problem in the optimal stopping framework. The objective is to determine the optimal stopping rule minimizing the long-run expected average cost per unit time considering partial information obtained from the process sampling at regular epochs. We prove the optimality of the control limit policy, i.e., the process is stopped and the search for assignable causes is initiated when the posterior probability that the process is out of control exceeds a control limit. An algorithm in the semi-Markov decision process framework is developed to calculate the optimal control limit and the corresponding average cost. Numerical examples are presented to illustrate the developed optimal control chart and to compare it with the traditional u-chart.

Keywords: Bayesian u-chart, economic design, optimal stopping, semi-Markov decision process, statistical process control

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Authors: Jun Su Park, Byung Kwan Oh, Jin Woo Hwang, Yousok Kim, Hyo Seon Park

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For the structural safety, the maximum stress calculated from the stress distribution of a structure is widely used. The stress distribution can be estimated by deformed shape of the structure obtained from measurement. Although the estimation of stress is strongly affected by the location and number of sensing points, most studies have conducted the stress estimation without reasonable basis on sensing plan such as the location and number of sensors. In this paper, an optimal sensing technique for estimating the stress distribution is proposed. This technique proposes the optimal location and number of sensing points for a 2-D frame structure while minimizing the error of stress distribution between analytical model and estimation by cubic smoothing splines using genetic algorithm. To verify the proposed method, the optimal sensor measurement technique is applied to simulation tests on 2-D steel frame structure. The simulation tests are performed under various loading scenarios. Through those tests, the optimal sensing plan for the structure is suggested and verified.

Keywords: genetic algorithm, optimal sensing, optimizing sensor placements, steel frame structure

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Authors: Wen Liang Chang

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In this study, the optimal replacement time and number of preventive maintenance (PM) actions were investigated for a second-hand device. Suppose that a user intends to use a second-hand device for manufacturing products, and that the device is replaced with a new one. Any device failure is rectified through minimal repair, thereby incurring a fixed repair cost to the user. If the new device fails within the FRW period, minimal repair is performed at no cost to the user. After the FRW expires, a failed device is repaired and the cost of repair is incurred by the user. In this study, two profit models were developed, and the optimal replacement time and number of PM actions were determined to maximize profits. Finally, the influence of the optimal replacement time and number of PM actions were elaborated on, using numerical examples.

Keywords: second-hand device, preventive maintenance, replacement time, device failure

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Authors: Serkan Aras, Emrah Gulay

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Combining various forecasting models is an important tool for researchers to attain more accurate forecasts. A great number of papers have shown that selecting single models as dissimilar models, or methods based on different information as possible leads to better forecasting performances. However, there is not a certain rule regarding the number of single models to be used in any combining methods. This study focuses on determining the optimal or near optimal number for single models with the help of statistical tests. An extensive experiment is carried out by utilizing some well-known time series data sets from diverse fields. Furthermore, many rival forecasting methods and some of the commonly used combining methods are employed. The obtained results indicate that some statistically significant performance differences can be found regarding the number of the single models in the combining methods under investigation.

Keywords: combined forecast, forecasting, M-competition, time series

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Authors: Min Dai, Hong Liu, Shuaijie Qian

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We study a portfolio selection problem of an investor who faces constraints on rebalancing frequency, which is common in pension fund investment. We formulate it as a multiple optimal stopping problem and utilize the dynamic programming principle. By numerically solving the corresponding Hamilton-Jacobi-Bellman (HJB) equation, we find a series of free boundaries characterizing optimal strategy, and the constraints significantly impact the optimal strategy. Even in the absence of transaction costs, there is a no-trading region, depending on the number of the remaining trading chances. We also find that the equivalent wealth loss caused by the constraints is large. In conclusion, our model clarifies the impact of the constraints on transaction frequency on the optimal strategy.

Keywords: portfolio selection, rebalancing frequency, optimal strategy, free boundary, optimal stopping

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Authors: Yuyan Yi, Jingyi Zheng, Nedret Billor

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Independent component analysis (ICA) is one of the most commonly used blind source separation (BSS) techniques for signal pre-processing, such as noise reduction and feature extraction. The main parameter in the ICA method is the number of independent components (IC). Although there have been several methods for the determination of the number of ICs, it has not been given sufficient attentionto this important parameter. In this study, wereview the mostused methods fordetermining the number of ICs and providetheir advantages and disadvantages. Further, wepropose an improved version of column-wise ICAByBlock method for the determination of the number of ICs.To assess the performance of the proposed method, we compare the column-wise ICAbyBlock with several existing methods through different ICA methods by using simulated and real signal data. Results show that the proposed column-wise ICAbyBlock is an effective and stable method for determining the optimal number of components in ICA. This method is simple, and results can be demonstrated intuitively with good visualizations.

Keywords: independent component analysis, optimal number, column-wise, correlation coefficient, cross-validation, ICAByblock

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Authors: Imèn Khanchouch, Malika Charrad, Mohamed Limam

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The interpretation of the quality of clusters and the determination of the optimal number of clusters is still a crucial problem in clustering. We focus in this paper on multi-SOM clustering method which overcomes the problem of extracting the number of clusters from the SOM map through the use of a clustering validity index. We then tested multi-SOM using real and artificial data sets with different evaluation criteria not used previously such as Davies Bouldin index, Dunn index and silhouette index. The developed multi-SOM algorithm is compared to k-means and Birch methods. Results show that it is more efficient than classical clustering methods.

Keywords: clustering, SOM, multi-SOM, DB index, Dunn index, silhouette index

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Authors: Ali Allahverdi, Harun Aydilek, Asiye Aydilek

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Minimizing the number of tardy jobs is an important factor to consider while making scheduling decisions. This is because on-time shipments are vital for lowering cost and increasing customers’ satisfaction. This paper addresses the single machine scheduling problem with the objective of minimizing the number of tardy jobs. The only known information is the lower and upper bounds for processing times, and deterministic job due dates. A dominance relation is established, and an algorithm is proposed. Several heuristics are generated from the proposed algorithm. Computational analysis indicates that the performance of one of the heuristics is very close to the optimal solution, i.e., on average, less than 1.5 % from the optimal solution.

Keywords: single machine scheduling, number of tardy jobs, heuristi, lower and upper bounds

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Authors: Mari Chaikovskaia, Jean-Philippe Gayon, Alain Quilliot

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We consider a fleet of elementary robots that can be connected in different ways to transport loads of different types. For instance, a single robot can transport a small load, and the association of two robots can either transport a large load or two small loads. We seek to determine the optimal number of robots to transport a set of loads in a given time interval, with or without reconfiguration. We show that the problem with reconfiguration is strongly NP-hard by a reduction to the bin-packing problem. Then, we study a special case with unit capacities and derive simple formulas for the minimum number of robots, up to 3 types of loads. For this special case, we compare the minimum number of robots with or without reconfiguration and show that the gain is limited in absolute value but may be significant for small fleets.

Keywords: fleet sizing, reconfigurability, robots, transportation

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Authors: Hossein Shokouhmand, Seyyed Mostafa Saadat

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In this paper, the effect of thermal dispersion on the performance of plate heat exchangers (PHEs) with sinusoidal plates is investigated. In this regard, the PHE is considered as a porous medium. The important property of a porous medium is porosity that is defined as the total fluid volume divided by the total volume occupied by the solid and fluid. A 2D array of parallel sinusoidal plates with laminar periodically developed forced convection and single-phase constant property flows and conduction in a homogenous solid phase in two directions is considered. The array of flows is counter and the flows heat capacities are equal. Numerical study of conjugate heat transfer and axial conduction in the solid phase with different plate thicknesses showed that there is an optimal porosity in which the efficiency of heat transfer is up to 4% more than the time when the porosity is near one. It is shown that the optimal porosity at zero angle of inclination depends both on Reynolds number and the aspect ratio. The optimal porosity increased while either the Reynolds number or waviness of plates increased.

Keywords: plate heat exchanger, optimal porosity, efficiency, aspect ratio

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Authors: Nathakhun Wiroonsri

Abstract:

There are various cluster validity measures used for evaluating clustering results. One of the main objectives of using these measures is to seek the optimal unknown number of clusters. Some measures work well for clusters with different densities, sizes and shapes. Yet, one of the weaknesses that those validity measures share is that they sometimes provide only one clear optimal number of clusters. That number is actually unknown and there might be more than one potential sub-optimal option that a user may wish to choose based on different applications. We develop two new cluster validity indices based on a correlation between an actual distance between a pair of data points and a centroid distance of clusters that the two points are located in. Our proposed indices constantly yield several peaks at different numbers of clusters which overcome the weakness previously stated. Furthermore, the introduced correlation can also be used for evaluating the quality of a selected clustering result. Several experiments in different scenarios, including the well-known iris data set and a real-world marketing application, have been conducted to compare the proposed validity indices with several well-known ones.

Keywords: clustering algorithm, cluster validity measure, correlation, data partitions, iris data set, marketing, pattern recognition

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Authors: M. F. F. Ab Rashid, A. N. Mohd Rose, N. M. Z. Nik Mohamed, W. S. Wan Harun, S. A. Che Ghani

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Traveling salesman problem with precedence constraint (TSPPC) is one of the most complex problems in combinatorial optimization. The existing algorithms to solve TSPPC cost large computational time to find the optimal solution. The purpose of this paper is to present an efficient genetic algorithm that guarantees optimal solution with less number of generations and iterations time. Unlike the existing algorithm that generates priority factor as chromosome, the proposed algorithm directly generates sequence of solution as chromosome. As a result, the proposed algorithm is capable of generating optimal solution with smaller number of generations and iteration time compare to existing algorithm.

Keywords: traveling salesman problem, sequencing, genetic algorithm, precedence constraint

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Authors: Amir Bak Khoshnevis, Mahdieh Khodadadi, Aghil Lotfi

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For a bluff body, roughness elements in simulating a turbulent boundary layer, leading to delayed flow separation, a smaller wake, and lower form drag. In the present work, flow past a circular cylinder with using tripping wires is studied experimentally. The wind tunnel used for modeling free stream is open blow circuit (maximum speed = 30m/s and maximum turbulence of free stream = 0.1%). The selected Reynolds number for all tests was constant (Re = 25000). The circular cylinder selected for this experiment is 20 and 400mm in diameter and length, respectively. The aim of this research is to find the optimal operation mode. In this study installed some tripping wires 1mm in diameter, with a different number of wires on the circular cylinder and the wake characteristics of the circular cylinder is studied. Results showed that by increasing number of tripping wires attached to the circular cylinder (6, 8, and 10, respectively), The optimal angle for the tripping wires with 1mm in diameter to be installed on the cylinder is 60̊ (or 6 wires required at angle difference of 60̊). Strouhal number for the cylinder with tripping wires 1mm in diameter at angular position 60̊ showed the maximum value.

Keywords: wake of circular cylinder, trip wire, velocity defect, strouhal number

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Authors: Satyendra Pratap Singh, S. P. Singh

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This paper presents a methodology using Gravitational Search Algorithm for optimal placement of Phasor Measurement Units (PMUs) in order to achieve complete observability of the power system. The objective of proposed algorithm is to minimize the total number of PMUs at the power system buses, which in turn minimize installation cost of the PMUs. In this algorithm, the searcher agents are collection of masses which interact with each other using Newton’s laws of gravity and motion. This new Gravitational Search Algorithm based method has been applied to the IEEE 14-bus, IEEE 30-bus and IEEE 118-bus test systems. Case studies reveal optimal number of PMUs with better observability by proposed method.

Keywords: gravitational search algorithm (GSA), law of motion, law of gravity, observability, phasor measurement unit

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Authors: Mohammad Amin Hamedirad, Seyed Javad Vaziri Kang Olyaei

Abstract:

Project planning and control are one of the most critical issues in the management of construction projects. Traditional methods of project planning and control, such as the critical path method or Gantt chart, are not widely used for planning projects with discrete and repetitive activities, and one of the problems of project managers is planning the implementation process and optimal allocation of its resources. Massive concreting projects is also a project with discrete and repetitive activities. This study uses the concept of simulating discrete events to manage resources, which includes finding the optimal number of resources considering various limitations such as limitations of machinery, equipment, human resources and even technical, time and implementation limitations using analysis of resource consumption rate, project completion time and critical points analysis of the implementation process. For this purpose, the concept of discrete-event simulation has been used to model different stages of implementation. After reviewing the various scenarios, the optimal number of allocations for each resource is finally determined to reach the maximum utilization rate and also to reduce the project completion time or reduce its cost according to the existing constraints. The results showed that with the optimal allocation of resources, the project completion time could be reduced by 90%, and the resulting costs can be reduced by up to 49%. Thus, allocating the optimal number of project resources using this method will reduce its time and cost.

Keywords: simulation, massive concreting, discrete event simulation, resource management

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Authors: Salem Ben Said

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In recent times the decimal number system to which we are accustomed has received serious competition from the binary number system. In this note, an approach is suggested to teaching and learning the binary number system using examples from the real world. More precisely, we will demonstrate the utility of the binary system in describing the optimal strategy to win the Chinese Nim game, and in telegraphy by decoding the hidden message on Perseverance’s Mars parachute written in the language of binary system. Finally, we will answer the question, “why do modern computers prefer the ternary number system instead of the binary system?”. All materials are provided in a format that is conductive to classroom presentation and discussion.

Keywords: binary number system, Nim game, telegraphy, computers prefer the ternary system

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Authors: Zongyan Li, Matt Best

Abstract:

This paper presents an optimization method for reducing the number of input channels and the complexity of the feed-forward NARX neural network (NN) without compromising the accuracy of the NN model. By utilizing the correlation analysis method, the most significant regressors are selected to form the input layer of the NN structure. An application of vehicle dynamic model identification is also presented in this paper to demonstrate the optimization technique and the optimal input layer structure and the optimal number of neurons for the neural network is investigated.

Keywords: correlation analysis, F-ratio, levenberg-marquardt, MSE, NARX, neural network, optimisation

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Authors: Alvaro Javier Ortega

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A large number of companies face the challenge of matching highly-skilled professionals to high-end positions by human resource deployment professionals. However, when the professional list and tasks to be matched are larger than a few dozens, this process result is far from optimal and takes a long time to be made. Therefore, an automated assignment algorithm for this workforce management problem is needed. The majority of companies are divided into several sectors or departments, where trained employees with different experience levels deal with a large number of tasks daily. Also, the execution order of all tasks is of mater consequence, due to some of these tasks just can be run it if the result of another task is provided. Thus, a wrong execution order leads to large waiting times between consecutive tasks. The desired goal is, therefore, creating accurate matches and a near-optimal execution order that maximizes the number of tasks performed and minimizes the idle time of the expensive skilled employees. The problem described before can be model as a mixed-integer non-linear programming (MINLP) as it will be shown in detail through this paper. A large number of MINLP algorithms have been proposed in the literature. Here, genetic algorithm solutions are considered and a comparison between two different mutation approaches is presented. The simulated results considering different complexity levels of assignment decisions show the appropriateness of the proposed model.

Keywords: employees, genetic algorithm, industry management, workforce

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Authors: R. Rajabpour, N. Talebbeydokhti, M. H. Ahmadi

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In recent years, new techniques for solving complex problems in engineering are proposed. One of these techniques is JPSO algorithm. With innovative changes in the nature of the jump algorithm JPSO, it is possible to construct a graph-based solution with a new algorithm called G-JPSO. In this paper, a new algorithm to solve the optimal control problem Fletcher-Powell and optimal control of pumps in water distribution network was evaluated. Optimal control of pumps comprise of optimum timetable operation (status on and off) for each of the pumps at the desired time interval. Maximum number of status on and off for each pumps imposed to the objective function as another constraint. To determine the optimal operation of pumps, a model-based optimization-simulation algorithm was developed based on G-JPSO and JPSO algorithms. The proposed algorithm results were compared well with the ant colony algorithm, genetic and JPSO results. This shows the robustness of proposed algorithm in finding near optimum solutions with reasonable computational cost.

Keywords: G-JPSO, operation, optimization, pumping station, water distribution networks

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Authors: Harshith Gowda K. S, Tejaskumar N, Shubhanga R. B, Gowtham N, Deekshith Gowda H. S

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Phasor measurement units (PMU) are playing an important role in the current power system for state estimation. It is necessary to have complete observability of the power system while minimizing the cost. For this purpose, the optimal location of the phasor measurement units in the power system is essential. In a bus system, zero injection buses need to be evaluated to minimize the number of PMUs. In this paper, the optimization problem is formulated using mixed integer programming to obtain the optimal location of the PMUs with increased observability. The formulation consists of with and without zero injection bus as constraints. The formulated problem is simulated using a CPLEX solver in the GAMS software package. The proposed method is tested on IEEE 30, IEEE 39, IEEE 57, and IEEE 118 bus systems. The results obtained show that the number of PMUs required is minimal with increased observability.

Keywords: PMU, observability, mixed integer programming (MIP), zero injection buses (ZIB)

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Authors: Zongjie Wang, Zhizhong Guo

Abstract:

While the regular optimal power flow model focuses on a single time scan, the optimization of power systems is typically intended for a time duration with respect to a desired objective function. In this paper, a temporal optimal power flow model for a time period is proposed. To reduce the computation burden needed for calculating temporal optimal power flow, a characteristic optimal power flow model is proposed, which employs different characteristic load patterns to represent the objective function and security constraints. A numerical method based on the interior point method is also proposed for solving the characteristic optimal power flow model. Both the temporal optimal power flow model and characteristic optimal power flow model can improve the systems’ desired objective function for the entire time period. Numerical studies are conducted on the IEEE 14 and 118-bus test systems to demonstrate the effectiveness of the proposed characteristic optimal power flow model.

Keywords: optimal power flow, time period, security, economy

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Authors: Getachew Tilahun, Oluwole Makinde, David Malonza

Abstract:

We propose and analyze a non-linear mathematical model for the transmission dynamics of pneumonia disease in a population of varying size. The deterministic compartmental model is studied using stability theory of differential equations. The effective reproduction number is obtained and also the local and global asymptotically stability conditions for the disease free and as well as for the endemic equilibria are established. The model exhibit a backward bifurcation and the sensitivity indices of the basic reproduction number to the key parameters are determined. Using Pontryagin’s maximum principle, the optimal control problem is formulated with three control strategies; namely disease prevention through education, treatment and screening. The cost effectiveness analysis of the adopted control strategies revealed that the combination of prevention and treatment is the most cost effective intervention strategies to combat the pneumonia pandemic. Numerical simulation is performed and pertinent results are displayed graphically.

Keywords: cost effectiveness analysis, optimal control, pneumonia dynamics, stability analysis, numerical simulation

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Authors: S. Sadallah

Abstract:

In this paper, dynamic programming is used to determine the optimal management of financial resources in company. Solution of the problem by consider into simpler substructures is constructed. The optimal management of internal capital of company are simulated. The tools applied in this development are based on graph theory. The software of given problems is built by using greedy algorithm. The obtained model and program maintenance enable us to define the optimal version of management of proper financial flows by using visual diagram on each level of investment.

Keywords: management, software, optimal, greedy algorithm, graph-diagram

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Authors: Hossein Kheiri, Bashir Naderi, Mohamad Reza Niknam

Abstract:

In this paper we study the optimal synchronization of chaotic T-system with complete uncertain parameter. Optimal control laws and parameter estimation rules are obtained by using Hamilton-Jacobi-Bellman (HJB) technique and Lyapunov stability theorem. The derived control laws are optimal adaptive control and make the states of drive and response systems asymptotically synchronized. Numerical simulation shows the effectiveness and feasibility of the proposed method.

Keywords: Lyapunov stability, synchronization, chaos, optimal control, adaptive control

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Authors: Vahid Rashtchi, Ashkan Pirooz

Abstract:

This paper applies the Imperialist Competitive Algorithm (ICA) to find the optimal place and size of Static Compensator (STATCOM) in power systems. The output of the algorithm is a two dimensional array which indicates the best bus number and STATCOM's optimal size that minimizes all bus voltage deviations from their nominal value. Simulations are performed on IEEE 5, 14, and 30 bus test systems. Also some comparisons have been done between ICA and the famous Particle Swarm Optimization (PSO) algorithm. Results show that how this method can be considered as one of the most precise evolutionary methods for the use of optimum compensator placement in electrical grids.

Keywords: evolutionary computation, imperialist competitive algorithm, power systems compensation, static compensators, voltage profile

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Authors: Ehsan Motamedian

Abstract:

Finding all optimal flux distributions of a metabolic model is an important challenge in systems biology. In this paper, a new algorithm is introduced to identify all alternate optimal solutions of a large scale metabolic network. The algorithm reduces the model to decrease computations for finding optimal solutions. The algorithm was implemented on the Escherichia coli metabolic model to find all optimal solutions for lactate and acetate production. There were more optimal flux distributions when acetate production was optimized. The model was reduced from 1076 to 80 variable fluxes for lactate while it was reduced to 91 variable fluxes for acetate. These 11 more variable fluxes resulted in about three times more optimal flux distributions. Variable fluxes were from 12 various metabolic pathways and most of them belonged to nucleotide salvage and extra cellular transport pathways.

Keywords: flux variability, metabolic network, mixed-integer linear programming, multiple optimal solutions

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