Minimum Number Of Iterations Research Articles

Vehicle routing problems based on Harris Hawks optimization

The vehicle routing problem (VRP) is one of the challenging problems in optimization and can be described as combinatorial optimization and NP-hard problem. Researchers have used many artificial intelligence techniques in order to try to solve this problem. Among these techniques, metaheuristic algorithms that can perform random search are the most promising because they can be used to find the right solution in the shortest possible time. Therefore, in this paper, the Harris hawks optimization (HHO) algorithm was used to attempt to solve the VRP. The algorithm was applied to 10 scenarios and the experimental results revealed that the HHO had a strong ability to check for and find the best route as compared to other metaheuristic algorithms, namely, simulated annealing and artificial bee colony optimization. The comparison was based on three criteria: minimum objective function obtained, minimum number of iterations required and satisfaction of capacity constraints. In all scenarios, the HHO showed clear superiority over the other methods.

Improving the Techno-Economic Pattern for Distributed Generation-Based Distribution Networks via Nature-Inspired Optimization Algorithms

The massive increase in the utilization of Distributed Generation (DG) units in the traditional Electric Distribution Networks (EDNs) enforces the distribution companies’ operators to enhance the technical performance of EDNs while considering economic perspectives. This challenge paves the way for developing a multi-objective optimization platform to tackle the techno-economic problems while respecting system uncertainties as well as the operational policy of the distribution companies. As a motivating solution for this multi-objective problem, this paper introduces the application of three nature-inspired algorithms as multi-objective optimization techniques for enhancing the techno-economic performance of EDNs through the integration of multiple Renewable Energy Resources (RERs). Grasshopper Optimization Algorithm (GOA), Salp Swarm Algorithm (SSA) and Moth Flame Optimization Algorithm (MFO), have been employed in this comparative study to minimize the active power losses, enhance the Fast Voltage Stability Index (FVSI) and reduce the total costs, considering the penetration level specified margin as well as and the framework of the DG units’ operating power factor constraints. The proposed algorithms have been implemented in the MATLAB environment and applied on various benchmark IEEE test systems (33-bus, 57-bus and 300-bus) as a mimic, small and large EDNs. A realistic part of the Egyptian distribution network (171-bus) is also introduced as a practical, applicable case study. The attained results show that the suggested optimization platform especially using MFO, is more effective and successful in determining and finding the optimal locations and capacities of different DG types for getting the optimal value of the objective function in minimum time within a minimum number of iterations.

New Approach to Obtain the Maximum Flow in a Network and Optimal Solution for the Transportation Problems

The maximum flow problem is also one of the highly regarded problems in the field of optimization theory in which the objective is to find a feasible flow through a flow network that obtains the maximum possible flow rate from source to sink. The literature demonstrates that different techniques have been developed in the past to handle the maximum amount of flow that the network can handle. The Ford-Fulkerson algorithm and Dinic's Algorithm are the two major algorithms for solving these types of problems. Also, the Max-Flow Min-Cut Theorem, the Scaling Algorithm, and the Push–relabel maximum flow algorithm are the most acceptable methods for finding the maximum flows in a flow network. In this novel approach, the paper develops an alternative method of finding the maximum flow between the source and target nodes of a network based on the "max-flow." Also, a new algorithmic approach to solving the transportation problem (minimizing the transportation cost) is based upon the new maximum flow algorithm. It is also to be noticed that this method requires a minimum number of iterations to achieve optimality. This study's algorithmic approach is less complicated than the well-known meta-heuristic algorithms in the literature. 

Calibração multi-objetivo do Tank Model utilizando diversos algoritmos genéticos e critérios de parada

ABSTRACT Calibration of hydrologic models estimates parameter values that cannot be measured and enable the rainfall-runoff processes simulation. Multi-objective evolutionary algorithms can make the calibration faster and more efficient through an iterative process. However, the standard stopping criterion used to stop the iterative process is to reach a pre-defined number of iterations defined by the modeller. Alternatively, the Ticona stopping criterion is based on the minimum number of iterations required to achieve a determined number of non-dominated solutions in the Pareto front, resulting in a reduction of the computational time without losing performance during the calibration processes. We evaluated the Ticona stopping criterion in the Tank Model calibration. The calibration processes were performed using data from two river basins, with three genetic algorithms and two objective functions. The Ticona stopping criterion required a computational time 27.4% to 44.1% lower than using the standard stopping criterion and were obtaining similar results in simulated streamflow time series and similar values of the best set of parameters.

A New Three-Step Root-Finding Numerical Method and Its Fractal Global Behavior

There is an increasing demand for numerical methods to obtain accurate approximate solutions for nonlinear models based upon polynomials and transcendental equations under both single and multivariate variables. Keeping in mind the high demand within the scientific literature, we attempt to devise a new nonlinear three-step method with tenth-order convergence while using six functional evaluations (three functions and three first-order derivatives) per iteration. The method has an efficiency index of about 1.4678, which is higher than most optimal methods. Convergence analysis for single and systems of nonlinear equations is also carried out. The same is verified with the approximated computational order of convergence in the absence of an exact solution. To observe the global fractal behavior of the proposed method, different types of complex functions are considered under basins of attraction. When compared with various well-known methods, it is observed that the proposed method achieves prespecified tolerance in the minimum number of iterations while assuming different initial guesses. Nonlinear models include those employed in science and engineering, including chemical, electrical, biochemical, geometrical, and meteorological models.

Optimisation of Thresholds in Probabilistic Rough Sets with Artificial Bee Colony Algorithm

The Probabilistic Rough Sets (PRS) theory determines the certainty of an object's inclusion into a class, resulting in the division of the entire data set into three regions under a concept. These regions, namely the positive, negative and boundary regions, are generated using an evaluation function and threshold values. The threshold optimisation and the construction and interpretation of an evaluation function offer various methods in the background. Even though most of the methods in the PRS follow an iterative strategy, they lack a common framework, usually affecting the comparison and overall performance evaluation among these methods. This proposed work aims to minimise the uncertainty in three regions via optimising the thresholds using the Artificial Bee Colony (ABC) algorithm. The ABC algorithm is adapted to generate a common framework that results in different optimal pairs of thresholds with a minimum number of iterations. By considering the probabilistic information about an equivalence class structure, we compare the results obtained from the proposed approach with the state-of-the-art methods like Information-Theoretic Rough Sets, Game-Theoretic Rough sets and Genetic Algorithm-based optimisation. The results reveal that the proposed algorithm outperforms existing techniques and leads to a superior method for threshold optimisation in the PRS.

Implementation of Structural Assemblies by Simultaneous Projection and Density-Based Topology Optimization

This article proposed a methodology that combines two well-known projections and modified density-based optimized techniques in one formulation methodology. This methodology contains an effective explicit geometric entity identified by shape variables that provide easy control in desired particular regions; implicit density-based topological optimization entities utilized topological variables that offer critical design elsewhere. Our main attractive key point of this combined formulation approach is structural assemblies. Structure always manufactures in many patches and joins them by utilizing the structural assemblies such as welding and riveting. It is not easy to execute the structural patches at the required region without acknowledging their dimensions. This proposed approach demonstrates the competence to impose the restrictions related to shape and topological variables of interfaces among the specific patches. Numerous standard numerical examples make sure the validation of the introduced methodology. It remarked that the optimal design could minimize compliance and the minimum number of iterations through numerically performed, concerning computational cost minimized without any kind loss of accuracy of the final structure.

A Novel UCP Model Based on Artificial Neural Networks and Orthogonal Arrays

Adequate estimation is a crucial factor for the implementation of software projects within set customer requirements. The use of Case Point Analysis (UCP) is the latest and most accurate method for estimating the effort and cost of realizing software products. This paper will present a new, improved UCP model constructed based on two different artificial neural network (ANN) architectures based on Taguchi Orthogonal Vector Plans. ANNs are an exceptional artificial intelligence tool that have been proven to be reliable and stable in this area of software engineering. The Taguchi method of Orthogonal Vector Plans is an optimization method that reduces the number of iterations required, which significantly shortens estimation time. The goal is to construct models that give a minimum magnitude relative error (MRE) value concerning previous approaches and techniques. A minimum number of iterations (less than six) and a minimum value of MMRE (less than 10%) have been achieved. The obtained results significantly improve the accuracy and reliability of estimating the effort and cost involved in the implementation of software projects.

Generalized Refinement of Gauss-Seidel Method for Consistently Ordered 2-Cyclic Matrices

This paper presents generalized refinement of Gauss-Seidel method of solving system of linear equations by considering consistently ordered 2-cyclic matrices. Consistently ordered 2-cyclic matrices are obtained while finite difference method is applied to solve differential equation. Suitable theorems are introduced to verify the convergence of this proposed method. To observe the effectiveness of this method, few numerical examples are given. The study points out that, using the generalized refinement of Gauss-Seidel method, we obtain a solution of a problem with a minimum number of iteration and obtain a greater rate of convergence than other previous methods.

Measuring the impact of the stock market index return on stocks return using the stochastic approximation

Value at Risk (VAR) is a risk measure frequently used in market finance. This tool gives an idea of the losses that may occur to a financial asset (share or option), but does not predict when these losses may occur. The objective of our work is to propose a method that allows us to know the state of the economy necessary for Microsoft's performance to suffer extreme losses with alpha probability. This represents a significant asset for investors to consider before trading on the stock market. To answer this problem, we will try to explain the VAR using the ROBBINS-MONRO-JOSEPH procedure for the estimation of a percentile for binary variables, as a function of a systemic risk factor. We will also propose a method for applying the procedure without using real-time experiments. We are going to estimate the different parameters of the process, based on the history of the data available for statistical modelling, then analyse the results of the convergence of the process over the iterations, and finally see the impact of adding a random element to the binary variable of the process on convergence. The final results are satisfying and seem to be in line with reality, but there is room for improvement, either by increasing the number of iterations needed to refine convergence, whereas the stochastic approximation aims to obtain a good estimate in a minimum number of iterations, or by applying other more recent procedures that show better results following simulations.

FPGA-Based Time-Domain Channel Estimation in Gaussian Mixture Model

The performance of time-domain channel estimation deteriorates due to the presence of Gaussian mixture model (GMM) noise, which results in high mean squared error (MSE) as a challenging issue. The performance of the estimator further decreases when the complexity of the estimator is high due to the high convergence rate. In this paper, an optimized channel estimation method is proposed with low complexity and high accuracy in the GMM environment. In this channel estimation, an improved Gauss-Seidel iterative method is utilized with a minimum number of iterations. The convergence rate of the Gauss-Seidel method is improved by estimating an appropriate initial guess value when no guard bands are used in the orthogonal frequency-division multiplexing (OFDM) symbol. Simulation results provide an acceptable MSE for GMM environments, up to the probability of 5% impulsive noise component. This paper also presents the design and implementation of the proposed estimator in the NEXYS-2 FPGA platform that provides resources allocation, reconfigurability, schematic, and the timing diagram for detailed insight.

The Minimum Number of Iterations Required to Replicate Binary Images using Discrete One-dimensional Dynamical Systems and a Retrocausal Updation Rule

The Minimum Number of Iterations Required to Replicate Binary Images using Discrete One-dimensional Dynamical Systems and a Retrocausal Updation Rule

Chaotic-based particle swarm optimization algorithm for optimal PID tuning in automatic voltage regulator systems

Introduction. In an electrical power system, the output of the synchronous generators varies due to disturbances or sudden load changes. These variations in output severely affect power system stability and power quality. The synchronous generator is equipped with an automatic voltage regulator to maintain its terminal voltage at rated voltage. Several control techniques utilized to improve the response of the automatic voltage regulator system, however, proportional integral derivative (PID) controller is the most frequently used controller but its parameters require optimization. Novelty. In this paper, the chaotic sequence based on the logistic map is hybridized with particle swarm optimization to find the optimal parameters of the PID for the automatic voltage regulator system. The logistic map chaotic sequence-based initialization and global best selection enable the algorithm to escape from local minima stagnation and improve its convergence rate resulting in best optimal parameters. Purpose. The main objective of the proposed approach is to improve the transient response of the automatic voltage regulator system by minimizing the maximum overshoot, settling time, rise time, and peak time values of the terminal voltage, and eliminating the steady-state error. Methods. In the process of parameter tuning, the Chaotic particle swarm optimization technique was run several times through the proposed hybrid objective function, which accommodates the advantages of the two most commonly used objective functions with a minimum number of iterations, and an optimal PID gain value was found. The proposed algorithm is compared with current metaheuristic algorithms including conventional particle swarm optimization, improved kidney algorithm, and others. Results. For performance evaluation, the characteristics of the integral of time multiplied squared error and Zwe-Lee Gaing objective functions are combined. Furthermore, the time-domain analysis, frequency-domain analysis, and robustness analysis are carried out to show the better performance of the proposed algorithm. The result shows that automatic voltage regulator tuned with the chaotic particle swarm optimization based PID yield improvement in overshoot, settling time, and function value of 14.41 %, 37.91 %, 1.73 % over recently proposed IKA, and 43.55 %, 44.5 %, 16.67 % over conventional particle swarm optimization algorithms. The improvement in transient response further improves the automatic voltage regulator system stability for electrical power systems.

Bayesian Optimisation of Large-scale Photonic Reservoir Computers

Reservoir computing is a growing paradigm for simplified training of recurrent neural networks, with a high potential for hardware implementations. Numerous experiments in optics and electronics yield comparable performance with digital state-of-the-art algorithms. Many of the most recent works in the field focus on large-scale photonic systems, with tens of thousands of physical nodes and arbitrary interconnections. While this trend significantly expands the potential applications of photonic reservoir computing, it also complicates the optimisation of the high number of hyper-parameters of the system. In this work, we propose the use of Bayesian optimisation for efficient exploration of the hyper-parameter space in a minimum number of iteration. We test this approach on a previously reported large-scale experimental system, compare it with the commonly used grid search, and report notable improvements in performance and the number of experimental iterations required to optimise the hyper-parameters. Bayesian optimisation thus has the potential to become the standard method for tuning the hyper-parameters in photonic reservoir computing.

Measuring the impact of the stock market index return on stocks return using the stochastic approximation

Value at Risk (VAR) is a risk measure frequently used in market finance. This tool gives an idea of the losses that may occur to a financial asset (share or option), but does not predict when these losses may occur. The objective of our work is to propose a method that allows us to know the state of the economy necessary for Microsoft's performance to suffer extreme losses with alpha probability. This represents a significant asset for investors to consider before trading on the stock market. To answer this problem, we will try to explain the VAR using the ROBBINS-MONRO-JOSEPH procedure for the estimation of a percentile for binary variables, as a function of a systemic risk factor. We will also propose a method for applying the procedure without using real-time experiments. We are going to estimate the different parameters of the process, based on the history of the data available for statistical modelling, then analyse the results of the convergence of the process over the iterations, and finally see the impact of adding a random element to the binary variable of the process on convergence. The final results are satisfying and seem to be in line with reality, but there is room for improvement, either by increasing the number of iterations needed to refine convergence, whereas the stochastic approximation aims to obtain a good estimate in a minimum number of iterations, or by applying other more recent procedures that show better results following simulations.

An Automatic Optimization Technique for the Calibration of a Physically Based Hydrological Rainfall-Runoff Model

Models are tools widely used in the prediction of hydrological phenomena. The present study aims to contribute to the implementation of an automatic optimization strategy of parameters for the calibration of a hydrological model based on the least action principle (HyMoLAP). The Downhill Simplex method is also known as the Nelder-Mead algorithm, which is a heuristic research method, is used to optimize the cost function on a given domain. The performance of the model is evaluated by the Nash Stucliffe Efficiency Index (NSE), the Root Mean Square Error (RMSE), the coefficient of determination (R2), the Mean Absolute Error (MAE). A comparative estimation is conducted using the Nash-Sutcliffe Modeling Efficiency Index and the mean relative error to evaluate the performance of the optimization method. It appears that the variation in water balance parameter values is acceptable. The simulated optimization method appears to be the best in terms of lower variability of parameter values during successive tests. The quality of the parameter sets obtained is good enough to impact the performance of the objective functions in a minimum number of iterations. We have analyzed the algorithm from a technical point of view, and we have carried out an experimental comparison between specific factors such as the model structure and the parameter’s values. The results obtained confirm the quality of the model (NSE = 0.90 and 0.75 respectively in calibration and validation) and allow us to evaluate the efficiency of the Nelder-Mead algorithm in the automatic calibration of the HyMoLAP model. The developed hybrid automatic calibration approach is therefore one of the promising ways to reduce computational time in rainfall-runoff modeling.

Integrating Iterative Machine Teaching and Active Learning into the Machine Learning Loop

Scholars and practitioners are defining new types of interactions between humans and machine learning algorithms that we can group under the umbrella term of Human-in-the-Loop Machine Learning (HITL-ML). This paper is focused on implementing two approaches to this topic—Iterative Machine Teaching (iMT) and Active Learning (AL)—and analyzing how to integrate them in the learning loop. iMT is a variation of Machine Teaching in which a machine acts as a teacher that tries to transfer knowledge to a machine learning model. The focus of the problem in iMT is how to obtain the optimal training set given a machine learning algorithm and a target model. The idea is to learn a target concept with a minimal number of iterations with the smallest dataset. Active Learning, in contrast, is a specialized type of supervised learning in which humans are incorporated in the loop to act as oracles that analyze unlabeled data. AL allows us to achieve greater accuracy with less data and less training. Our proposal to incorporate iMT and AL into the machine learning loop is to use iMT as a technique to obtain the “Minimum Viable Data (MVD)” for training a learning model, that is, a dataset that allows us to increase speed and reduce complexity in the learning process by allowing to build early prototypes. Next, we will use AL to refine this first prototype by adding new data in an iterative and incremental way. We carried out several experiments to test the feasibility of our proposed approach. They show that the algorithms trained with the teachers converge faster than those that have been trained in a conventional way. Also, AL helps the model to avoid getting stuck and to keep improving after the first few iterations. The two approaches investigated in this paper can be considered complementary, as they correspond to different stages in the learning process.

An Effective Alternative New Approach in Solving Transportation Problems

The Transportation problem is one of the most colorful and demanding problems in the history of Operations Research. Many researchers have paid attention to solve the problem using different approaches. In certain approaches focused on finding an initial basic feasible solution and the other to find the optimal solution. It can be noticed that these methods have advantages and disadvantages. Out of all the methods that can be found in the literature, Northwest, Least Cost and Vogel’s Approximation methods are the most prominent and renowned methods in finding an initial basic feasible solution. Also, the Modified Distribution (MODI) Method and Stepping Stone Method are the most acceptable methods in finding the optimal solution to the transportation problem. In this research paper, we propose an alternative method that finds the optimal or nearly optimal solution to the transportation problem. This method which is based on an iterative algorithm can be applied to balance as well as unbalanced transportation problems. It is also to be noticed that this method requires a minimum number of iterations to reach the optimality as compared to the other existing methods. Also, we have developed a new method of finding an optimal solution for both balanced and unbalanced transportation problems.

Cicada Swarm Optimization: A New Method for Optimizing Persistent Problems

This paper proposes a new meta-heuristic swarm optimization algorithm called Cicada Swarm Optimization (CISO) algorithm, which mimics the behavior of bio-inspired swarm optimization methods. The CISO algorithm is tested with 23 benchmark functions and taken two problems engineering design, pressure vessel problem and himmelblau’s problem. The performance of CISO algorithm is compared with meta-heuristic well-known and recently proposed algorithms (Cockroach Swarm Optimization (CSO), Grasshopper Optimization algorithm (GOA) and Particle Swarm Optimization (PSO)). The obtained results showed that the proposed algorithm succeeded in improving the test functions and solved engineering design problems that could not be improved by other algorithms according to the chosen parameters and the limits of the research space, also showed that CISO has a faster convergence with the minimum number of iterations and also have an accurate calculation efficiency Satisfactory compared to other optimization algorithms.

Distinguishability of discrete‐time linear systems

AbstractThis article introduces the notion of absolutely distinguishable discrete‐time dynamic systems, with particular applicability to linear time‐invariant and linear parameter‐varying systems. The motivation for this novel type of distinguishability stems, in particular, from the stability and performance requirements of worst‐case adaptive control methodologies. The main results presented herein show that, in most practical cases, a persistence of excitation type of condition and a minimum number of iterations are required to properly distinguish two dynamic systems. We also demonstrate that the former constraint can be written as a lower bound on the intensity of the exogenous disturbances. The applicability of the developed theory is illustrated with a set of examples.