scholarly journals Optimal control of fractional integro-differential systems based on a spectral method and grey wolf optimizer

2020 ◽  
Vol 10 (1) ◽  
pp. 55-65 ◽  
Author(s):  
Raheleh Khanduzi ◽  
Asyieh Ebrahimzadeh ◽  
Samaneh Panjeh Ali Beik
Keyword(s):  
Optimal Control ◽  
Search Algorithm ◽  
Optimal Solution ◽  
Approximate Solutions ◽  
Grey Wolf Optimizer ◽  
Grey Wolf ◽  
Optimal Value ◽  
Local Methods ◽  
The Cost ◽  
Solution Accuracy

This paper elaborated an effective and robust metaheuristic algorithm with acceptable performance based on solution accuracy. The algorithm applied in solution of the optimal control of fractional Volterra integro-differential (FVID) equation which be substituted by nonlinear programming (NLP). Subsequently the FIVD convert the problem to a NLP by using spectral collocation techniques and thereafter we execute the grey wolf optimizer (GWO) to improve the speed and accuracy and find the solutions of the optimal control and state as well as the optimal value of the cost function. It is mentioned that the utilization of the GWO is simple, due to the fact that the GWO is global search algorithm, the method can be applied to find optimal solution of the NLP. The efficiency of the proposed scheme is shown by the results obtained in comparison with the local methods. Further, some illustrative examples introduced with their approximate solutions and the results of the present approach compared with those achieved using other methods.

scholarly journals Smart Energy Management of Residential Microgrid System by a Novel Hybrid MGWOSCACSA Algorithm

Energies ◽  
2020 ◽  
Vol 13 (13) ◽  
pp. 3500 ◽  
Author(s):  
Bishwajit Dey ◽  
Fausto Pedro García Márquez ◽  
Sourav Kr. Basak
Keyword(s):  
Low Voltage ◽  
Search Algorithm ◽  
Hybrid Approach ◽  
Energy Resources ◽  
Grey Wolf Optimizer ◽  
Grey Wolf ◽  
Renewable Energy Resources ◽  
Generation Cost ◽  
Sine Cosine Algorithm ◽  
The Impact

Optimal scheduling of distributed energy resources (DERs) of a low-voltage utility-connected microgrid system is studied in this paper. DERs include both dispatchable fossil-fueled generators and non-dispatchable renewable energy resources. Various real constraints associated with adjustable loads, charging/discharging limitations of battery, and the start-up/shut-down time of the dispatchable DERs are considered during the scheduling process. Adjustable loads are assumed to the residential loads which either operates throughout the day or for a particular period during the day. The impact of these loads on the generation cost of the microgrid system is studied. A novel hybrid approach considers the grey wolf optimizer (GWO), sine cosine algorithm (SCA), and crow search algorithm (CSA) to minimize the overall generation cost of the microgrid system. It has been found that the generation costs rise 50% when the residential loads were included along with the fixed loads. Active participation of the utility incurred 9–17% savings in the system generation cost compared to the cases when the microgrid was operating in islanded mode. Finally, statistical analysis has been employed to validate the proposed hybrid Modified Grey Wolf Optimization-Sine Cosine Algorithm-Crow Search Algorithm (MGWOSCACSA) over other algorithms used.

scholarly journals An Improved Grey Wolf Optimizer for a Supplier Selection and Order Quantity Allocation Problem

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1457
Author(s):  
Avelina Alejo-Reyes ◽  
Erik Cuevas ◽  
Alma Rodríguez ◽  
Abraham Mendoza ◽  
Elias Olivares-Benitez
Keyword(s):  
Supplier Selection ◽  
Search Strategy ◽  
Optimization Problems ◽  
Displacement Vector ◽  
Optimal Solution ◽  
Optimization Techniques ◽  
Grey Wolf Optimizer ◽  
Grey Wolf ◽  
Order Quantity ◽  
Hunting Behavior

Supplier selection and order quantity allocation have a strong influence on a company’s profitability and the total cost of finished products. From an optimization perspective, the processes of selecting the right suppliers and allocating orders are modeled through a cost function that considers different elements, such as the price of raw materials, ordering costs, and holding costs. Obtaining the optimal solution for these models represents a complex problem due to their discontinuity, non-linearity, and high multi-modality. Under such conditions, it is not possible to use classical optimization methods. On the other hand, metaheuristic schemes have been extensively employed as alternative optimization techniques to solve difficult problems. Among the metaheuristic computation algorithms, the Grey Wolf Optimization (GWO) algorithm corresponds to a relatively new technique based on the hunting behavior of wolves. Even though GWO allows obtaining satisfying results, its limited exploration reduces its performance significantly when it faces high multi-modal and discontinuous cost functions. In this paper, a modified version of the GWO scheme is introduced to solve the complex optimization problems of supplier selection and order quantity allocation. The improved GWO method called iGWO includes weighted factors and a displacement vector to promote the exploration of the search strategy, avoiding the use of unfeasible solutions. In order to evaluate its performance, the proposed algorithm has been tested on a number of instances of a difficult problem found in the literature. The results show that the proposed algorithm not only obtains the optimal cost solutions, but also maintains a better search strategy, finding feasible solutions in all instances.

scholarly journals An Improved Grey Wolf Optimizer Based on Differential Evolution and OTSU Algorithm

2020 ◽  
Vol 10 (18) ◽  
pp. 6343
Author(s):  
Yuanyuan Liu ◽  
Jiahui Sun ◽  
Haiye Yu ◽  
Yueyong Wang ◽  
Xiaokang Zhou
Keyword(s):  
Differential Evolution ◽  
Image Recognition ◽  
Optimal Solution ◽  
Tsallis Entropy ◽  
Grey Wolf Optimizer ◽  
Initial Population ◽  
Grey Wolf ◽  
Particle Swarm Optimizer ◽  
De Algorithm ◽  
Local Optimal Solution

Aimed at solving the problems of poor stability and easily falling into the local optimal solution in the grey wolf optimizer (GWO) algorithm, an improved GWO algorithm based on the differential evolution (DE) algorithm and the OTSU algorithm is proposed (DE-OTSU-GWO). The multithreshold OTSU, Tsallis entropy, and DE algorithm are combined with the GWO algorithm. The multithreshold OTSU algorithm is used to calculate the fitness of the initial population. The population is updated using the GWO algorithm and the DE algorithm through the Tsallis entropy algorithm for crossover steps. Multithreshold OTSU calculates the fitness in the initial population and makes the initial stage basically stable. Tsallis entropy calculates the fitness quickly. The DE algorithm can solve the local optimal solution of GWO. The performance of the DE-OTSU-GWO algorithm was tested using a CEC2005 benchmark function (23 test functions). Compared with existing particle swarm optimizer (PSO) and GWO algorithms, the experimental results showed that the DE-OTSU-GWO algorithm is more stable and accurate in solving functions. In addition, compared with other algorithms, a convergence behavior analysis proved the high quality of the DE-OTSU-GWO algorithm. In the results of classical agricultural image recognition problems, compared with GWO, PSO, DE-GWO, and 2D-OTSU-FA, the DE-OTSU-GWO algorithm had accuracy in straw image recognition and is applicable to practical problems. The OTSU algorithm improves the accuracy of the overall algorithm while increasing the running time. After adding the DE algorithm, the time complexity will increase, but the solution time can be shortened. Compared with GWO, DE-GWO, PSO, and 2D-OTSU-FA, the DE-OTSU-GWO algorithm has better results in segmentation assessment.

Self-adaptive multi-purpose Grey Wolf optimization for efficient routing of wireless ad hoc networks

2018 ◽  
Vol 09 (05) ◽  
pp. 1850036
Author(s):  
Sandeep Raskar ◽  
Kamatchi Iyer
Keyword(s):  
Wireless Ad Hoc Networks ◽  
Ad Hoc ◽  
Routing Algorithm ◽  
Network Routing ◽  
Grey Wolf Optimizer ◽  
Grey Wolf ◽  
Least Cost Path ◽  
Shortest Path Routing ◽  
Hoc Networks ◽  
The Cost

One of the well-known issues in the field of network routing is the Shortest Path Routing (SPR). The objective is to find the least-cost path with minimum delay and link breaks. Even though there are many algorithms to solve SPR, the cost, as well as link breaks, are indeed more thought-provoking in the real-time application. This paper intends to develop a routing approach that solves the challenges like route establishment and route recovery. The selection of the optimal route is done by adopting a generalized multi-purpose optimization algorithm named Grey Wolf Optimizer. Along with this, this paper adopts Neural Network (NN) to predict the node movements in the ad hoc network. The proposed routing algorithm is compared to the conventional approaches, and the significance of the approach is described clearly.

scholarly journals Developing Software of Global Optimization Method Based on Grey Wolf Optimizer

2021 ◽  
Vol 11 (2) ◽  
pp. 59-73
Author(s):  
A.V. Panteleev ◽  
I.A. Belyakov
Keyword(s):  
Optimization Method ◽  
Step Function ◽  
Algorithm Analysis ◽  
Grey Wolf Optimizer ◽  
Grey Wolf ◽  
Test Functions ◽  
Global Extremum ◽  
The Cost ◽  
Bioinspired Algorithms ◽  
Selection Of

This article discusses the development of software that allows to simulate the algorithm of the “Grey Wolf Optimizer” method. This algorithm belongs to the class of metaheuristic algorithms that allow finding a global extremum on a set of admissible solutions. This algorithm is being the most efficiently used in a situation where the cost function is specified in the form of a black box. The algorithm belongs to both bioinspired algorithms and to the class of algorithms of Particle Swarm Optimization. To analyze the efficiency of the algorithm, software was created that allows to vary the parameters of the method. The article contains examples of the program’s work on various test functions. The purpose of the program is to collect and analyze statistical results, making possible to evaluate the final result. The program provides to build graphs that make it possible to make a more thorough assessment of the results obtained. The program has a step-by-step function that allows one to analyze the specifics and features of the algorithm. Analysis of statistical data provides more detailed selection of the parameters of the algorithm.

Software Release Planning Using Grey Wolf Optimizer

2020 ◽  
pp. 1-44
Author(s):  
Vibha Verma ◽  
Neha Neha ◽  
Anu G. Aggarwal
Keyword(s):  
Optimization Problems ◽  
Cost Model ◽  
Optimal Solution ◽  
Reduction Factor ◽  
Grey Wolf Optimizer ◽  
Reliability Growth ◽  
Grey Wolf ◽  
Software Cost ◽  
Release Planning ◽  
Software Release

This chapter presents the application of grey wolf optimizer in software release planning considering warranty based on the proposed mathematical model that measures reliability growth of software systems. Hence, optimal release and warranty time is determined while minimizing the overall software development cost. The software cost model is based on failure phenomenon modelled by incorporating fault removal efficiency, fault reduction factor, and error generation. The model has been validated on the fault dataset of ERP systems. Sensitivity analysis has been carried out to study the discrete changes in the cost parameter due to changes in optimal solution. The work significantly contributes to the literature by fulfilling gaps of reliability growth models, release problems considering warranty, and efficient ways for solving optimization problems. Further, the grey wolf optimizer result has been compared with genetic algorithm and particle swarm optimization techniques.

scholarly journals A Note on Optimal Control Problem Governed by Schrödinger Equation

Open Physics ◽  
2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Yusuf Koçak ◽  
Ercan Çelik ◽  
Nigar Yıldırım Aksoy
Keyword(s):  
Optimal Control ◽  
Variational Inequality ◽  
Schrödinger Equation ◽  
Optimal Control Problem ◽  
Existence And Uniqueness ◽  
Schrodinger Equation ◽  
Optimal Solution ◽  
Necessary Condition ◽  
Existence And Uniqueness Theorem ◽  
The Cost

AbstractIn this work, we present some results showing the controllability of the linear Schrödinger equation with complex potentials. Firstly we investigate the existence and uniqueness theorem for solution of the considered problem. Then we find the gradient of the cost functional with the help of Hamilton-Pontryagin functions. Finally we state a necessary condition in the form of variational inequality for the optimal solution using this gradient.

scholarly journals Modified Discrete Grey Wolf Optimizer Algorithm for Multilevel Image Thresholding

2017 ◽  
Vol 2017 ◽  
pp. 1-16 ◽  
Author(s):  
Linguo Li ◽  
Lijuan Sun ◽  
Jian Guo ◽  
Jin Qi ◽  
Bin Xu ◽  
...  
Keyword(s):  
Image Segmentation ◽  
Optimal Solution ◽  
Weight Coefficient ◽  
Grey Wolf Optimizer ◽  
Grey Wolf ◽  
Original Algorithm ◽  
Image Thresholding ◽  
Bee Colony ◽  
Optimal Thresholds ◽  
Objective Function Values

The computation of image segmentation has become more complicated with the increasing number of thresholds, and the option and application of the thresholds in image thresholding fields have become an NP problem at the same time. The paper puts forward the modified discrete grey wolf optimizer algorithm (MDGWO), which improves on the optimal solution updating mechanism of the search agent by the weights. Taking Kapur’s entropy as the optimized function and based on the discreteness of threshold in image segmentation, the paper firstly discretizes the grey wolf optimizer (GWO) and then proposes a new attack strategy by using the weight coefficient to replace the search formula for optimal solution used in the original algorithm. The experimental results show that MDGWO can search out the optimal thresholds efficiently and precisely, which are very close to the result examined by exhaustive searches. In comparison with the electromagnetism optimization (EMO), the differential evolution (DE), the Artifical Bee Colony (ABC), and the classical GWO, it is concluded that MDGWO has advantages over the latter four in terms of image segmentation quality and objective function values and their stability.

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