scholarly journals Optimal solution of the fractional order breast cancer competition model

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
H. Hassani ◽  
J. A. Tenreiro Machado ◽  
Z. Avazzadeh ◽  
E. Safari ◽  
S. Mehrabi
Keyword(s):  
Breast Cancer ◽  
Fractional Order ◽  
Legendre Polynomials ◽  
Numerical Experiments ◽  
Optimal Solution ◽  
Optimization Method ◽  
Competition Model ◽  
Basis Functions ◽  
Cell Populations ◽  
Operational Matrices

AbstractIn this article, a fractional order breast cancer competition model (F-BCCM) under the Caputo fractional derivative is analyzed. A new set of basis functions, namely the generalized shifted Legendre polynomials, is proposed to deal with the solutions of F-BCCM. The F-BCCM describes the dynamics involving a variety of cancer factors, such as the stem, tumor and healthy cells, as well as the effects of excess estrogen and the body’s natural immune response on the cell populations. After combining the operational matrices with the Lagrange multipliers technique we obtain an optimization method for solving the F-BCCM whose convergence is investigated. Several examples show that a few number of basis functions lead to the satisfactory results. In fact, numerical experiments not only confirm the accuracy but also the practicability and computational efficiency of the devised technique.

scholarly journals Optimal Solution of the Fractional Order Breast Cancer Competition Model

2021 ◽  
Author(s):  
H. Hassani ◽  
J. A. Tenreiro Machado ◽  
Zakieh Avazzadeh ◽  
Elaheh Safari ◽  
S. Mehrabi
Keyword(s):  
Breast Cancer ◽  
Fractional Order ◽  
Legendre Polynomials ◽  
General Procedure ◽  
Optimal Solution ◽  
Competition Model ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
Numerical Examples ◽  
Multipliers Method

Abstract This paper discusses the fractional order breast cancer competition model (F-BCCM), which considers population dynamics among cancer stem, tumor and healthy cells, as well as the effects of excess estrogen and the body’s natural immune response on the cell populations. Generalized shifted Legendre polynomials and their operational matrices are presented in the scope of a general procedure for the solution of the F-BCCM. The application of the Lagrange multipliers method transforms the F-BCCM into a system of algebraic equations. Additionally, the convergence analysis of the method and two illustrative numerical examples complement the study.Mathematics Subject Classification: 97M60; 41A58; 92C42.

CONTINUOUS-TIME FRACTIONAL ORDER LINEAR SYSTEMS IDENTIFICATION USING CHEBYSHEV WAVELET

2020 ◽  
Vol 6 (8(77)) ◽  
pp. 23-28
Author(s):  
Shuen Wang ◽  
Ying Wang ◽  
Yinggan Tang
Keyword(s):  
Linear Systems ◽  
Fractional Order ◽  
Continuous Time ◽  
Fractional Integration ◽  
Operational Matrices ◽  
Computation Complexity ◽  
Order Linear ◽  
Fractional Integration Operator ◽  
Systems Identification ◽  
Chebyshev Wavelet

In this paper, the identification of continuous-time fractional order linear systems (FOLS) is investigated. In order to identify the differentiation or- ders as well as parameters and reduce the computation complexity, a novel identification method based on Chebyshev wavelet is proposed. Firstly, the Chebyshev wavelet operational matrices for fractional integration operator is derived. Then, the FOLS is converted to an algebraic equation by using the the Chebyshev wavelet operational matrices. Finally, the parameters and differentiation orders are estimated by minimizing the error between the output of real system and that of identified systems. Experimental results show the effectiveness of the proposed method.

scholarly journals An Adaptive Optimization Method Based on Learning Rate Schedule for Neural Networks

2021 ◽  
Vol 11 (2) ◽  
pp. 850
Author(s):  
Dokkyun Yi ◽  
Sangmin Ji ◽  
Jieun Park
Keyword(s):  
Artificial Intelligence ◽  
Cost Function ◽  
Numerical Experiments ◽  
Global Minimum ◽  
Optimization Method ◽  
Learning Method ◽  
Adaptive Optimization ◽  
The Cost ◽  
Proof Of Convergence ◽  
Learning Data

Artificial intelligence (AI) is achieved by optimizing the cost function constructed from learning data. Changing the parameters in the cost function is an AI learning process (or AI learning for convenience). If AI learning is well performed, then the value of the cost function is the global minimum. In order to obtain the well-learned AI learning, the parameter should be no change in the value of the cost function at the global minimum. One useful optimization method is the momentum method; however, the momentum method has difficulty stopping the parameter when the value of the cost function satisfies the global minimum (non-stop problem). The proposed method is based on the momentum method. In order to solve the non-stop problem of the momentum method, we use the value of the cost function to our method. Therefore, as the learning method processes, the mechanism in our method reduces the amount of change in the parameter by the effect of the value of the cost function. We verified the method through proof of convergence and numerical experiments with existing methods to ensure that the learning works well.

scholarly journals Economic Development Based on a Mathematical Model: An Optimal Solution Method for the Fuel Supply of International Road Transport Activity

Energies ◽  
2021 ◽  
Vol 14 (10) ◽  
pp. 2963
Author(s):  
Melinda Timea Fülöp ◽  
Miklós Gubán ◽  
György Kovács ◽  
Mihály Avornicului
Keyword(s):  
Decision Making ◽  
Ad Hoc ◽  
Market Competition ◽  
Optimal Solution ◽  
Cost Savings ◽  
Cost Effective ◽  
Optimization Method ◽  
Optimal Decision ◽  
Environmental Damage ◽  
Fuel Cost

Due to globalization and increased market competition, forwarding companies must focus on the optimization of their international transport activities and on cost reduction. The minimization of the amount and cost of fuel results in increased competition and profitability of the companies as well as the reduction of environmental damage. Nowadays, these aspects are particularly important. This research aims to develop a new optimization method for road freight transport costs in order to reduce the fuel costs and determine optimal fueling stations and to calculate the optimal quantity of fuel to refill. The mathematical method developed in this research has two phases. In the first phase the optimal, most cost-effective fuel station is determined based on the potential fuel stations. The specific fuel prices differ per fuel station, and the stations are located at different distances from the main transport way. The method developed in this study supports drivers’ decision-making regarding whether to refuel at a farther but cheaper fuel station or at a nearer but more expensive fuel station based on the more economical choice. Thereafter, it is necessary to determine the optimal fuel volume, i.e., the exact volume required including a safe amount to cover stochastic incidents (e.g., road closures). This aspect of the optimization method supports drivers’ optimal decision-making regarding optimal fuel stations and how much fuel to obtain in order to reduce the fuel cost. Therefore, the application of this new method instead of the recently applied ad-hoc individual decision-making of the drivers results in significant fuel cost savings. A case study confirmed the efficiency of the proposed method.

Well Placement Technique and Production Optimization for Mature Field - A Case Study of L-X Field

2020 ◽  
Vol 46 ◽  
pp. 168-179
Author(s):  
Patrick Nwafor ◽  
Kelani Bello
Keyword(s):  
Oil And Gas ◽  
Optimization Technique ◽  
Optimal Solution ◽  
Oil And Gas Industry ◽  
Optimization Method ◽  
Simulation Software ◽  
Production Optimization ◽  
Direct Optimization ◽  
Well Placement ◽  
Local Optimal Solution

A Well placement is a well-known technique in the oil and gas industry for production optimization and are generally classified into local and global methods. The use of simulation software often deployed under the direct optimization technique called global method. The production optimization of L-X field which is at primary recovery stage having five producing wells was the focus of this work. The attempt was to optimize L-X field using a well placement technique.The local methods are generally very efficient and require only a few forward simulations but can get stuck in a local optimal solution. The global methods avoid this problem but require many forward simulations. With the availability of simulator software, such problem can be reduced thus using the direct optimization method. After optimization an increase in recovery factor of over 20% was achieved. The results provided an improvement when compared with other existing methods from the literatures.

Thermomechanical Response of Commercially Pure Titanium under Large Plastic Deformation at High Strain Rates

2012 ◽  
Vol 548 ◽  
pp. 174-178 ◽  
Author(s):  
Chong Yang Gao ◽  
Wei Ran Lu
Keyword(s):  
Pure Titanium ◽  
Optimal Solution ◽  
Optimization Method ◽  
Strain Rates ◽  
Commercially Pure Titanium ◽  
Thermomechanical Response ◽  
Commercially Pure ◽  
Different Temperatures ◽  
Cp Ti ◽  
Constitutive Parameters

By using a dislocation-based plastic constitutive model for hcp metals developed by us recently, the dynamic thermomechanical response of an important industrial material, commercially pure titanium (CP-Ti), was described at different temperatures and strain rates. The constitutive parameters of the material are determined by an efficient optimization method for a globally optimal solution. The model can well predict the dynamic response of CP-Ti by the comparison with experimental data and the Nemat-Nasser-Guo model.

scholarly journals GA-Based Optimization Method for Mobile Crane Repositioning Route Planning

2021 ◽  
Vol 11 (13) ◽  
pp. 6010
Author(s):  
Han-Seong Gwak ◽  
Hong-Chul Lee ◽  
Byoung-Yoon Choi ◽  
Yirong Mi
Keyword(s):  
Operating Time ◽  
Route Planning ◽  
Optimal Solution ◽  
Optimization Method ◽  
Computational Method ◽  
Test Cases ◽  
Construction Sites ◽  
Productivity Improvement ◽  
Planning Optimization ◽  
Mobile Crane

Mobile cranes have been used extensively as essential equipment at construction sites. The productivity improvement of the mobile crane affects the overall productivity of the construction project. Hence, various studies have been conducted regarding mobile crane operation planning. However, studies on solving RCP (the repositioning mobile crane problem) are insufficient. This article presents a mobile crane reposition route planning optimization method (RPOS) that minimizes the total operating time of mobile crane. It converts the construction site into a mathematical model, determines feasible locations of the mobile crane, and identifies near-global optimal solution (s) (i.e., the placement point sequences of mobile crane) by implementing genetic algorithm and dijkstra’s algorithm. The study is of value to practitioners because RPOS provides an easy-to-use computerized tool that reduces the lengthy computations relative to data processing and Genetic Algorithms (GAs). Test cases verify the validity of the computational method.

A Systematic Optimization Design Method for Thermal Management of Passenger Vehicles

2021 ◽  
pp. 1-27
Author(s):  
Jie Zhang ◽  
Qidong Wang ◽  
Han Zhang ◽  
Min Zhang ◽  
Jianwei Lin
Keyword(s):  
Prediction Model ◽  
Surface Temperature ◽  
Thermal Management ◽  
Optimization Design ◽  
Cfd Simulation ◽  
Optimal Solution ◽  
Optimization Method ◽  
Drive Shaft ◽  
Management Problem ◽  
Systematic Optimization

Abstract In this study, a systematic optimization method for the thermal management problem of passenger vehicle was proposed. This article addressed the problem of the drive shaft sheath surface temperature exceeded allowable value. Initially, the causes and initial measures of the thermal problem were studied through computational fluid dynamics (CFD) simulation. Furthermore, the key measures and the relevant parameters were determined through Taguchi method and significance analysis. A prediction model between the parameters and optimization objective was built by radial basis function neural network (RBFNN). Finally, the prediction model and particle swarm optimization (PSO) algorithm were combined to calculate the optimal solution, and the optimal solution was selected for simulation and experiment verification. Experiment results indicated that this method reduced the drive shaft sheath surface temperature promptly, the decreasing amplitude was 22%, which was met the experimental requirements.

Multi-Objective Trajectory Optimization of Free-Floating Space Manipulator Using NSGA-II

2015 ◽  
Vol 713-715 ◽  
pp. 800-804 ◽  
Author(s):  
Gang Chen ◽  
Cong Wei ◽  
Qing Xuan Jia ◽  
Han Xu Sun ◽  
Bo Yang Yu
Keyword(s):  
Trajectory Optimization ◽  
Interpolation Method ◽  
Optimal Solution ◽  
Optimization Method ◽  
Joint Space ◽  
Motion Path ◽  
Objective Functions ◽  
Nsga Ii ◽  
Space Manipulator ◽  
Multi Objective

In this paper, a kind of multi-objective trajectory optimization method based on non-dominated sorting genetic algorithm II (NSGA-II) is proposed for free-floating space manipulator. The aim is to optimize the motion path of the space manipulator with joint angle constraints and joint velocity constraints. Firstly, the kinematics and dynamics model are built. Secondly, the 3-5-3 piecewise polynomial is selected as interpolation method for trajectory planning of joint space. Thirdly, three objective functions are established to simultaneously minimize execution time, energy consumption and jerk of the joints. At last, the objective functions are combined with the NSGA-II algorithm to get the Pareto optimal solution set. The effectiveness of the mentioned method is verified by simulations.

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