Payame Noor University
Biquarterly Research Journal of Control and Optimization in applied Mathematics
2383-3130
2538-5615
1
2
2016
10
01
The Control Parametrization Enhancing Technique for Multi-Objective Optimal Control of HIV Dynamic
1
21
EN
Hassan
Zarei
Department of Mathematic, Payame Noor University, Tehran, Iran
zarei2003@gmail.com
In this paper, a computational approach is adopted for solving a multi-objective optimal control problem (MOOCP) formulation of optimal drug scheduling in human immunodeficiency (HIV) virus infected by individuals. The MOOCP, which uses a mathematical model of HIV infection, has some incompatible objectives. The objectives are maximizing the survival time of patients, the level of D4+ T-cells and the level of cytotoxic T-lymphocytes (CTLs), and minimizing the viral load and the drug costs. In this approach the fuzzy goals described by the linear membership functions, are incorporated for the objectives and the optimal solution is investigated by maximizing the degree of attainment of the aggregated fuzzy goals resulting a fuzzy goal optimal control problem (FGOCP). Using the minimum operator for aggregation of fuzzy goals, the FGOCP is converted into a constrained optimal control problem (OCP) in canonical form. The control parametrization enhancing technique (CPET) is used for approximating the OCP by an optimal parameter selection problem, with the final goal of implementing continuous and interrupted (structured treatment interruptions, STI) combinations of reverse transcriptase inhibitor (RTI) and protease inhibitor (PI) drug efficacies. Efficiency of the proposed method is confirmed by numerical simulations.
Multi-objective problem,Optimal control,Fuzzy goal programming,Therapy optimization
http://mathco.journals.pnu.ac.ir/article_3392.html
http://mathco.journals.pnu.ac.ir/article_3392_b126b5fd552ee258e1bd281c8a5dc268.pdf
Payame Noor University
Biquarterly Research Journal of Control and Optimization in applied Mathematics
2383-3130
2538-5615
1
2
2016
12
01
Numerical Solution of Optimal Heating of Temperature Field in Uncertain Environment Modelled by the use of Boundary Control
23
38
EN
Ali
Nehrani
faculty of mathematical sciences, university of guilan, rasht, iran
nehrani@gmail.com
Mohammad
Keyanpour
Faculty of mathematical sciences, University of Guilan, Rasht, Iran
m.keyanpour@gmail.com
In the present paper, optimal heating of temperature field which is modelled as a boundary optimal control problem, is investigated in the uncertain environments and then it is solved numerically. In physical modelling, a partial differential equation with stochastic input and stochastic parameter are applied as the constraint of the optimal control problem. Controls are implemented as Dirichlet boundary conditions and representing the heating elements on the boundary of the field. In numerical quantification, stochastic input and parameter are approximated via Karhunen-Lo'eve expansion and inserted to the problem. In fact, for numerical discretization of the problem stochastic Galerkin method is applied to generalize polynomial chaos. Numerical optimization is performed via gradient method. The problem is fully implemented and in order to show the applicability of the method, numerical examples are solved and numerical results are represented through figures.
Boundary optimal control,Stochastic partial differential equation,Stochastic quantification,Gradient method
http://mathco.journals.pnu.ac.ir/article_3395.html
http://mathco.journals.pnu.ac.ir/article_3395_2c4e86ec7879dc9ee757e6be0008d18b.pdf
Payame Noor University
Biquarterly Research Journal of Control and Optimization in applied Mathematics
2383-3130
2538-5615
1
2
2016
09
01
Robust Control Synchronization on Multi-Story Structure under Earthquake Loads and Random Forces using H∞ Algorithm
39
52
EN
Javad
Mesbahi
PNU, Applied Mathematics Department
j_mesbahi@pnu.ac.ir
Alaeddin
Malek
Applied Mathematics Dept. Tarbiat Modares University
Tehran, Iran
malamath1336@gmail.com
Behnoush
Salimbahrami
Civil Eng Dept. PayameNoor University
bsbahrami@yahoo.com
In this paper, the concept of synchronization control along with robust H∞ control are considered to evaluate the seismic response control on multi-story structures. To show the accuracy of the novel algorithm, a five-story structure is evaluated under the EL-Centro earthquake load. In order to find the performance of the novel algorithm, random and uncertainty processes corresponding to Riccati equation is solved under a specific dynamic. Time history graphs corresponding to maximum displacement and floors force control are presented and evaluated. Despite the existence of random process and uncertainty in structure, stability and optimal performances are shown.
Synchronization,Random process and uncertainty,Robust H∞ control,EL-Centro earthquake load,Riccati equation
http://mathco.journals.pnu.ac.ir/article_3397.html
http://mathco.journals.pnu.ac.ir/article_3397_ac7064440ef6ea12174108d5882a4940.pdf
Payame Noor University
Biquarterly Research Journal of Control and Optimization in applied Mathematics
2383-3130
2538-5615
1
2
2016
12
01
Solving System of Nonlinear Equations by using a New Three-Step Method
53
62
EN
Mehdi
Ahmadi
Department of Mathematics, Malayer University, Malayer, Iran.
mehdi.ahmadi@stu.malayeru.ac.ir
Hamid
Esmaeili
Department of Mathematics, Bu-Ali Sina University, Hamedan, Iran.
esmaeili@basu.ac.ir
R
Erfanifar
Department of Mathematics, Bu-Ali Sina University, Hamedan, Iran.
rerfanifar92@basu.ac.ir
In this paper, we suggest a fifth order convergence three-step method for solving system of nonlinear equations. Each iteration of the method requires two function evaluations, two first Fr'{e}chet derivative evaluations and two matrix inversions. Hence, the efficiency index is $5^{1/({2n+4n^{2}+frac{4}{3}n^{3}})}$, which is better than that of other three-step methods. The advantages of the method lie in the feature that this technique not only achieves an approximate solution with high accuracy, but also improves the calculation speed. Also, under several mild conditions the convergence analysis of the proposed method is provided. An efficient error estimation is presented for the approximate solution. Numerical examples are included to demonstrate the validity and applicability of the method and the comparisons are made with the existing results.
Nonlinear equations,Iterative method,Convergence order,Efficiency index
http://mathco.journals.pnu.ac.ir/article_3398.html
http://mathco.journals.pnu.ac.ir/article_3398_cee896e67e39e179b12bcb4a52ca7cc3.pdf
Payame Noor University
Biquarterly Research Journal of Control and Optimization in applied Mathematics
2383-3130
2538-5615
1
2
2016
12
01
Comparative Analysis of Machine Learning Algorithms with Optimization Purposes
63
75
EN
Rohollah
Alesheykh
Payame Noor University
alesheykh@pnu.ac.ir
The field of optimization and machine learning are increasingly interplayed and optimization in different problems leads to the use of machine learning approaches. Machine learning algorithms work in reasonable computational time for specific classes of problems and have important role in extracting knowledge from large amount of data. In this paper, a methodology has been employed to optimize the precision of defect detection of concrete slabs depending on their qualitative evaluation. Based on this idea, some machine learning algorithms such as C4.5 decision tree, RIPPER rule learning method and Bayesian network have been studied to explore the defect of concrete and to supply a decision system to speed up the defect detection process. The results from the examinations show that the proposed RIPPER rule learning algorithm in combination with Fourier Transform feature extraction method could get a defect detection rate of 93% as compared to other machine learning algorithms.
decision tree,Bayesian network,rule learning algorithm,optimization,Soft Computing
http://mathco.journals.pnu.ac.ir/article_3399.html
http://mathco.journals.pnu.ac.ir/article_3399_eac798a614b48609ebe90618f6dd2bca.pdf
Payame Noor University
Biquarterly Research Journal of Control and Optimization in applied Mathematics
2383-3130
2538-5615
1
2
2016
09
01
Fuzzy Number-Valued Fuzzy Graph
77
86
EN
Siyamak
Firouzian
Department of Mathematics, Payame Noor University (PNU) Tehran, Iran
siamfirouzian@pnu.ac.ir
Mohamad
Adabitabar Firozja
Department of mathematics, Qaemshar Branch, Islamic Azad University, Qaemshahr, Iran
mohamadsadega@yahoo.com
Graph theory has an important role in the area of applications of networks and clustering. In the case of dealing with uncertain data, we must utilize ambiguous data such as fuzzy value, fuzzy interval value or values of fuzzy number. In this study, values of fuzzy number were used. Initially, we utilized the fuzzy number value fuzzy relation and then proposed fuzzy number-value fuzzy graph on nodes and arcs. In this study, some properties of the graph on fuzzy number-value fuzzy graph were examined. First, we define the Cartesian product, composition, union and join operators on fuzzy number-value fuzzy graphs and then prove some of their properties and and give some examples for every one of definitions. We also introduced the notion of homomorphism, weak isomorphism,weak co-isomorphism, isomorphism, complete, weak complete and compliment on the fuzzy number fuzzy graphs and prove some of their properties and also present some examples for every one of them.
Fuzzy numbers,Relation,Fuzzy relation,Graph,Fuzzy graph
http://mathco.journals.pnu.ac.ir/article_3400.html
http://mathco.journals.pnu.ac.ir/article_3400_454ff85596b1356c9aa00b9fcbbcae7f.pdf