Payame Noor University (PNU)Control and Optimization in Applied Mathematics2383-31301220161001The Control Parametrization Enhancing Technique for Multi-Objective Optimal Control of HIV Dynamicکنترل بهینه چندهدفه دینامیک HIV به کمک تکنیک پارامتری کردن کنترل1213392ENHassanZareiDepartment of Mathematic, Payame Noor University, Tehran, IranJournal Article20160627In 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.https://mathco.journals.pnu.ac.ir/article_3392_b126b5fd552ee258e1bd281c8a5dc268.pdfPayame Noor University (PNU)Control and Optimization in Applied Mathematics2383-31301220161201Numerical Solution of Optimal Heating of Temperature Field in Uncertain Environment Modelled by the use of Boundary Controlحل عددی گرمادهی بهینه میدان دمایی در محیط تصادفی مدلسازی شده با استفاده از کنترل مرزی23383395ENAliNehranifaculty of mathematical sciences, university of guilan, rasht, iranMohammadKeyanpourFaculty of mathematical sciences, University of Guilan, Rasht, IranJournal Article20160112In 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.https://mathco.journals.pnu.ac.ir/article_3395_2c4e86ec7879dc9ee757e6be0008d18b.pdfPayame Noor University (PNU)Control and Optimization in Applied Mathematics2383-31301220160901Robust Control Synchronization on Multi-Story Structure under Earthquake Loads and Random Forces using H∞ Algorithmهماهنگسازی الگوریتم کنترل مقاوم H∞ برای سازههای چند طبقه تحت بار زلزله و نیروهای تصادفی39523397ENJavadMesbahiPNU, Applied Mathematics DepartmentAlaeddinMalekApplied Mathematics Dept. Tarbiat Modares University
Tehran, IranBehnoushSalimbahramiCivil Eng Dept. PayameNoor UniversityJournal Article20151214In 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.https://mathco.journals.pnu.ac.ir/article_3397_ac7064440ef6ea12174108d5882a4940.pdfPayame Noor University (PNU)Control and Optimization in Applied Mathematics2383-31301220161201Solving System of Nonlinear Equations by using a New Three-Step Methodحل دستگاه معادلات غیرخطی با استفاده از یک روش سه گامی جدید53623398ENMehdiAhmadiDepartment of Mathematics, Malayer University, Malayer, Iran.HamidEsmaeiliDepartment of Mathematics, Bu-Ali Sina University, Hamedan, Iran.RErfanifarDepartment of Mathematics, Bu-Ali Sina University, Hamedan, Iran.Journal Article20151113In 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.https://mathco.journals.pnu.ac.ir/article_3398_cee896e67e39e179b12bcb4a52ca7cc3.pdfPayame Noor University (PNU)Control and Optimization in Applied Mathematics2383-31301220161201Comparative Analysis of Machine Learning Algorithms with Optimization Purposesتحلیل تطبیقی الگوریتمهای یادگیری ماشین با اهداف بهینهسازی63753399ENRohollahAlesheykhPayame Noor UniversityJournal Article20160205The 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.https://mathco.journals.pnu.ac.ir/article_3399_eac798a614b48609ebe90618f6dd2bca.pdfPayame Noor University (PNU)Control and Optimization in Applied Mathematics2383-31301220160901Fuzzy Number-Valued Fuzzy Graphگراف فازی با مقدار عدد فازی مقدار77863400ENSiyamakFirouzianDepartment of Mathematics, Payame Noor University (PNU) Tehran, IranMohamadAdabitabar FirozjaDepartment of mathematics, Qaemshar Branch, Islamic Azad University, Qaemshahr, IranJournal Article20160411Graph 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.https://mathco.journals.pnu.ac.ir/article_3400_454ff85596b1356c9aa00b9fcbbcae7f.pdf