Payame Noor University (PNU)Control and Optimization in Applied Mathematics2383-31309120240501A Fuzzy Sliding Mode Control for Nonlinear Leader-Follower Multi-Agent Systems134992010.30473/coam.2023.64817.1209ENNegarIzadiDepartment of Mathematics, Faculty of Sciences, University of Zanjan, P.O. Box 45371-38791, Zanjan, IranMohammad TaghiDastjerdiDepartment of Mathematics, Faculty of Sciences, University of Zanjan, P.O. Box 45371-38791, Zanjan, IranJournal Article20220717In this paper, we present a new approach for achieving leader-follower consensus in a network of nonlinear dynamic agents with an undirected graph topology, using a fuzzy sliding mode controller (FSMC) for Multi-Agent Systems (MASs). Our proposed sliding mode controller is based on a separating hyperplane that effectively addresses the consensus problem in MASs. Additionally, we design a fuzzy controller to eliminate the chattering phenomenon. According to the communication graph topology and the Lyapunov stability condition, the proposed FSMC satisfies the consensus condition. One significant advantage of our approach is that the system states converge to the sliding surface quickly and remain on the surface, thereby ensuring better tracking performance. We validate the effectiveness of our proposed approach through simulation results.https://mathco.journals.pnu.ac.ir/article_9920_68265e771ccc6d462f4cb2820b883299.pdfPayame Noor University (PNU)Control and Optimization in Applied Mathematics2383-31309120240501Dynamical Behaviour of Fractional Order SEIR Mathematical Model for Infectious Disease Transmission35481018910.30473/coam.2023.64849.1210ENRezaAkbariDepartment of Mathematics, Payame Noor University (PNU), Tehran, IranLeaderNavaeiDepartment of Statistics, Payame Noor University (PNU), Tehran, Iran,MohammadShahriariDepartment of Mathematics, Maragheh University, Maragheh, Iran.Journal Article20220722This paper presents an extension of the SEIR mathematical model for infectious disease transmission to a fractional-order model. The model is formulated using the Caputo derivative of order α ∈ (0, 1]. We study the stability of equilibrium points, including the disease-free equilibrium $(E_{f})$, and the infected steady-state equilibrium $(E_{e})$ using the stability theorem of Fractional Differential Equations. The model is also analyzed under certain conditions, and it is shown that the disease-free equilibrium is locally asymptotically stable. Additionally, the extended Barbalat’s lemma is applied to the fractional-order system, and a suitable Lyapunov functional is constructed to demonstrate the global asymptotic stability of the infected steady-state equilibrium. To validate the theoretical results, a numerical simulation of the problem is conducted.<br /> https://mathco.journals.pnu.ac.ir/article_10189_6a7211b03c96a361b1c1edaa6a41d94b.pdfPayame Noor University (PNU)Control and Optimization in Applied Mathematics2383-31309120240501Efficient Solution of Nonlinear Unconstraint Optimization Problems using Quasi-Newton's Method: A Revised Approach49651028810.30473/coam.2023.64138.1204ENHajarAlimoradDepartment of Mathematics,
Jahrom University, Jahrom, P.O. Box 74135-111, IranJournal Article20220521While many real-world optimization problems typically involve multiple constraints, unconstrained problems hold practical and fundamental significance. They can arise directly in specific applications or as transformed versions of constrained optimization problems. Newton's method, a notable numerical technique within the category of line search algorithms, is widely used for function optimization. The search direction and step length play crucial roles in this algorithm. This paper introduces an algorithm aimed at enhancing the step length within the Broyden quasi-Newton process. Additionally, numerical examples are provided to compare the effectiveness of this new method with another approach.https://mathco.journals.pnu.ac.ir/article_10288_e5163b25fa0128cdeb957eecb272f9db.pdfPayame Noor University (PNU)Control and Optimization in Applied Mathematics2383-31309120240501Hesitant Fuzzy Equation67791036010.30473/coam.2023.68208.1240ENFatemehBabakordiDepartment of Mathematics, Faculty of Science, Gonbad Kavous University, Gonbad Kavous, Iran.Nemat AllahTaghi-NezhadDepartment of Mathematics, Faculty of Science, Gonbad Kavous University, Gonbad Kavous, Iran.Journal Article20230616This paper presents the introduction of two novel equation types: the partial hesitant fuzzy equation and the half hesitant fuzzy equation. Additionally, an efficient method is proposed to solve these equations by defining four solution categories: Controllable, Tolerable Solution Set (TSS), Controllable Solution Set (CSS), and Algebraic Solution Set (ASS). Furthermore, the paper establishes eight theorems that explore different types of solutions and lay out the conditions for the existence and non-existence of hesitant fuzzy solutions. The practicality of the proposed method is demonstrated through numerical examples.https://mathco.journals.pnu.ac.ir/article_10360_40062fefd890ab189664babdc44e862c.pdfPayame Noor University (PNU)Control and Optimization in Applied Mathematics2383-31309120240501Big Data Analytics and Data Mining Optimization Techniques for Air Traffic Management81961047610.30473/coam.2023.66151.1222ENAbbas AliRezaeeDepartment of Computer Engineering and Information Technology, Payame Noor University, Tehran, IranHadisAhmadian YazdiDepartment of Computer Engineering, Neyshabur Branch, Islamic Azad University, Neyshabur, IranMahdiYousefzadeh AghdamDepartment of Computer Engineering, Mashhad Branch, Islamic Azad University, Mashhad, IranSaharGhareiiAviation Engineer, Mashhad Airport, Mashhad, Iran.Journal Article20221204With the advancements in science and technology, the industrial and aviation sectors have witnessed a significant increase in data. A vast amount of data is generated and utilized continuously. It is imperative to employ data mining techniques to extract and uncover knowledge from this data. Data mining is a method that enables the extraction of valuable information and hidden relationships from datasets. However, the current aviation data presents challenges in effectively extracting knowledge due to its large volume and diverse structures. Air Traffic Management (ATM) involves handling Big data, which exceeds the capacity of conventional acquisition, matching, management, and processing within a reasonable timeframe. Aviation Big data exists in batch forms and streaming formats, necessitating the utilization of parallel hardware and software, as well as stream processing, to extract meaningful insights. Currently, the map-reduce method is the prevailing model for processing Big data in the aviation industry. This paper aims to analyze the evolving trends in aviation Big data processing methods, followed by a comprehensive investigation and discussion of data analysis techniques. We implement the map-reduce optimization of the K-Means algorithm in the Hadoop and Spark environments. The K-Means map-reduce is a crucial and widely applied clustering method. Finally, we conduct a case study to analyze and compare aviation Big data related to air traffic management in the USA using the K-Means map-reduce approach in the Hadoop and Spark environments. The analyzed dataset includes flight records. The results demonstrate the suitability of this platform for aviation Big data, considering the characteristics of the aviation dataset. Furthermore, this study presents the first application of the designed program for air traffic management.https://mathco.journals.pnu.ac.ir/article_10476_d70494acda1717ef52028b37c523117c.pdfPayame Noor University (PNU)Control and Optimization in Applied Mathematics2383-31309120240501Optimizing Supply Chain Design for Sustainability and Reliability: A Comparative Study of Augmented Epsilon and Normalized Normal Constraint Methods971301036110.30473/coam.2023.67540.1230ENSajadAmirianDepartment of Industrial Management, Faculty of Management and Accounting, Allameh Tabataba’i University, Tehran, Iran.MaghsoudAmiriDepartment of Industrial Management, Faculty of Management and Accounting, Allameh Tabataba’i University, Tehran, Iran.Mohammad TaghiTaghavifardDepartment of Industrial Management, Faculty of Management and Accounting, Allameh Tabataba’i University, Tehran, Iran.Journal Article20230408Integrating sustainability and reliability represents a synergistic approach that can be explored through the problem of a closed-loop supply chain network design (SCND). This study is conducted in three stages: mathematical modeling, model solution using exact methods, and evaluation of the solution methods. In the first stage, a mixed-integer linear programming (MILP) model is developed in a multi-objective, multi-product, and multi-period framework. The objectives of the proposed model aim to maximize profitability, social responsibility, and reliability. In the second stage, two methods, namely Augmented $\varepsilon$-Constraint (AEC) and Normalized Normal Constraint (NNC), are implemented in the GAMS software to solve the model and identify the optimal Pareto solutions. In the third stage, the Shannon Entropy technique is employed to determine the criteria weights, and the VIKOR technique is utilized to select the superior solution method. The overall performance accuracy of the proposed model is measured using four samples from a numerical example with randomly generated data based on the objective function coefficients. The results indicate the presence of a conflict among the three objective functions. Consequently, decision-makers should consider sacrificing some profitability to enhance environmental protection and improve reliability. In terms of three criteria, run time, diversification metric, and general distance, the NNC method is given priority over the AEC method. Even when the criteria are given equal weight, the superiority of the NNC method remains unchanged. The application of the proposed model across different industries represents a significant research direction for future research.https://mathco.journals.pnu.ac.ir/article_10361_6699ac23162a62a1b4664a1940bd571c.pdfPayame Noor University (PNU)Control and Optimization in Applied Mathematics2383-31309120240501An Efficient Variable Neighborhood Search for Solving Multi-Criteria Project Portfolio Selection131147981810.30473/coam.2023.65380.1213ENAli AkbarSohrabiFaculty of Mathematical Sciences, Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran.RezaGhanbariFaculty of Mathematical Sciences, Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran.KhatereGhorbani-MoghadamMosaheb Institute of Mathematics, Kharazmi University, Tehran, Iran.Journal Article20220906Project portfolio selection is a critical challenge for many organizations as they often face budget constraints that limit their ability to support all available projects. To address this issue, organizations seek to select a feasible subset of projects that maximizes utility. While several models for project portfolio selection based on multiple criteria have been proposed, they are typically NP-hard problems. In this study, we propose an efficient Variable Neighborhood Search (VNS) algorithm to solve these problems. Our algorithm includes a formula for computing the difference value of the objective function, which enhances its accuracy and ensures that selected projects meet desired criteria. We demonstrate the effectiveness of our algorithm through rigorous testing and comparison with a genetic algorithm (GA) and CPLEX. The results of the Wilcoxon non-parametric test confirm that our algorithm outperforms both GA and CPLEX in terms of speed and accuracy. Moreover, the variance of the relative error of our algorithm is less than that of GA.https://mathco.journals.pnu.ac.ir/article_9818_207d25dd9030d48d15eea9e04b896d54.pdfPayame Noor University (PNU)Control and Optimization in Applied Mathematics2383-31309120240501Solving Fractional Optimal Control-Affine Problems via Fractional-Order Hybrid Jacobi Functions1491681041410.30473/coam.2023.68826.1243ENZeinabBararyDepartment of Applied Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran.AllahBakhshYazdani CheratiDepartment of Applied Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran.SomayehNematiDepartment of Applied Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran.Journal Article20230814This paper proposes and analyzes an applicable approach for numerically computing the solution of fractional optimal control-affine problems. The fractional derivative in the problem is considered in the sense of Caputo. The approach is based on a fractional-order hybrid of block-pulse functions and Jacobi polynomials. First, the corresponding Riemann-Liouville fractional integral operator of the introduced basis functions is calculated. Then, an approximation of the fractional derivative of the unknown state function is obtained by considering an approximation in terms of these basis functions. Next, using the dynamical system and applying the fractional integral operator, an approximation of the unknown control function is obtained based on the given approximations of the state function and its derivatives. Subsequently, all the given approximations are substituted into the performance index. Finally, the optimality conditions transform the problem into a system of algebraic equations. An error upper bound of the approximation of a function based on the fractional hybrid functions is provided. The method is applied to several numerical examples, and the experimental results confirm the efficiency and capability of the method. Furthermore, they demonstrate a good agreement between the approximate and exact solutions. https://mathco.journals.pnu.ac.ir/article_10414_9a4bfbfec2d71c4afaebbbc6b8542d09.pdfPayame Noor University (PNU)Control and Optimization in Applied Mathematics2383-31309120240501Solving Linear Fractional Programming Problems in Uncertain Environments: A Novel Approach with Grey Parameters1691831059210.30473/coam.2023.67881.1235ENFaridPourofoghiDepartment of Mathematics, Payame Noor University (PNU), P.O. Box 19395-4697, Tehran, Iran.DavoodDarvishi SalokolaeiDepartment of Mathematics, Payame Noor University (PNU), P.O. Box19395-4697, Tehran, Iran.Journal Article20230513Fractional programming is a significant nonlinear planning tool within operation research. It finds applications in diverse domains such as resource allocation, transportation, production programming, performance evaluation, and finance. In practical scenarios, uncertainties often make it challenging to determine precise coefficients for mathematical models. Consequently, utilizing indefinite coefficients instead of definite ones is recommended in such cases. Grey systems theory, along with probability theory, randomness, fuzzy logic, and rough sets, is an approach that addresses uncertainty. In this study, we address the problem of linear fractional programming with grey coefficients in the objective function. To tackle this problem, a novel approach based on the variable change technique proposed by Charnes and Cooper, along with the convex combination of intervals, is employed. The article presents an algorithm that determines the solution to the grey fractional programming problem using grey numbers, thus capturing the uncertainty inherent in the objective function. To demonstrate the effectiveness of the proposed method, an example is solved using the suggested approach. The result is compared with solutions obtained using the whitening method, employing Hu and Wong's technique and the Center and Greyness Degree Ranking method. The comparison confirms the superiority of the proposed method over the whitening method, thus suggesting adopting the grey system approach in such situations.https://mathco.journals.pnu.ac.ir/article_10592_3d258d58e119e85194adc03f0522a3d3.pdfPayame Noor University (PNU)Control and Optimization in Applied Mathematics2383-31309120240501A Hybrid Floyd-Warshall and Graph Coloring Algorithm for Finding the Smallest Number of Colors Needed for a Distance Coloring of Graphs1851941062610.30473/coam.2023.68880.1244ENHanifaMosawiDepartment of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad 91775, Iran.0000-0001-8960-588XMostafaTavakolliDepartment of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad 91775, Iran.KhatereGhorbani-MoghadamMosaheb Institute of Mathematics, Kharazmi University, Tehran, Iran.Journal Article20230826Graph coloring is a crucial area of research in graph theory, with numerous algorithms proposed for various types of graph coloring, particularly graph p-distance coloring. In this study, we employ a recently introduced graph coloring algorithm to develop a hybrid algorithm approximating the chromatic number p-distance, where $p$ represents a positive integer number. We apply our algorithm to molecular graphs as practical applications of our findings.https://mathco.journals.pnu.ac.ir/article_10626_1d3b0b6b1881cfc48c06bf561ecafcc0.pdfPayame Noor University (PNU)Control and Optimization in Applied Mathematics2383-31309120240501Mathematical Modeling and Optimal Control of Carbon Dioxide Emissions1952021044310.30473/coam.2023.67777.1233ENFahimehAkhavan GhassabzadeDepartment of Mathematics, Faculty of Sciences, University of Gonabad, Gonabad, Iran.MinaBagherpoorfardDepartment of Mathematics, Fasa Branch, Islamic Azad university, Fasa, Iran.Journal Article20230502This paper aims to demonstrate the flexibility of mathematical models in analyzing carbon dioxide emissions and account for memory effects. The use of real data amplifies the importance of this study. This research focuses on developing a mathematical model utilizing fractional-order differential equations to represent carbon dioxide emissions stemming from the energy sector. By comparing simulation results with real-world data, it is determined that the fractional model exhibits superior accuracy when contrasted with the classical model. Additionally, an optimal control strategy is proposed to minimize the levels of carbon dioxide, CO2, and associated implementation costs. The fractional optimal control problem is addressed through the utilization of an iterative algorithm, and the effectiveness of the model is verified by presenting comparative results.https://mathco.journals.pnu.ac.ir/article_10443_0d3845bc98097debd6059e66539f8c18.pdfPayame Noor University (PNU)Control and Optimization in Applied Mathematics2383-31309120240501Optimality Conditions for Properly Efficient Solutions of Nonsmooth Multiobjective GSIP2032191056710.30473/coam.2023.67823.1234ENAli AsgharHojatifardDepartment of Mathematics, Payame Noor University (PNU), P.O. Box 19395-4697, Tehran, Iran.NaderKanziDepartment of Mathematics, Payame Noor University (PNU), P.O. Box 19395-4697, Tehran, Iran.ShahriarFarahmand RadDepartment of Mathematics, Payame Noor University (PNU), P.O. Box 19395-4697, Tehran, Iran.Journal Article20230504This paper aims to establish first-order necessary optimality conditions for non-smooth multi-objective generalized semi-infinite programming problems. These problems involve inequality constraints whose index set depends on the decision vector, and all emerging functions are assumed to be locally Lipschitz. We introduce a new constraint qualification for these problems. Building upon this qualification, we derive an upper estimate for the Clarke sub-differential of the value function of the problem. Furthermore, we demonstrate the necessary optimality conditions for properly efficient solutions to the problem.https://mathco.journals.pnu.ac.ir/article_10567_371f1f6f183e2110108e1d9013598022.pdf