Rama Amiri; Mohammad Zarebnia; Reihaneh Raisi Tousi
Abstract
A shearlet frame approach is used to solve $n$-dimensional wave equations numerically. By the presented procedure, the shearlet coefficients are obtained via separate time-independent partial differential equations. The proposed method has the advantage of separation ...
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A shearlet frame approach is used to solve $n$-dimensional wave equations numerically. By the presented procedure, the shearlet coefficients are obtained via separate time-independent partial differential equations. The proposed method has the advantage of separation of spatial and temporal parameters. The issues of convergence and best approximation are also discussed.
Hajar Alimorad; Alireza Fakharzadeh Jahromi
Abstract
In this paper, we model and solve the problem of optimal shaping and placing to put sensors for a 3-D wave equation with constant damping in a bounded open connected subset of 3-dimensional space. The place of sensor is modeled by a subdomain of this region ...
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In this paper, we model and solve the problem of optimal shaping and placing to put sensors for a 3-D wave equation with constant damping in a bounded open connected subset of 3-dimensional space. The place of sensor is modeled by a subdomain of this region of a given measure. By using an approach based on the embedding process, first, the system is formulated in variational form; then, by defining two positive Radon measures, the problem is represented in a space of measures. In this way, the shape design problem is turned into an infinite linear problem whose solution is guaranteed. In this step, the optimal solution (optimal control, optimal region, and optimal energy) is identified by a 2-phase optimization search technique applying two subsequent approximation steps. Moreover, some numerical simulations are given to compare this new method with other methods.
Farid Pourofoghi; Davood Darvishi Salokolaei
Abstract
Linear programming problems have exact parameters. In most real-world, we are dealing with situations in which accurate data and complete information are not available. Uncertainty approaches such as fuzzy and random can be used to deal with uncertainties in real-life. ...
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Linear programming problems have exact parameters. In most real-world, we are dealing with situations in which accurate data and complete information are not available. Uncertainty approaches such as fuzzy and random can be used to deal with uncertainties in real-life. Fuzzy and stochastic theories cannot be used if the number of experts and the level of experience is so low that it is impossible to extract membership functions or the number of samples is small. To solve these problems, the grey system theory is proposed. In this paper, a linear programming problem in a grey environment with resources in interval grey numbers is considered. Most of the proposed methods for solving grey linear programming problems become common linear programming problems. However, we seek to solve the problem directly without turning it into a standard linear programming problem for the purpose of maintaining uncertainty in the original problem data in the final solution. For this purpose, we present a method based on the duality theory for solving the grey linear programming problems. This method is more straightforward and less complicated than previous methods. We emphasize that the concept presented is beneficial for real and practical conditions in management and planning problems. Therefore, we shall illustrate our method with some examples in different situations.
Control and Optimization
Jahangir Alizadeh; Hamid Khaloozadeh
Abstract
In the present study, a novel methodology is developed to enlarge the Region of Attraction (ROA) at the point of equilibrium of an input-affine nonlinear control system. Enlarging the ROA for non-polynomial dynamical systems is developed by designing a nonlinear state feedback controller ...
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In the present study, a novel methodology is developed to enlarge the Region of Attraction (ROA) at the point of equilibrium of an input-affine nonlinear control system. Enlarging the ROA for non-polynomial dynamical systems is developed by designing a nonlinear state feedback controller through the State-Dependent Riccati Equation (SDRE). Consequently, its process is defined in the form of Sum-of-Squares (SOS) optimization problem with control and non-control constraints. Of note, the proposed technique is effective in estimating the ROA for a nonlinear system functioning on polynomial or non-polynomial dynamics. In the present study, the application of the proposed scheme are shown by numerical simulations.
Abbas Bashiri; Seyed Mehdi Mirhosseini-Alizamini; Mohammad Mehdi Nasrabadi
Abstract
Evaluation of advertising marketing campaigns is a very important and complex task, so far no comprehensive model has been presented in this regard. The present study aims to provide a decision framework for evaluating marketing campaigns. This article collects real-world ...
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Evaluation of advertising marketing campaigns is a very important and complex task, so far no comprehensive model has been presented in this regard. The present study aims to provide a decision framework for evaluating marketing campaigns. This article collects real-world data from an Iranian bank deposit marketing campaign. For this purpose, 250 cases were considered to extract the rules and 60 cases were considered as test data. Information is provided on 15 important parameters of marketing education, defaults, age, occupation, marriage, day, contact, balance, housing, loans, previous contact, previous outcome, month, call duration, and campaigns. A fuzzy expert system was designed with 12 rules after reviewing the rules and removing similar and contradictory rules by using their degree calculation. In this system, by integrating some factors, finally, 6 input variables and one output variable were considered that were used by the product inference engine, singleton fuzzifier, and center average defuzzifier. It was observed that the designed fuzzy expert system provides very good results.
Gholamreza Hesamian
Abstract
A fuzzy distance measure is introduced in this paper to evaluate the fuzzy distance between two fuzzy numbers. For this purpose, alpha-values of fuzzy numbers are used to develop an integral-based fuzzy distance measure. The properties of the proposed fuzzy distance measure ...
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A fuzzy distance measure is introduced in this paper to evaluate the fuzzy distance between two fuzzy numbers. For this purpose, alpha-values of fuzzy numbers are used to develop an integral-based fuzzy distance measure. The properties of the proposed fuzzy distance measure are verified. The proposed fuzzy distance measure is also compared with other fuzzy distance measures.
Ali Nemati; Ali Alizadeh; Fahime Soltanian
Abstract
This paper presents a numerical solution of a class of fractional optimal control problems (FOCPs) in a bounded domain having a noise function by the spectral Ritz method. The Bernstein polynomials with the fractional operational matrix are applied to approximate the unknown functions. ...
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This paper presents a numerical solution of a class of fractional optimal control problems (FOCPs) in a bounded domain having a noise function by the spectral Ritz method. The Bernstein polynomials with the fractional operational matrix are applied to approximate the unknown functions. By substituting these estimated functions into the cost functional, an unconstrained nonlinear optimization problem is achieved. In order to solve this optimization problem, the Matlab software and its optimization toolbox are used. In the considered FOCP, the performance index is expressed as a function of both state and control functions. The method is robust enough because of its computational consistency in the presence of the noise function. Moreover, the proposed scheme has a good pliability satisfying the given initial and boundary conditions. At last, some test problems are investigated to confirm the efficiency and applicability of the new method.
Control and Optimization
Zahra Abbasi; Nasser Akhoundi
Abstract
Product reviews in E-commerce websites such as restaurants, movies, E-commerce products, etc., are essential resources for consumers to make purchasing decisions on various items. In this paper, we model discovering groups with maximum descriptively ...
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Product reviews in E-commerce websites such as restaurants, movies, E-commerce products, etc., are essential resources for consumers to make purchasing decisions on various items. In this paper, we model discovering groups with maximum descriptively from E-commerce website of the form $<i,u,s>$, where $i\in \mathcal{I}$ (the set of items or products), $u\in \mathcal{U}$ (the set of users) and $s$ is the integer rating that user $u$ has assigned to the item $i$. Labeled groups from user's attributes are found by solving an optimization problem. The performance of the approach is examined by some experiments on real data-sets.
Mohammad Ali Vali; Mahdi Mashayekhi Esfichar; Shahriar Farahmand Rad
Abstract
Iterative feedback tuning (IFT) is an algorithm for adjusting the coefficients of the integer-order type proportional-integral-derivative (PID) controllers without needing a system model. The IFT algorithm is performed iteratively with the aim of optimizing the control coefficients at each ...
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Iterative feedback tuning (IFT) is an algorithm for adjusting the coefficients of the integer-order type proportional-integral-derivative (PID) controllers without needing a system model. The IFT algorithm is performed iteratively with the aim of optimizing the control coefficients at each stage via an objective function. In this research, for the first time, the IFT algorithm is used to adjust all the coefficients of the fractional order PID controllers, i.e., PI^α D^β controllers to have optimal performance. For this purpose, fractional order calculations and the integer-order version of the IFT algorithm are firstly presented, and the novel IFT algorithm is then used to adjust coefficients of the PI^α D^β controller. Finally, the performance of the proposed method is illustrated and verified through some examples.
Mojtaba Salehi; Efat Jabarpour
Abstract
The relief logistics and humanitarian supply chain in academic literature refer to the process of planning, execution, and effective controlling of the flow of costs and information and storage of necessary goods and materials from the point of origin to consumption with the primary ...
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The relief logistics and humanitarian supply chain in academic literature refer to the process of planning, execution, and effective controlling of the flow of costs and information and storage of necessary goods and materials from the point of origin to consumption with the primary purpose of reducing and relieving the affected people suffer. This paper discusses a multi-objective model for multi-period location-distribution-routing problems considering the evacuation of casualties and homeless people and fuzzy paths in relief logistics. Firstly, an uncertain multi-objective model of the problem was developed based on uncertain parameters of demand, time, and transport capacity, and then, using the fuzzy programming method, uncertain parameters of the problem were controlled. As the problem is NP-hard and GAMS software has not able to solve the model in larger sizes, meta-heuristic algorithms of NSGA-II and MOPSO were used to solve the problem.
Control and Optimization
Mohammad Darvisahzadeh; Ahmad Shahvarani Semnani; Hassan Alamolhodaei,; Hassan Behzadi
Abstract
Experiences of teaching Integral have indicated that the vast majorities of Iranian university students commit numerous errors while solving integral problems and have weak skills in this field; we might even say that they hide away from integral and consider it the nightmare of mathematics. On ...
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Experiences of teaching Integral have indicated that the vast majorities of Iranian university students commit numerous errors while solving integral problems and have weak skills in this field; we might even say that they hide away from integral and consider it the nightmare of mathematics. On the other hand, Integral is the base of pure and applied mathematics for all students of science, especially engineering, which some of their lessons are dependent on it directly or indirectly, so it is important to pay attention to it. Through descriptive method-exposed factor, an exam has been conducted in the form of three questions, the first of which is consisted of 4 sections on fifty students from different fields, and then interviews were conducted with a few of those students about their answers in order to study the students' behaviors when solving integral problems and to determine the type of their errors. By analyzing the performance of students in this test, we can see that students often struggle with integral and mostly have a feeble performance in solving trigonometric integrals. They want to learn computational integral instead of how to conceptualize integral in their minds correctly. The error most committed by university students was procedural errors, which arise from using derivative instead of integral. Besides most of the mistakes happen in solving definite integrals, and calculating finite areas between two curves. This is due to a lack of understanding of integrals and a lack of information in other areas of mathematics.
Mostafa Tavakolli
Abstract
Let $S= \{e_1,\,e_2, \ldots,\,e_m\}$ be an ordered subset of edges of a connected graph $G$. The edge $S$-representation of an edge set $M\subseteq E(G)$ with respect to $S$ is the vector $r_e(M|S) = (d_1,\,d_2,\ldots,\,d_m)$, where $d_i=1$ if $e_i\in M$ and $d_i=0$ ...
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Let $S= \{e_1,\,e_2, \ldots,\,e_m\}$ be an ordered subset of edges of a connected graph $G$. The edge $S$-representation of an edge set $M\subseteq E(G)$ with respect to $S$ is the vector $r_e(M|S) = (d_1,\,d_2,\ldots,\,d_m)$, where $d_i=1$ if $e_i\in M$ and $d_i=0$ otherwise, for each $i\in\{1,\ldots , k\}$. We say $S$ is a global forcing set for maximal matchings of $G$ if $r_e(M_1|S)\neq r_e(M_2|S)$ for any two maximal matchings $M_1$ and $M_2$ of $G$. A global forcing set for maximal matchings of $G$ with minimum cardinality is called a minimum global forcing set for maximal matchings, and its cardinality, denoted by $\varphi_{gm}$, is the global forcing number (GFN for short) for maximal matchings. Similarly, for an ordered subset $F = \{v_1,\,v_2, \ldots,\,v_k\}$ of $V(G)$, the $F$-representation of a vertex set $I\subseteq V(G)$ with respect to $F$ is the vector $r(I|F) = (d_1,\,d_2,\ldots,\,d_k)$, where $d_i=1$ if $v_i\in I$ and $d_i=0$ otherwise, for each $i\in\{1,\ldots , k\}$. We say $F$ is a global forcing set for independent dominatings of $G$ if $r(D_1|F)\neq r(D_2|F)$ for any two maximal independent dominating sets $D_1$ and $D_2$ of $G$. A global forcing set for independent dominatings of $G$ with minimum cardinality is called a minimum global forcing set for independent dominatings, and its cardinality, denoted by $\varphi_{gi}$, is the GFN for independent dominatings. In this paper, we study the GFN for maximal matchings under several types of graph products. Also, we present some upper bounds for this invariant. Moreover, we present some bounds for $\varphi_{gm}$ of some well-known graphs.
Control and Optimization
Mostafa Nouri Jouybari; Yahya Talebi Rostami; Siyamak Firouzian
Abstract
In this study, $R$ and $M$ are assumed to be a commutative ring with non-zero identity $M$ and an $R$-module, respectively. Scalar Product Graph of $M$, denoted by $G_R(M)$, is a graph with the vertex-set $M$ and two different vertices $a$ and $b$ in ...
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In this study, $R$ and $M$ are assumed to be a commutative ring with non-zero identity $M$ and an $R$-module, respectively. Scalar Product Graph of $M$, denoted by $G_R(M)$, is a graph with the vertex-set $M$ and two different vertices $a$ and $b$ in $M$ are connected if and only if there exists $r$ belong to $R$ such that $a=rb$ or $b=ra$. This paper studies some properties of such weakly perfect graphs.
Farshid Pouralizadeh Moghaddam; Hossein Gholizade Narm
Abstract
In this paper, a synthesis method based on robust model predictive control is developed for compensation of uncertain time-delays in networked control systems with bounded disturbance. The proposed method uses linear matrix inequalities and uncertainty polytope to model uncertain ...
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In this paper, a synthesis method based on robust model predictive control is developed for compensation of uncertain time-delays in networked control systems with bounded disturbance. The proposed method uses linear matrix inequalities and uncertainty polytope to model uncertain time-delays and system disturbances. The continuous system with time-delay is discretized using uncertainty polytope. Then, the discretized model together with model disturbance is compensated. Uncertain parameters and additive disturbances are included in the controller design explicitly and robust stability is guaranteed in this method. The proposed method is applied to a level process. It is simulated by applying conventional RMPC as well. The simulation results show the effectiveness of the proposed method compared with the conventional algorithm of the RMPC\footnote{Robust Model Predictive Control} method.
Mohammad Gholami Baladezaei; Morteza Gachpazan; Akbar Hashemi Borzabadi
Abstract
In this paper, the benefits of 1/G'-expansion technique are utilized to create a direct scheme for extracting approximate solutions for a class of optimal control problems. In the given approach, first state and control functions have been parameterized as a power series, ...
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In this paper, the benefits of 1/G'-expansion technique are utilized to create a direct scheme for extracting approximate solutions for a class of optimal control problems. In the given approach, first state and control functions have been parameterized as a power series, which is constructed according to the solutions of a Bernoulli differential equation, where the number of terms in produced power series is determined by the balance method. A proportionate replacement and solving the created optimization problem lead to suitable solutions close to the analytical ones for the main problem. Numerical experiments are given to evaluate the quality of the proposed method.
Mahmoud Mahmoudi; Delaram Ahmad Ghondaghsaz
Abstract
In this paper, we present a new approach to solving stochastic differential equations and the Vasicek equation by using Brownian wavelets and multiple Ito-integral. Firstly, the calculation of the multiple Ito-integral based on the structure of Brownian motion is presented ...
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In this paper, we present a new approach to solving stochastic differential equations and the Vasicek equation by using Brownian wavelets and multiple Ito-integral. Firstly, the calculation of the multiple Ito-integral based on the structure of Brownian motion is presented and the error of Ito-integrate computation is minimized under this condition. Then, the Brownian wavelets 1D and 3D based on coefficients Brownian motion are introduced. After that, a system of linear and nonlinear equations of coefficients Brownian motion is obtained such that by solving this system the approximate solution of the Vasicek equation is obtained. In the last section, some numerical examples are given.
Control and Optimization
Sara Mansourinasab; Mahdi Sojoodi; Seyed Reza Moghadasi
Abstract
Conventional model predictive control (MPC) methods are usually implemented to systems with discrete-time dynamics laying on smooth vector space $ \mathbf{R}^n$. In contrast, the configuration space of the majority of mechanical systems is not expressed as Euclidean space. Therefore, ...
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Conventional model predictive control (MPC) methods are usually implemented to systems with discrete-time dynamics laying on smooth vector space $ \mathbf{R}^n$. In contrast, the configuration space of the majority of mechanical systems is not expressed as Euclidean space. Therefore, the MPC method in this paper has developed on a smooth manifold as the configuration space of the attitude control of a 3D pendulum. The Lie Group Variational Integrator (LGVI) equations of motion of the 3D pendulum have been considered as the discrete-time update equations since the LGVI equations preserve the group structure and conserve quantities of motion. The MPC algorithm is applied to the linearized dynamics of the 3D pendulum according to its LGVI equations around the equilibrium using diffeomorphism. Also, as in standard MPC algorithms, convex optimization is solved at each iteration to compute the control law. In this paper, the linear matrix inequality (LMI) is used to solve the convex optimization problem under constraints. A numerical example illustrates the design procedure.
Amir Hosein Mohajerzadeh; Abbas Ali Rezaee; Morteza Bigdeli
Abstract
Estimating the target parameter while the prior distribution function is known, and several observations which are provided by the sensor node is the main goal in this paper. In wireless sensor networks (WSN), nodes sense the environment and send data to a sink node called ...
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Estimating the target parameter while the prior distribution function is known, and several observations which are provided by the sensor node is the main goal in this paper. In wireless sensor networks (WSN), nodes sense the environment and send data to a sink node called Fusion Center (FC). FC collects data and estimates the observed parameter with user-defined precision. The proposed algorithm increases network lifetime and has an efficient estimation process. For this purpose, the proposed algorithm schedules node’s activity and determines the multihop path between nodes and FC. Simulation and performance analysis demonstrates proposed algorithm fulfills its goals.
Ghasem Ahmadi
Abstract
Rough extreme learning machines (RELMs) are rough-neural networks with one hidden layer where the parameters between the inputs and hidden neurons are arbitrarily chosen and never updated. In this paper, we propose RELMs with a stable online learning algorithm for the identification ...
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Rough extreme learning machines (RELMs) are rough-neural networks with one hidden layer where the parameters between the inputs and hidden neurons are arbitrarily chosen and never updated. In this paper, we propose RELMs with a stable online learning algorithm for the identification of continuous-time nonlinear systems in the presence of noises and uncertainties, and we prove the global asymptotically convergence of the proposed learning algorithm using the Lyapunov stability theory. Then, we use the proposed methodology to identify the chaotic systems of Duffing's oscillator and Lorentz system. Simulation results show the efficiency of the proposed model.
Hamed Soroush
Abstract
In this paper, we study nonsmooth optimization problems with quasiconvex functions using topological subdifferential. We present some necessary and sufficient optimality conditions and characterize topological pseudoconvex functions. Finally, the Mond-Weir type ...
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In this paper, we study nonsmooth optimization problems with quasiconvex functions using topological subdifferential. We present some necessary and sufficient optimality conditions and characterize topological pseudoconvex functions. Finally, the Mond-Weir type weak and strong duality results are stated for the problems.
Sayed Kahlil Ekrami
Abstract
In this paper, we prove that every orthogonally higher ring derivation is a higher ring derivation. Also we find the general solution of the pexider orthogonally higher ring derivations\begin{align*}\left\{\begin{array}{lr}f_n(x+y)=g_n(x)+h_n(y), ...
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In this paper, we prove that every orthogonally higher ring derivation is a higher ring derivation. Also we find the general solution of the pexider orthogonally higher ring derivations\begin{align*}\left\{\begin{array}{lr}f_n(x+y)=g_n(x)+h_n(y), \;\left\langle x,y \right\rangle =0,\\f_n(xy) = \sum_{i+j=n} g_i(x)h_j(y).\end{array}\right.\end{align*}Then we prove that for any approximate pexider orthogonally higher ring derivation under some control functions $ \varphi(x,y) $ and $ \psi(x,y) $, there exists a unique higher ring derivation $ D=\{d_n\}_{n=0}^\infty $, near $ \{f_n\}_{n=0}^\infty $, $ \{g_n\}_{n=0}^\infty $ and $ \{h_n\}_{n=0}^\infty $ estimated by $ \varphi $ and $ \psi $.
Ali Akbar Sohrabi; Reza Ghanbari; Khatere Ghorbani-Moghadam
Abstract
Project 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. ...
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Project 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.
Mehdi Zavieh; Hossein Kheiri; Bashir Naderi
Abstract
In this paper, we use a graphical algorithm to control and synchronization of a chaotic system. Most of the controllers designed for synchronizing chaotic systems are complex, but the controllers designed using contraction and graphical methods are often simple and linear. ...
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In this paper, we use a graphical algorithm to control and synchronization of a chaotic system. Most of the controllers designed for synchronizing chaotic systems are complex, but the controllers designed using contraction and graphical methods are often simple and linear. Therefore, we explain the relationship between contraction analysis and the graphical method for controlling and synchronizing chaotic systems. We apply this approach to control and synchronize the chaotic Genesio-Tesi system. The stability of the error system in synchronization is investigated using the contraction method. Finally, we provide numerical simulations to demonstrate the effectiveness of the proposed method.
Control and Optimization
Negar Izadi; Mohammad Taghi Dastjerdi
Abstract
In 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 ...
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In 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.
Control and Optimization
Reza Akbari; Leader Navaei; Mohammad Shahriari
Abstract
This 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 ...
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This 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.
