Hajar Alimorad
Abstract
While 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, ...
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While 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.
Control and Optimization
Masoomeh Ebrahimipour; Saeed Nezhadhosein; Seyed Mehdi Mirhosseini-Alizamini
Abstract
This paper presents an optimal robust adaptive technique for controlling a certain class of uncertain nonlinear affine systems. The proposed approach combines sliding mode control, a linear quadratic regulator for optimality, and gradient descent as an adaptive controller. ...
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This paper presents an optimal robust adaptive technique for controlling a certain class of uncertain nonlinear affine systems. The proposed approach combines sliding mode control, a linear quadratic regulator for optimality, and gradient descent as an adaptive controller. The convergence of the sliding mode control process is proven using two theorems based on the Lyapunov function. Simulation results for pendulum and inverted pendulum systems demonstrate that the proposed method outperforms both the linear quadratic regulator technique and the sliding mode control regarding reduced chattering and improved reaching time.
Control and Optimization
Fatemeh Babakordi; Nemat Allah Taghi-Nezhad
Abstract
This 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 ...
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This 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.
Control and Optimization
Sajad Amirian; Maghsoud Amiri; Mohammad Taghi Taghavifard
Abstract
Integrating 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, ...
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Integrating 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.
Control and Optimization
Zeinab Barary; AllahBakhsh Yazdani Cherati; Somayeh Nemati
Abstract
This 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 ...
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This 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.
Control and Optimization
Fahimeh Akhavan Ghassabzade; Mina Bagherpoorfard
Abstract
This 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 ...
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This 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.
Control and Optimization
Abbas Ali Rezaee; Hadis Ahmadian Yazdi; Mahdi Yousefzadeh Aghdam; Sahar Ghareii
Abstract
With 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 ...
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With 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.
Control and Optimization
Ali Asghar Hojatifard; Nader Kanzi; Shahriar Farahmand Rad
Abstract
This 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 ...
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This 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.
Control and Optimization
Farid Pourofoghi; Davood Darvishi Salokolaei
Abstract
Fractional 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 ...
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Fractional 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.
Control and Optimization
Hanifa Mosawi; Mostafa Tavakolli; Khatere Ghorbani-Moghadam
Abstract
Graph 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 ...
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Graph 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.
