conducted research on the key components of fractional calculus, and fractional differential equations and Das (2007) focused on the en- gineering perspective of this issue. Aghababa (2016) introduced a fractional **control** method for chaos **control** of integer-**order** non-autono- mous chaotic systems based on the **sliding** **mode** **control**. Zhong et al. (2015) developed fraction- al **order** **sliding** observer **mode** structures for the fractional **order** nonlinear system models. They investigated the asymptotic stability of error by Lyapunov stability analysis approach. Bisheban and Mahmoodabadi (2013) proposed the de- coupled SMC technique to stabilize an inverted pendulum, which was **optimized** by **Multi**-ob- jective particle swarm **algorithm** to reduce the normalized angle error of the pole and distance error of the cart, concurrently.

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A numerical **model** of the 5-story example **building** structure with two MR dampers is implemented in SIMULINK and MATLAB. **Using** this numerical **model**, time history analyses of 15 seconds with a time step of 0.005 sec are performed in **order** to investigate the **control** performance of MR dampers controlled by the MOGA **optimized** MISO ANFIS. The MOGA based optimization is performed with the population size of 100 individuals. An upper limit on the number of generations is specified to be 1000. As the number of generations increases, the **control** performance of the elite (i.e. non-dominated) individuals is improved. After optimization run, a set of optimal solutions is obtained. Optimization results show that two **objective** function values of every solution in optimal record are less than 1. It means that the MOGA **optimized** MISO-ANFISs can provide better **control** performance in reducing both displacement and acceleration responses compared to the MIMO fuzzy controller.

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III. EXPERIMENTAL RESULTS AND ANALYSIS The proposed **algorithm** is implemented **using** MATLAB 2012 MathWorks, Inc. software tool with 3GB RAM and 2.67 GHz processor. The performance of the proposed approach is tested on four datasets collected from UCI Machine Learning Repository [18], which is a collection of widely used real-world datasets for Data Mining and KDD community. For each dataset the proposed GA had 100 individuals in the population and was executed for 200 generations. The proposed **algorithm** was terminated when the maximum number of generations has reached. The performance of proposed **algorithm** is evaluated and compared with the well-known Apriori **Algorithm** and previous technique proposed by M. Ramesh et al. [19]. The default parameters of the Apriori **Algorithm** and proposed GA are used to make the comparison completely fair. The results for four datasets are an average over 10 executions. The summary of used datasets is given in Table II.

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Searching invisible information and pattern from large database is the work of data mining. **High** dimensionality is become a curse for data mining which generates problem while training the data. The curse of dimensionality can be reduced by **using** feature selection Technique. works on regression problem to select a group of feature to search the subset of the important factor that achieves efficient prediction [3], The step of Finding an optimal variable subset from original feature set is a feature selection Technique. The application in which there are large numbers of variable the feature selection is enforced to reduce the variable. The aim of feature selection is to find an appropriate feature that is required for target output. It removes the irrelevant and redundant feature from original feature sets. As showed by our broad test think about, the proposed structure accomplishes unrivaled component determination execution and alluring properties [16], Relevant feature provide useful information and redundant feature are those that are not useful than the selected features. So, feature selection is an important phase in efficient learning of large **multi**-feature data sets.

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As can be seen at Figure 1, there are two **objective**(s), which is to minimize both cost function (y (1)) and time (y (2)). In this optimization process, decision variables indicated by worker’s working hours that was denoted by notation w(1) and w(2) remarked number of workers.

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Chapter 4 presents the detailed methodology of the proposed **algorithm** called Global Criterion **Genetic** **Algorithm** (GCGA). Moreover, the modelling of the rotational inverted pendulum through derivation from the equations of motion is presented.

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The fractional-**order** diﬀerential operator is a generalization of an integer-**order** diﬀer- ential operator. There are three commonly used deﬁnitions of the fractional-**order** diﬀer- ential operator, viz. Grunwald–Letnikov, Riemann–Liouville, and Caputo [, ]. How- ever, in applications of fractional calculus in science and engineering, the Caputo deriva- tive and Riemann-Liouville are mostly used. In the literature [–], mostly the Caputo derivative is preferred since the initial value of a fractional diﬀerential equation with Ca- puto derivative is the same as that of an integer diﬀerential equation. Hence we derive the fractional-**order** **model** of PMSG from () with the Caputo fractional **order** deﬁnition, which is deﬁned as

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The main difference between the state estimation required for the PID **control** law and the MFSMC **control** law is the MFSMC **algorithm** requires full state feedback including absolute position, all Euler angles, and both the linear and angular velocities and accelerations. An IMU was used for state estimation of the required signals. The IMU consists of an accelerometer sensor which measures the three-axial accelerations and a gyroscope sensor measures the three rotational velocities providing direct measurements for the 𝑋̈, 𝑌̈, 𝑍̈, Ф̇, 𝛳̇, and 𝜓̇ states. The sensors are placed closed to the center-of-mass of the quadcopter to provide the most accurate data for linear acceleration at the center-of-gravity location. However, the sensors contain errors such a measurement bias. The bias can initially be removed by initializing the sensors at a static straight- and-level condition. Ideally, the accelerometer should output zero acceleration along the X and Y directions and 1 g along the Z direction and the gyroscope should read zero rotational velocities in all three axes for the straight-and-level static condition. During initialization, sensor measurements are recorded to calculate the sensor biases which are subsequently subtracted from each of the corresponding sensor signals.

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Formula (1) is the overall **objective**, minimize (2)~(4) and get the three subtotals. Formula (2) is the total of purchased cost of equipment, equipment operating cost and cost of equipment configuration of each plan period; Formula (3) show the largest deviation between each equipment’s load and capacity. It is nonlinear integer expression; Formula (4) expresses the total number of component move across the cell. Formula (5) shows that certain operation of a component only can be arranged to the only equipment to produce and process; formula (6) is the balance equation of the total number of equipment. Formula (7) shows that production capacity of each cell during every plan period that can satisfy the manufacture requirement. Formula (8) shows the amount of equipment k that add to cell I at the beginning of plan period t, it is decided by the differences between the amount of equipment k in cell I during the current plan period and the former plan period. Formula (9) shows the amount of equipment k disassembly from cell I at the beginning of plan period t. Formula (10) limits the maximum number and the minimum number of each cell. Formula (11) and (12) shows the decision variable’s 0-1 constrain and the nonnegative integer constrain.

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Oduguwa, Tiwari, Fiorentino and Roy use three different MOEAs to determine a good protein-ligand configuration for a given target protein and its binding components [118]. The three algorithms PAES, SPEA and NSGA-II are inves- tigated regarding their drug candidate discovery abilities for the protein-ligand docking problem. The framework including these three algorithms makes use of a specific chromosome structure comprising three coordinates of the chro- mosome in the target axes system, two angles of the chromosome compared to the reference compound and a set of relative coordinates of the chromosome in the compound axes system. PAES, SPEA and NSGA-II are compared to each other in solving a 3-**objective** MOP comprising the internal energy of the compound, the protein-compound couple’ s Van der Waals and electrostatic energy of interaction as well as the shape complementaries. The population size was set to 100, and 500 generations were performed. NSGA-II and PAES performed best, but the optimal solutions were found by all three MOEAs. Lee, Shin and Zhang published the NSGA-II with constrained tournament selection for the DNA sequence optimization [104]. The DNA sequence pro- blem is formulated as a 4-**objective** MOP with two constraints. The constraints are the number of bases G and C and the melting temperature. This specific NSGA-II uses a two-stage crossover process. The first stage is a sequence set level crossover, which is performed by an exchange of the sequences between two chromosomes. The second step is the one-point crossover. Furthermore, the one-point mutation is used on every chromosome. The constrained tourna- ment selection favors solutions, which are feasible, have less penalty or belong to a better front. Therefore, the selection process comprises three cases: First- ly, the feasible solutions are selected, secondly the one with less penalty is selected and thirdly the dominating one is selected or otherwise the one with the larger crowding distance. The sum of penalties is used for each constraint as the penalty of the chromosome. The experiments were performed with a population size of 1000 and 200 generations.

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Abstrak—Selama tiga dekade terakhir, banyak metode pemrograman matematis telah dikembangkan untuk memecahkan masalah optimasi. Namun, ada satu metode telah ditemukan yang sepenuhnya efisien dan kuat untuk berbagai masalah teknik optimasi. Kebanyakan aplikasi dalam desain teknik sipil melibatkan pemilihan pada satu set variabel desain yang menggambarkan perilaku dan kinerja dari masalah tertentu yang memenuhi persyaratan dan spesifikasi tertentu sesuai kode kepraktisan. Pengenalan **Genetic** **Algorithm** (GA) ke dalam bidang optimasi telah membuka jalan baru untuk penelitian karena telah terbukti berhasil diterapkan ketika metode tradisional menemui kegagalan. GA lebih efisien dan luas dalam prosedur pencarian secara global yang didasarkan pada pendekatan stokastik yang bergantung pada strategi "survival of the fittest". GA merupakan algoritma pencarian yang didasarkan pada konsep seleksi alam dan genetika secara alami. Pada penelitian ini **Multi**-tujuan optimasi dan konfigurasi dari truss dua dimensi dilakukan dengan menggunakan algoritma genetik. Beberapa hal dilakukan GA untuk menentukan kombinasi terbaik dari parameter GA seperti ukuran populasi dan probabilitas mutasi, hal ini untuk mendapatkan skala yang lebih baik untuk sisa berjalan. Dengan membandingkan hasil dari ukuran dan ukuran- konfigurasi optimasi, dapat diperoleh dari pengurangan yang signifikan dalam berat badan dan defleksi. Ukuran-konfigurasi optimasi menghasilkan bobot yang lebih ringan dan ukuran optimasi perpindahan yang kecil Hasil dengan menggunakan GA diperoleh relatif mudah dalam hal komputasi dan hasil ini sangat kompetitif dibandingkan dengan yang diperoleh dari metode selain optimasi truss.

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The switching power converters represent a particular class of variable structure systems (VSS). The latter are by definition nonlinear discrete systems that change structure or appear as various continuous nonlinear systems according to the state of the system [18]. Therefore, these converters can take advantage of nonlinear **control** techniques developed for this class of systems. Indeed, the power converters being endowed with a switching device, it is easy to design a discontinuous **control** law. The **Sliding** **Mode** **Control** (SMC) appeared in the Soviet Union in the 60s, which comes from the theory of VSS, allows accomplishing this task. This command leads to stability even in the presence of large variations in the supply or load, to good dynamic response and a simple implementation [19,20,21].

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decision making involving multiple competing objectives relies on choosing a design solution from an optimal set of solutions. [4] A study on the convergence of **Multi**-**objective** Evolutionary Algorithms is discussed by Tushar Goel et.al. It is discussed in the paper that **high** computational cost has been a major impediment to the widespread use of evolutionary algorithms in industry [5]. A Cumulative Evidential Stopping Criterion for **Multi**-**objective** Optimization Evolutionary Algorithms is discussed by Luis Martí, et.al. In this work a novel and efficient **algorithm** independent stopping criterion, called the MGBM criterion, suitable for **Multi**- **objective** Optimization Evolutionary Algorithms (MOEAs) is presented[6].Examining the relationship between **algorithm** stopping criteria and performance **using** elitist **genetic** **algorithm** is discussed by Jin-Lee Kim. A major disadvantage of **using** a **genetic** **algorithm** for solving a complex problem is that it requires a relatively large amount of computational time to search for the solution space before the solution is finally attained in the paper [7]. On the disruption level of polynomial mutation for evolutionary **multi**- **objective** optimization algorithms is studied by Mohammad Hadman. This paper looks at two variants of polynomial mutation used in various evolutionary optimization algorithms for mutli-**objective** problems [8]. Self-adaptive mechanism for **multi**-**objective** evolutionary algorithms is reported by Fanchao Zeng. In the paper it is discussed that evolutionary algorithms can efficiently solve **multi**-**objective** optimization problems (MOPs) by obtaining diverse and near-optimal solution sets. However, the performance of **multi**-**objective** evolutionary algorithms (MOEAs) is often limited by the suitability of their corresponding parameter settings with respect to different optimization problems [9].

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The quest for **high** Lift-to-Drag ratios leads designers to reduce as much as possible non-lifting parts of the vehicle. This requires, reducing and eliminating if possible tail surfaces and eventually resorting to flying wings. Such aerodynamic shapes do not exhibit much natural transverse stability and only provide limited **control** authority. It is, therefore, imperative to avoid situations where sideslip angle values exceed maximum **control** authority. The approach investigated in this work is an impulsive lateral **control** for driving to a quasi-null value the sideslip angle in a timely fashion, whenever eventually its value may exceed some maximum critical value. This impulsive **control** is powered by on-off thrusters and is supposed to be only used a few times during the flight, when such exceptional circumstances require it.

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In this paper, based on a fractional **order** Bergman minimal **model**, a robust strategy for regulation of blood glucose in type 1 diabetic patients is presented. Glucose/insulin concentration in the patient body is controlled through the injection under the patients skin by the pump. Many various con- trollers for this system have been proposed in the literature. However, most of them have consider the system as an integer **order** system. Moreover, the majority of the presented methods suffer from an important disadvantage that is long settling time of the **control** system. Thus, the contribution of this paper in comparison with previous related works is presenting a fractional back-stepping **sliding** **mode** **control** that considerably reduces the required time for glucose to reach its desired level. Due to the **sliding** **mode** design, the proposed controller is robust against external disturbances. Due to the back-stepping design, convergence of each state variable of the system to its desired value can be guaranteed separately. Simulation results verify the satisfactory performance of the proposed controller.

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Motif discovery is one of the fundamental problems that have important applications in identify- ing drug targets and regulatory sites. Regulatory sites on DNA sequence normally correspond to shared conservative sequence patterns among the regulatory regions of correlated genes. These conserved sequence patterns are called motifs. Identifying motifs and corresponding instances is very important, so biologists can investigate the interactions between DNA and proteins, gene regulation, cell development and cell reaction under physiological and pathological conditions. In this work, we developed a motif finding **algorithm** based on a **multi**-**objective** **genetic** **algorithm** technique and incorporated the hypergeometric scoring function to enable it discover gapped mo- tifs from organisms with challenging genomic structure such as the malaria parasite. The runtime performance of our resulting **algorithm**, EMOGAMOD (Extended **Multi** **Objective** **Genetic** **Algorithm** MOtif Discovery) was evaluated with that of some common motif discovery algorithms and the result was remarkable.

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However, FO SMC has been successfully applied in a wide range of engineering applications, it suffers from an inevitable problem, namely chattering phenomenon, leading to increasing the **control** effort and triggering the **high**-frequency dynamics of the system. Several research works have been dedicated to lessen the effects of the chattering, such as [12,13]. Another important topic in designing the SMC is the convergence speed and reaching phase in the finite time [14,15]. In [14], an adaptive terminal SMC was developed to **control** a power system. In [15], an adaptive nonlinear SMC scheme was proposed for a class of fourth-**order** systems.

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