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Showing papers presented at "Soft Computing in 2017"
Journal Article•10.1016/J.ASOC.2017.01.015•
Empirical Mode Decomposition based ensemble deep learning for load demand time series forecasting

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Xueheng Qiu1, Ye Ren1, Ponnuthurai Nagaratnam Suganthan1, Gehan A. J. Amaratunga2•
Nanyang Technological University1, University of Cambridge2
1 May 2017
TL;DR: An ensemble deep learning method has been proposed for load demand forecasting that composes of Empirical Mode Decomposition and Deep Belief Network and results demonstrated attractiveness of the proposed method compared with nine forecasting methods.
Abstract: Graphical abstractDisplay Omitted HighlightsAn ensemble deep learning method has been proposed for load demand forecasting.The hybrid method composes of Empirical Mode Decomposition and Deep Belief Network.Empirical Mode Decomposition based methods outperform the single structure models.Deep learning shows more advantages when the forecasting horizon increases. Load demand forecasting is a critical process in the planning of electric utilities. An ensemble method composed of Empirical Mode Decomposition (EMD) algorithm and deep learning approach is presented in this work. For this purpose, the load demand series were first decomposed into several intrinsic mode functions (IMFs). Then a Deep Belief Network (DBN) including two restricted Boltzmann machines (RBMs) was used to model each of the extracted IMFs, so that the tendencies of these IMFs can be accurately predicted. Finally, the prediction results of all IMFs can be combined by either unbiased or weighted summation to obtain an aggregated output for load demand. The electricity load demand data sets from Australian Energy Market Operator (AEMO) are used to test the effectiveness of the proposed EMD-based DBN approach. Simulation results demonstrated attractiveness of the proposed method compared with nine forecasting methods.

443 citations

Journal Article•10.1007/S00500-016-2161-7•
An improved ant colony algorithm for robot path planning

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Jianhua Liu1, Jianguo Yang1, Huaping Liu2, Xingjun Tian, Meng Gao •
Donghua University1, Tsinghua University2
1 Oct 2017
TL;DR: To solve the problems of convergence speed in the ant colony algorithm, an improved ant colony optimization algorithm is proposed for path planning of mobile robots in the environment that is expressed using the grid method.
Abstract: To solve the problems of convergence speed in the ant colony algorithm, an improved ant colony optimization algorithm is proposed for path planning of mobile robots in the environment that is expressed using the grid method. The pheromone diffusion and geometric local optimization are combined in the process of searching for the globally optimal path. The current path pheromone diffuses in the direction of the potential field force during the ant searching process, so ants tend to search for a higher fitness subspace, and the search space of the test pattern becomes smaller. The path that is first optimized using the ant colony algorithm is optimized using the geometric algorithm. The pheromones of the first optimal path and the second optimal path are simultaneously updated. The simulation results show that the improved ant colony optimization algorithm is notably effective.

379 citations

Journal Article•10.1007/S00500-016-2071-8•
A novel collaborative optimization algorithm in solving complex optimization problems

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Wu Deng, Huimin Zhao1, Huimin Zhao2, Li Zou3, Li Zou4, Li Zou1, Guangyu Li4, Guangyu Li1, Xinhua Yang1, Daqing Wu5, Daqing Wu6 •
Dalian Jiaotong University1, Guangxi University for Nationalities2, Southwest Jiaotong University3, Chongqing University4, University of South China5, Nanjing University of Information Science and Technology6
1 Aug 2017
TL;DR: The experiment results show that the proposed MGACACO algorithm can avoid falling into the local extremum, and takes on better search precision and faster convergence speed.
Abstract: To overcome the deficiencies of weak local search ability in genetic algorithms (GA) and slow global convergence speed in ant colony optimization (ACO) algorithm in solving complex optimization problems, the chaotic optimization method, multi-population collaborative strategy and adaptive control parameters are introduced into the GA and ACO algorithm to propose a genetic and ant colony adaptive collaborative optimization (MGACACO) algorithm for solving complex optimization problems. The proposed MGACACO algorithm makes use of the exploration capability of GA and stochastic capability of ACO algorithm. In the proposed MGACACO algorithm, the multi-population strategy is used to realize the information exchange and cooperation among the various populations. The chaotic optimization method is used to overcome long search time, avoid falling into the local extremum and improve the search accuracy. The adaptive control parameters is used to make relatively uniform pheromone distribution, effectively solve the contradiction between expanding search and finding optimal solution. The collaborative strategy is used to dynamically balance the global ability and local search ability, and improve the convergence speed. Finally, various scale TSP are selected to verify the effectiveness of the proposed MGACACO algorithm. The experiment results show that the proposed MGACACO algorithm can avoid falling into the local extremum, and takes on better search precision and faster convergence speed.

372 citations

Journal Article•10.1016/J.ASOC.2017.06.004•
Study on an improved adaptive PSO algorithm for solving multi-objective gate assignment

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Wu Deng1, Huimin Zhao2, Xinhua Yang2, Juxia Xiong3, Meng Sun2, Bo Li2 •
Nanjing University of Information Science and Technology1, Dalian Jiaotong University2, Guangxi University for Nationalities3
1 Oct 2017
TL;DR: The experiment results show that the DOADAPO algorithm can improve the convergence speed and enhance the local search ability and global search ability, and the multi-objective optimization model of gate assignment can improved the comprehensive service of gate assignments.
Abstract: Display Omitted An improved adaptive PSO based on Alpha-stable distribution and dynamic fractional calculus is studied.A new multi-objective optimization model of gate assignment problem is proposed.The actual data are used to demonstrate the effectiveness of the proposed method. Gate is a key resource in the airport, which can realize rapid and safe docking, ensure the effective connection between flights and improve the capacity and service efficiency of airport. The minimum walking distances of passengers, the minimum idle time variance of each gate, the minimum number of flights at parking apron and the most reasonable utilization of large gates are selected as the optimization objectives, then an efficient multi-objective optimization model of gate assignment problem is proposed in this paper. Then an improved adaptive particle swarm optimization(DOADAPO) algorithm based on making full use of the advantages of Alpha-stable distribution and dynamic fractional calculus is deeply studied. The dynamic fractional calculus with memory characteristic is used to reflect the trajectory information of particle updating in order to improve the convergence speed. The Alpha-stable distribution theory is used to replace the uniform distribution in order to escape from the local minima in a certain probability and improve the global search ability. Next, the DOADAPO algorithm is used to solve the constructed multi-objective optimization model of gate assignment in order to fast and effectively assign the gates to different flights in different time. Finally, the actual flight data in one domestic airport is used to verify the effectiveness of the proposed method. The experiment results show that the DOADAPO algorithm can improve the convergence speed and enhance the local search ability and global search ability, and the multi-objective optimization model of gate assignment can improve the comprehensive service of gate assignment. It can effectively provide a valuable reference for assigning the gates in hub airport.

357 citations

Journal Article•10.1007/S00500-016-2262-3•
Application of reproducing kernel algorithm for solving second-order, two-point fuzzy boundary value problems

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Omar Abu Arqub1, Mohammed Al-Smadi1, Shaher Momani2, Tasawar Hayat3•
Al-Balqa` Applied University1, University of Jordan2, Quaid-i-Azam University3
1 Dec 2017
TL;DR: This paper investigates the analytic and approximate solutions of second-order, two-point fuzzy boundary value problems based on the reproducing kernel theory under the assumption of strongly generalized differentiability.
Abstract: In this paper, we investigate the analytic and approximate solutions of second-order, two-point fuzzy boundary value problems based on the reproducing kernel theory under the assumption of strongly generalized differentiability. The solution methodology is based on generating the orthogonal basis from the obtained kernel functions, while the orthonormal basis is constructing in order to formulate and utilize the solutions with series form in terms of their r-cut representation in the space $$\oplus _{j=1}^2 W_2^3 \left[ {a,b}\right] $$źj=12W23a,b. An efficient computational algorithm is provided to guarantee the procedure and to confirm the performance of the proposed method. Results of numerical experiments are provided to illustrate the theoretical statements in order to show potentiality, generality, and superiority of our algorithm for solving such fuzzy equations. Graphical results, tabulated data, and numerical comparisons are presented and discussed quantitatively to illustrate the possible fuzzy solutions.

320 citations

Journal Article•10.1515/JAISCR-2017-0004•
A Survey of Artificial Intelligence Techniques Employed for Adaptive Educational Systems within E-Learning Platforms

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Khalid Colchester1, Hani Hagras1, Daniyal M. Alghazzawi2, Ghadah Aldabbagh2•
University of Essex1, King Abdulaziz University2
1 Jan 2017
TL;DR: A survey of raised and related topics to the field of artificial intelligence techniques employed for adaptive educational systems within e-learning, their advantages and disadvantages, and a discussion of the importance of using those techniques to achieve more intelligent and adaptive e- learning environments.
Abstract: The adaptive educational systems within e-learning platforms are built in response to the fact that the learning process is different for each and every learner. In order to provide adaptive e-learning services and study materials that are tailor-made for adaptive learning, this type of educational approach seeks to combine the ability to comprehend and detect a person's specific needs in the context of learning with the expertise required to use appropriate learning pedagogy and enhance the learning process. Thus, it is critical to create accurate student profiles and models based upon analysis of their affective states, knowledge level, and their individual personality traits and skills. The acquired data can then be efficiently used and exploited to develop an adaptive learning environment. Once acquired, these learner models can be used in two ways. The first is to inform the pedagogy proposed by the experts and designers of the adaptive educational system. The second is to give the system dynamic self-learning capabilities from the behaviors exhibited by the teachers and students to create the appropriate pedagogy and automatically adjust the e-learning environments to suit the pedagogies. In this respect, artificial intelligence techniques may be useful for several reasons, including their ability to develop and imitate human reasoning and decision-making processes (learning-teaching model) and minimize the sources of uncertainty to achieve an effective learning-teaching context. These learning capabilities ensure both learner and system improvement over the lifelong learning mechanism. In this paper, we present a survey of raised and related topics to the field of artificial intelligence techniques employed for adaptive educational systems within e-learning, their advantages and disadvantages, and a discussion of the importance of using those techniques to achieve more intelligent and adaptive e-learning environments.

284 citations

Journal Article•10.1016/J.ASOC.2017.03.045•
A systematic review and meta-Analysis of SWARA and WASPAS methods: Theory and applications with recent fuzzy developments

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Abbas Mardani1, Mehrbakhsh Nilashi1, Mehrbakhsh Nilashi2, Norhayati Zakuan1, Nanthakumar Loganathan1, Somayeh Soheilirad1, Muhamad Zameri Mat Saman1, Othman Ibrahim1 •
Universiti Teknologi Malaysia1, Islamic Azad University2
1 Aug 2017
TL;DR: In this article, a systematic review of methodologies and applications with recent fuzzy developments of two new MCDM utility determining approaches including step-wise weight assessment ratio analysis (SWARA) and the Weighted Aggregated Sum Product Assessment (WASPAS) is presented.
Abstract: The Multiple Criteria Decision Making (MCDM) utility determining approaches and fuzzy sets are considered to be new development approaches, which have been recently presented, extended, and used by some scholars in area of decision making. There is a lack of research regarding to systematic literature review and classification of study about these approaches. Therefore; in the present study, the attempt is made to present a systematic review of methodologies and applications with recent fuzzy developments of two new MCDM utility determining approaches including Step-wise Weight Assessment Ratio Analysis (SWARA) and the Weighted Aggregated Sum Product Assessment (WASPAS) and fuzzy extensions which discussed in recent years. Regarding this, some major databases including Web of Science, Scopus and Google Scholar have been nominated and systematic and meta-analysis method which called “PRISMA” has been proposed. In addition, the selected articles were classified based on authors, the year of publication, journals and conferences names, the technique and method used, research objectives, research gap and problem, solution and modeling, and finally results and findings. The results of this study can assist decision-makers in handling information such as stakeholders’ preferences, interconnected or contradictory criteria and uncertain environments. In addition, findings of this study help to practitioners and academic for adopting the new MCDM utility techniques such as WASPAS and SWARA in different application areas and presenting insight into literature.

281 citations

Journal Article•10.1016/J.ASOC.2017.01.008•
Chaotic gravitational constants for the gravitational search algorithm

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Seyedali Mirjalili1, Amir H. Gandomi2•
Griffith University1, Michigan State University2
1 Apr 2017
TL;DR: Ten chaotic maps are embedded into the gravitational constant of the recently proposed population-based meta-heuristic algorithm called Gravitational Search Algorithm (GSA) and it is demonstrated that sinusoidal map is the best map for improving the performance of GSA significantly.
Abstract: Display Omitted Chaotic maps have been embedded into Gravitational Search Algorithms (GSA) for the first time.The problem of trapping in local minima in GSA has been improved by the chaotic maps.The convergence rate of GSA has been improved.The statistical test allowed us to judge about the significance of the results.An adaptive normalization is proposed to smoothly transit from the exploration phase to the exploitation phase. In a population-based meta-heuristic, the search process is divided into two main phases: exploration versus exploitation. In the exploration phase, a random behavior is fruitful to explore the search space as extensive as possible. In contrast, a fast exploitation toward the promising regions is the main objective of the latter phase. It is really challenging to find a proper balance between these two phases because of the stochastic nature of population-based meta-heuristic algorithms. The literature shows that chaotic maps are able to improve both phases. This work embeds ten chaotic maps into the gravitational constant (G) of the recently proposed population-based meta-heuristic algorithm called Gravitational Search Algorithm (GSA). Also, an adaptive normalization method is proposed to transit from the exploration phase to the exploitation phase smoothly. As case studies, twelve shifted and biased benchmark functions evaluate the performance of the proposed chaos-based GSA algorithms in terms of exploration and exploitation. A statistical test called Wilcoxon rank-sum is done to judge about the significance of the results as well. The results demonstrate that sinusoidal map is the best map for improving the performance of GSA significantly.

273 citations

Journal Article•10.1016/J.ASOC.2017.02.007•
Ensemble particle swarm optimizer

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Nandar Lynn1, Ponnuthurai Nagaratnam Suganthan1•
Nanyang Technological University1
1 Jun 2017
TL;DR: The performance of the proposed ensemble particle swarm optimization algorithm (EPSO) is evaluated using the CEC2005 real-parameter optimization benchmark problems and compared with each individual algorithm and other state-of-the-art optimization algorithms to show the superiority of the proposal.
Abstract: Display Omitted Ensemble of particle swarm optimization algorithms with self-adaptive mechanism called EPSO is proposed in this paper.In EPSO, the population is divided into small and large subpopulations to enhance population diversity.In small subpopulation, comprehensive learning PSO (CLPSO) is used to preserve the population diversity.In large subpopulation, inertia weight PSO, CLPSO, FDR-PSO, HPSO-TVAC and LIPS are hybridized together as an ensemble approach.Self-adaptive mechanism is employed to identify the best algorithm by learning from their previous experiences so that best-performing algorithm is assigned to individuals in the large subpopulation. According to the No Free Lunch (NFL) theorem, there is no single optimization algorithm to solve every problem effectively and efficiently. Different algorithms possess capabilities for solving different types of optimization problems. It is difficult to predict the best algorithm for every optimization problem. However, the ensemble of different optimization algorithms could be a potential solution and more efficient than using one single algorithm for solving complex problems. Inspired by this, we propose an ensemble of different particle swarm optimization algorithms called the ensemble particle swarm optimizer (EPSO) to solve real-parameter optimization problems. In each generation, a self-adaptive scheme is employed to identify the top algorithms by learning from their previous experiences in generating promising solutions. Consequently, the best-performing algorithm can be determined adaptively for each generation and assigned to individuals in the population. The performance of the proposed ensemble particle swarm optimization algorithm is evaluated using the CEC2005 real-parameter optimization benchmark problems and compared with each individual algorithm and other state-of-the-art optimization algorithms to show the superiority of the proposed ensemble particle swarm optimization (EPSO) algorithm.

266 citations

Journal Article•10.1007/S00500-016-2247-2•
SVM or deep learning? A comparative study on remote sensing image classification

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Peng Liu1, Kim-Kwang Raymond Choo2, Lizhe Wang1, Fang Huang3•
Chinese Academy of Sciences1, University of South Australia2, University of Electronic Science and Technology of China3
1 Dec 2017
TL;DR: Auto-encoder and support vector machine can also perform better than SAE in some circumstances, and active learning schemes can be used to achieve high classification accuracy in both methods.
Abstract: With constant advancements in remote sensing technologies resulting in higher image resolution, there is a corresponding need to be able to mine useful data and information from remote sensing images. In this paper, we study auto-encoder (SAE) and support vector machine (SVM), and to examine their sensitivity, we include additional umber of training samples using the active learning frame. We then conduct a comparative evaluation. When classifying remote sensing images, SVM can also perform better than SAE in some circumstances, and active learning schemes can be used to achieve high classification accuracy in both methods.

261 citations

Journal Article•10.1016/J.ASOC.2016.12.024•
An evaluation of Convolutional Neural Networks for music classification using spectrograms

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Yandre M. G. Costa, Luiz S. Oliveira, Carlos N. Silla1•
The Catholic University of America1
1 Mar 2017
TL;DR: The experiments show that the CNN compares favorably to other classifiers in several scenarios, hence, it is a very interesting alternative for music genre recognition.
Abstract: Graphical abstractDisplay Omitted HighlightsMusic classification using spectrograms and Convolutional Neural Networks.Compare results with state of the art in Latin Music Database, ISMIR 2004 and African music collection.Assessing complementarity between Convolutional Neural Networks and classifiers built with hand-crafted features. Music genre recognition based on visual representation has been successfully explored over the last years. Classifiers trained with textural descriptors (e.g., Local Binary Patterns, Local Phase Quantization, and Gabor filters) extracted from the spectrograms have achieved state-of-the-art results on several music datasets. In this work, though, we argue that we can go further with the time-frequency analysis through the use of representation learning. To show that, we compare the results obtained with a Convolutional Neural Network (CNN) with the results obtained by using handcrafted features and SVM classifiers. In addition, we have performed experiments fusing the results obtained with learned features and handcrafted features to assess the complementarity between these representations for the music classification task. Experiments were conducted on three music databases with distinct characteristics, specifically a western music collection largely used in research benchmarks (ISMIR 2004 Database), a collection of Latin American music (LMD database), and a collection of field recordings of ethnic African music. Our experiments show that the CNN compares favorably to other classifiers in several scenarios, hence, it is a very interesting alternative for music genre recognition. Considering the African database, the CNN surpassed the handcrafted representations and also the state-of-the-art by a margin. In the case of the LMD database, the combination of CNN and Robust Local Binary Pattern achieved a recognition rate of 92%, which to the best of our knowledge, is the best result (using an artist filter) on this dataset so far. On the ISMIR 2004 dataset, although the CNN did not improve the state of the art, it performed better than the classifiers based individually on other kind of features.
Journal Article•10.1016/J.ASOC.2016.11.026•
Classification of human cancer diseases by gene expression profiles

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Hanaa Salem1, Gamal Attiya2, Nawal El-Fishawy2•
Delta State University1, Menoufia University2
1 Jan 2017
TL;DR: A new methodology based on the gene expression profiles to classify human cancer diseases is presented, which combines both Information Gain and Standard Genetic Algorithm and improves the classification performance of other classifiers generally.
Abstract: Display Omitted DNA microarrays appearances empowered the simultaneous observing of expression levels of a large number of genes.In the proposed methodology, Information gain (IG) is first used for feature selection, then Genetic Algorithm (GA) is employed for feature reduction and finally Genetic Programming (GP) is used for cancer types' classification. A cancers disease in virtually any of its types presents a significant reason behind death surrounding the world. In cancer analysis, classification of varied tumor types is of the greatest importance. Microarray gene expressions datasets investigation has been seemed to provide a successful framework for revising tumor and genetic diseases. Despite the fact that standard machine learning ML strategies have effectively been valuable to realize significant genes and classify category type for new cases, regular limitations of DNA microarray data analysis, for example, the small size of an instance, an incredible feature number, yet reason for limitation its investigative, medical and logical uses. Extending the interpretability of expectation and forecast approaches while holding a great precision would help to analysis genes expression profiles information in DNA microarray dataset all the most reasonable and proficiently. This paper presents a new methodology based on the gene expression profiles to classify human cancer diseases. The proposed methodology combines both Information Gain (IG) and Standard Genetic Algorithm (SGA). It first uses Information Gain for feature selection, then uses Genetic Algorithm (GA) for feature reduction and finally uses Genetic Programming (GP) for cancer types' classification. The suggested system is evaluated by classifying cancer diseases in seven cancer datasets and the results are compared with most latest approaches. The use of proposed system on cancers datasets matching with other machine learning methodologies shows that no classification technique commonly outperforms all the others, however, Genetic Algorithm improve the classification performance of other classifiers generally.
Journal Article•10.1007/S00500-016-2307-7•
Biogeography-based learning particle swarm optimization

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Xu Chen1, Huaglory Tianfield2, Congli Mei1, Wenli Du3, Guohai Liu1 •
Jiangsu University1, Glasgow Caledonian University2, East China University of Science and Technology3
1 Dec 2017
TL;DR: This paper explores biogeography-based learning particle swarm optimization (BLPSO), whereby each particle updates itself by using the combination of its own personal best position and personal best positions of all other particles through the BBO migration.
Abstract: This paper explores biogeography-based learning particle swarm optimization (BLPSO). Specifically, based on migration of biogeography-based optimization (BBO), a new biogeography-based learning strategy is proposed for particle swarm optimization (PSO), whereby each particle updates itself by using the combination of its own personal best position and personal best positions of all other particles through the BBO migration. The proposed BLPSO is thoroughly evaluated on 30 benchmark functions from CEC 2014. The results are very promising, as BLPSO outperforms five well-established PSO variants and several other representative evolutionary algorithms.
Journal Article•10.1016/J.ASOC.2016.10.030•
Automatic surface defect detection for mobile phone screen glass based on machine vision

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Chuanxia Jian1, Jian Gao1, Yinhui Ao1•
Guangdong University of Technology1
1 Mar 2017
TL;DR: An improved fuzzy c-means cluster (IFCM) algorithm is developed, and the proposed algorithms are validated using a number of experimental tests on MPSG images, showing that it has better performance than other methods.
Abstract: Display Omitted A surface defect detection system is proposed for mobile phone screen glass. This system achieves 94% in sensitivity and 97.33% in specificity.The proposed system takes approximate 1.6601s to detect a MPSG. The detection accuracy and speed can meet the needs of online detection for MPSG.Compared with other methods used in the experiment, the proposed improved fuzzy c-means can segment the surface defects in MPSG more accurately. Defect detection using machine vision technology plays an important role in the manufacturing process of mobile phone screen glass (MPSG). This study proposes an improved detection algorithm for MPSG defect recognition and segmentation. Considering the problem of MPSG image misalignment caused by vibrations in the mobile stages, a contour-based registration (CR) method is used to generate the template image used to align the MPSG images. Based on this registration result, the combination of subtraction and projection (CSP) is used to identify defects on the MPSG image, which can eliminate the influence of fluctuation in ambient illumination. To segment the defects with a fuzzy grey boundary from a noisy MPSG image, an improved fuzzy c-means cluster (IFCM) algorithm is developed in this study. A defect detection system is developed, and the proposed algorithms are validated using a number of experimental tests on MPSG images. The testing results demonstrate that the approach proposed in this study can effectively detect various defects on MPSG and that it has better performance than other methods.
Journal Article•10.1016/J.ASOC.2017.05.012•
A hierarchical global path planning approach for mobile robots based on multi-objective particle swarm optimization

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Thi Thoa Mac1, Cosmin Copot2, Duc Trung Tran1, Robin De Keyser3•
Hanoi University of Science and Technology1, University of Antwerp2, Ghent University3
1 Oct 2017
TL;DR: A proposed particle swarm optimization with an accelerated update methodology based on Pareto dominance principle is employed to generate the global optimal path with the focus on minimizing the path length and maximizing the path smoothness.
Abstract: Display Omitted A novel hierarchical global path planning approach for mobile robots in a cluttered environment.A proposed particle swarm optimization with an accelerated update methodology based on Pareto dominance principle.Providing optimal global robot paths with computational efficiency. In this paper, a novel hierarchical global path planning approach for mobile robots in a cluttered environment is proposed. This approach has a three-level structure to obtain a feasible, safe and optimal path. In the first level, the triangular decomposition method is used to quickly establish a geometric free configuration space of the robot. In the second level, Dijkstra's algorithm is applied to find a collision-free path used as input reference for the next level. Lastly, a proposed particle swarm optimization called constrained multi-objective particle swarm optimization with an accelerated update methodology based on Pareto dominance principle is employed to generate the global optimal path with the focus on minimizing the path length and maximizing the path smoothness. The contribution of this work consists in: (i) The development of a novel optimal hierarchical global path planning approach for mobile robots moving in a cluttered environment; (ii) The development of proposed particle swarm optimization with an accelerated update methodology based on Pareto dominance principle to solve robot path planning problems; (iii) Providing optimal global robot paths in terms of the path length and the path smoothness taking into account the physical robot system limitations with computational efficiency. Simulation results in various types of environments are conducted in order to illustrate the superiority of the hierarchical approach.
Journal Article•10.1016/J.ASOC.2016.12.027•
A simulated annealing heuristic for the hybrid vehicle routing problem

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Vincent F. Yu1, A. A. N. Perwira Redi1, Yosi Agustina Hidayat2, Oktaviyanto Jimat Wibowo2•
National Taiwan University of Science and Technology1, Bandung Institute of Technology2
1 Apr 2017
TL;DR: A simulated annealing (SA) heuristic is proposed to solve the hybrid vehicle routing problem (HVRP), which is an extension of the Green Vehicle Routing Problem (G-VRP) and results show that the proposed SA effectively solves HVRP.
Abstract: Display Omitted This research proposes the hybrid vehicle routing problem (HVRP), which is an extension of the green vehicle routing problem.A simulated annealing (SA) heuristic is proposed to solve HVRP.Computational results show that the proposed SA effectively solves HVRP.Sensitivity analysis has been conducted to understand the effect of hybrid vehicles and charging stations on the travel cost. This study proposes the Hybrid Vehicle Routing Problem (HVRP), which is an extension of the Green Vehicle Routing Problem (G-VRP). We focus on vehicles that use a hybrid power source, known as the Plug-in Hybrid Electric Vehicle (PHEV) and generate a mathematical model to minimize the total cost of travel by driving PHEV. Moreover, the model considers the utilization of electric and fuel power depending on the availability of either electric charging or fuel stations.We develop simulated annealing with a restart strategy (SA_RS) to solve this problem, and it consists of two versions. The first version determines the acceptance probability of a worse solution using the Boltzmann function, denoted as SA_RSBF. The second version employs the Cauchy function to determine the acceptance probability of a worse solution, denoted as SA_RSCF. The proposed SA algorithm is first verified with benchmark data of the capacitated vehicle routing problem (CVRP), with the result showing that it performs well and confirms its efficiency in solving CVRP. Further analysis show that SA_RSCF is preferable compared to SA_RSBF and that SA with a restart strategy performs better than without a restart strategy. We next utilize the SA_RSCF method to solve HVRP. The numerical experiment presents that vehicle type and the number of electric charging stations have an impact on the total travel cost.
Journal Article•10.1007/S00500-016-2211-1•
Multiple criteria decision making based on Bonferroni means with hesitant fuzzy linguistic information

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Xunjie Gou1, Zeshui Xu1, Zeshui Xu2, Huchang Liao1•
Sichuan University1, Nanjing University of Information Science and Technology2
1 Nov 2017
TL;DR: In this paper, two aggregation operators for hesitant fuzzy linguistic term sets are introduced, which are the hesitation fuzzy linguistic Bonferroni mean operator and the weighted hesitant fuzzy linguistics Bonferronsi mean operators.
Abstract: In recent decades, different extensional forms of fuzzy sets have been developed. However, these multitudinous fuzzy sets are unable to deal with quantitative information better. Motivated by fuzzy linguistic approach and hesitant fuzzy sets, the hesitant fuzzy linguistic term set was introduced and it is a more reasonable set to deal with quantitative information. During the process of multiple criteria decision making, it is necessary to propose some aggregation operators to handle hesitant fuzzy linguistic information. In this paper, two aggregation operators for hesitant fuzzy linguistic term sets are introduced, which are the hesitant fuzzy linguistic Bonferroni mean operator and the weighted hesitant fuzzy linguistic Bonferroni mean operator. Correspondingly, several properties of these two aggregation operators are discussed. Finally, a practical case is shown in order to express the application of these two aggregation operators. This case mainly discusses how to choose the best hospital about conducting the whole society resource management research included in a wisdom medical health system.
Journal Article•10.1016/J.ASOC.2017.01.033•
A generalized dynamic fuzzy neural network based on singular spectrum analysis optimized by brain storm optimization for short-term wind speed forecasting

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Xuejiao Ma1, Yu Jin1, Qingli Dong1•
Dongbei University of Finance and Economics1
1 May 2017
TL;DR: A model that combines a denoising method with a dynamic fuzzy neural network to address the problems above is proposed and can both satisfactorily approximates the actual value and be used as an effective and simple tool for the planning of smart grids.
Abstract: An effective hybrid model is proposed to forecast the short-term wind speed.A new data preprocessing method is put forward.The fuzzy neural network is modified.Three comparative experiments are performed to prove the validity of the hybrid model. Wind speed forecasting plays a pivotal role in power dispatching and normal operations of power grids. However, it is both a difficult and challenging problem to achieve high-precision forecasting for the wind speed because the original sequence includes many nonlinear stochastic signals. The current conventional forecasting methods are more suitable for capturing linear trends, and artificial neural networks easily fall into a local optimum. This paper proposes a model that combines a denoising method with a dynamic fuzzy neural network to address the problems above. Singular spectrum analysis optimized by brain storm optimization is applied to preprocess the original wind speed data to obtain a smoother sequence, and a generalized dynamic fuzzy neural network is utilized to perform the forecasting. With a smaller and simpler structure of the neural network, the model can effectively achieve a rapid learning rate and accurate forecasting. Three experimental results, which cover 10-min, 30-min and 60-min interval wind speed time series data, demonstrate that the model can both satisfactorily approximates the actual value and be used as an effective and simple tool for the planning of smart grids.
Journal Article•10.1016/J.ASOC.2016.08.051•
Application of a new combined intuitionistic fuzzy MCDM approach based on axiomatic design methodology for the supplier selection problem

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Glin Bykzkan1, Fethullah Ger1•
Galatasaray University1
1 Mar 2017
TL;DR: In this paper, the authors proposed a new combined intuitionistic fuzzy (IF) MCDM approach for effective supplier selection, which is used for evaluating and selecting a suitable supplier is a complex problem which involves a number of different criteria.
Abstract: This study proposes a new combined intuitionistic fuzzy (IF) MCDM approach for effective supplier selection.IF Analytic Hierarchy Process is used to determine the supplier evaluation criteria weights.IF Axiomatic Design is used in order to evaluate potential suppliers.A case study from Turkey is provided to validate the proposed integrated IF MCDM approach.This study can be useful to researchers and to organizations in designing better satisfying supplier evaluation systems. Evaluating and selecting a suitable supplier is a complex problem which involves a number of different criteria. In literature, there are various multi-criteria decision making (MCDM) methods available with their own characteristic features. The focus of this study is intuitionistic fuzzy (IF) MCDM methods which have attracted much attention from academics and practitioners in recent years. IF sets are widely used to tackle imprecise and uncertain decision information in decision making due to their capability of accommodating the hesitation in human decision processes. This study proposes a new integrated methodology that is used for the first time in the literature. This approach consists of intuitionistic fuzzy analytic hierarchy process (IFAHP), an MCDM technique, for determining the weights of supplier evaluation criteria, and the concept of intuitionistic fuzzy axiomatic design (IFAD) principles for ranking competing supplier alternatives with respect to their overall performance. Decision makers assessments and opinions are extended to the IF environment in this approach and furthermore, the group decision making (GDM) approach is utilized in order to overcome uncertainties and vagueness, minimize the partiality of decision process and to avoid bias. This study contributes to supplier selection and IF sets literature by providing a combined framework based on IFAHP and IFAD methodology for the first time. To assess the validity of the proposed integrated IF MCDM approach, a case study from Turkey is provided. This study can be useful to researchers in better understanding the supplier selection problem theoretically, as well as to organizations in designing better satisfying supplier evaluation systems.
Journal Article•10.1007/S00500-016-2118-X•
Failure mode and effect analysis using MULTIMOORA method with continuous weighted entropy under interval-valued intuitionistic fuzzy environment

[...]

Hao Zhao1, Jian-Xin You1, Hu-Chen Liu2•
Tongji University1, Shanghai University2
1 Sep 2017
TL;DR: A novel approach based on interval-valued intuitionistic fuzzy sets (IVIFSs) and MULTIMOORA method to handle the uncertainty and vagueness from FMEA team members’ subjective assessments and to get a more accurate ranking of failure modes identified in FMEa is presented.
Abstract: Failure mode and effect analysis (FMEA) is a prospective risk assessment tool used to identify, assess and eliminate potential failure modes in various industries to improve security and reliability. However, the conventional risk priority number (RPN) method has been widely criticized for the deficiencies in risk factor weights, calculation of RPN, evaluation of failure modes, etc. In this paper, we present a novel approach for FMEA based on interval-valued intuitionistic fuzzy sets (IVIFSs) and MULTIMOORA method to handle the uncertainty and vagueness from FMEA team members’ subjective assessments and to get a more accurate ranking of failure modes identified in FMEA. In this proposed model, interval-valued intuitionistic fuzzy (IVIF) continuous weighted entropy is applied for risk factor weighting and the IVIF-MULTIMOORA method is used to determine the risk priority order of failure modes. Finally, an illustrative case is provided to demonstrate the effectiveness and practicality of the proposed FMEA and a comparison analysis with other relevant methods is conducted to show its merits.
Journal Article•10.1007/S00500-015-1818-Y•
Single-valued neutrosophic similarity measures based on cotangent function and their application in the fault diagnosis of steam turbine

[...]

Jun Ye1•
Shaoxing University1
1 Feb 2017
TL;DR: In this article, the authors proposed two cotangent similarity measures for single-valued neutrosophic sets (SVNSs) based on the COTangent function.
Abstract: Similarity measure is an important tool in pattern recognition and fault diagnosis. This paper proposes two cotangent similarity measures for single-valued neutrosophic sets (SVNSs) based on cotangent function. Then, the weighted cotangent similarity measures are introduced by considering the importance of each element. Moreover, by the comparison between the cotangent similarity measures of SVNSs and existing cosine similarity measure of SVNSs, the developed cotangent similarity measures demonstrate their advantages and rationality and in some cases can overcome some disadvantages of the cosine similarity measure defined in vector space. Finally, the cotangent similarity measures are applied to the fault diagnosis of steam turbine. The proposed fault diagnosis method demonstrates its effectiveness and rationality by the comparative analysis with the cosine similarity measure in the fault diagnosis of steam turbine.
Journal Article•10.1016/J.ASOC.2017.01.039•
Model-based methods for continuous and discrete global optimization

[...]

Thomas Bartz-Beielstein, Martin Zaefferer
1 Jun 2017
TL;DR: A taxonomy is introduced, which is useful as a guideline for selecting adequate model-based optimization tools and a new approach for combining surrogate information via stacking is proposed in the third part.
Abstract: Graphical abstractDisplay Omitted HighlightsUp-to-date survey and comprehensive taxonomy of surrogate model based optimization algorithms.Covers continuous and discrete/combinatorial search spaces.Presents six strategies for dealing with discrete data structures.New strategy for model selection and combination in surrogate model-based optimization.Outlook on important challenges (model selection, dimensionality, benchmarks, definiteness) and research directions. The use of surrogate models is a standard method for dealing with complex real-world optimization problems. The first surrogate models were applied to continuous optimization problems. In recent years, surrogate models gained importance for discrete optimization problems. This article takes this development into consideration. The first part presents a survey of model-based methods, focusing on continuous optimization. It introduces a taxonomy, which is useful as a guideline for selecting adequate model-based optimization tools. The second part examines discrete optimization problems. Here, six strategies for dealing with discrete data structures are introduced. A new approach for combining surrogate information via stacking is proposed in the third part. The implementation of this approach will be available in the open source R package SPOT2. The article concludes with a discussion of recent developments and challenges in continuous and discrete application domains.
Journal Article•10.1016/J.ASOC.2017.03.038•
On a novel uncertain soft set model

[...]

Jianming Zhan1, Muhammad Irfan Ali, Nayyar Mehmood2•
Hubei University1, International Islamic University, Islamabad2
1 Jul 2017
TL;DR: A kind of novel soft set model called a Z-soft fuzzy rough set is presented by means of three uncertain models: soft sets, rough sets and fuzzy sets, which is an important generalization of Z- soft rough fuzzy sets.
Abstract: Graphical abstractDisplay Omitted HighlightsA novel Z-soft fuzzy rough set model is constructed.Novel idea and new results are different from Meng-SFR-model and Sun-SFR-model.A kind of decision making method based on the Z-SFR-sets is investigated.The comparisons of numerical experimentation are given.An overview of techniques based on some types of soft set models are discussed. In this paper, a kind of novel soft set model called a Z-soft fuzzy rough set is presented by means of three uncertain models: soft sets, rough sets and fuzzy sets, which is an important generalization of Z-soft rough fuzzy sets. As a novel Z-soft fuzzy rough set, its applications in the corresponding decision making problems are established. It is noteworthy that the underlying concepts keep the features of classical Pawlak rough sets. Moreover, this novel approach will involve fewer calculations when one applies this theory to algebraic structures. In particular, an approach for the method of decision making problem with respect to Z-soft fuzzy rough sets is proposed and the validity of the decision making methods is testified by a given example. At the same time, an overview of techniques based on some types of soft set models is investigated. Finally, the numerical experimentation algorithm is developed, in which the comparisons among three types of hybrid soft set models are analyzed.
Journal Article•10.1016/J.ASOC.2017.05.029•
Evolutionary learning based sustainable strain sensing model for structural health monitoring of high-rise buildings

[...]

Byung Kwan Oh1, Kyu Jin Kim1, Yousok Kim2, Hyo Seon Park1, Hojjat Adeli3 •
Yonsei University1, Hongik University2, Ohio State University3
1 Sep 2017
TL;DR: A sustainable strain-sensing model that employs an artificial neural network (ANN) to estimate the strain responses of columns depending on the wind-induced behavior of high-rise buildings and can build a relationship between the wind data and strain of vertical members is presented.
Abstract: Strain sensor network-based structural health monitoring systems have been used to assess the safety of high-rise buildings. In consideration of life cycle of high-rise buildings, long-term measurement by sensors should be required. However, because of unpredictable problems such as the lack of durability of sensors and data loggers, disruption in communication, and loss of data, long-term strain measurement of major structural members is currently infeasible. For sustainable safety assessment of high-rise buildings, this paper presents a sustainable strain-sensing model that employs an artificial neural network (ANN) to estimate the strain responses of columns depending on the wind-induced behavior of high-rise buildings. The ANN model used in the paper is based on evolutionary learning consists of training in radial basis function neural network (RBFN) and evolving in genetic algorithm. In this evolutionary RBFN (ERBFN). Weights between layers are trained and variables of Gaussian function in the RBFN are evolved to estimate strain responses of the column of the high-rise building structure. A wind tunnel test was performed to produce wind data and strains in column members in a high-rise building model. In the wind tunnel test, a specimen consisting of a core, perimeter columns, and outriggers is used to simulate the conditions of typical high-rise buildings with a slenderness ratio of 5.0. The proposed model is trained and verified by using the wind data such as wind speeds and directions and the corresponding strains measured with fiber optic grating sensors. In addition to estimation of the maximum and minimum values of strains in vertical members in a high-rise building, it is found that the proposed model can build a relationship between the wind data and strain of vertical members.
Journal Article•10.1016/J.ASOC.2016.12.052•
A physically based and machine learning hybrid approach for accurate rainfall-runoff modeling during extreme typhoon events

[...]

Chih-Chieh Young1, Wen-Cheng Liu, Ming-Chang Wu•
National Taiwan University1
1 Apr 2017
TL;DR: A novel hybrid model which integrates the outputs of physically based hydrologic modeling system into support vector machine is developed to predict hourly runoff discharges in Chishan Creek basin in southern Taiwan.
Abstract: Display OmittedArchitecture of (a) the neural network (NN) and (b) support vector machine (SVM). A physically based and machine learning hybrid approach is developed.The hourly runoff discharges during typhoon events are predicted.Three individual methods and their hybrid combinations are compared.The proposed model shows the superiority in 6h-ahead forecasting.The roles of the two components in the hybrid framework are clarified. Accurate rainfall-runoff modeling during typhoon events is an essential task for natural disaster reduction. In this study, a novel hybrid model which integrates the outputs of physically based hydrologic modeling system into support vector machine is developed to predict hourly runoff discharges in Chishan Creek basin in southern Taiwan. Seven storms (with a total of 1200 data sets) are used for model calibration (training) and validation. Six statistical indices (mean absolute error, root mean square error, correlation coefficient, error of time to peak discharge, error of peak discharge, and coefficient of efficiency) are employed to assess prediction performance. Overall, superiority of the present approach especially for a longer (6-h) lead time prediction is revealed through a systematic comparison among three individual methods (i.e., the physically based hydrologic model, artificial neural network, and support vector machine) as well as their two hybrid combinations. Besides, our analysis and in-depth discussions further clarify the roles of physically based and data-driven components in the proposed framework.
Journal Article•10.1007/S00500-016-2246-3•
Spectral---spatial multi-feature-based deep learning for hyperspectral remote sensing image classification

[...]

Lizhe Wang, Jiabin Zhang1, Peng Liu2, Kim-Kwang Raymond Choo3, Fang Huang4 •
Yanshan University1, Chinese Academy of Sciences2, University of South Australia3, University of Electronic Science and Technology of China4
1 Jan 2017
TL;DR: A hybrid of principle component analysis (PCA), guided filtering, deep learning architecture into hyperspectral data classification, and as a mature dimension reduction architecture, PCA is capable of reducing the redundancy of hyperspectrals information.
Abstract: Hyperspectral remote sensing has a strong ability in information expression, so it provides better support for classification. The methods proposed to deal the hyperspectral data classification problems were build one by one. However, most of them committed to spectral feature extraction that means wasting some valuable information and poor classification results. Thus, we should pay more attention to multi-features. And on the other hand, due to extreme requirements for classification accuracy, we should hierarchically explore more deep features. The first thought is machine learning, but the traditional machine learning classifiers, like the support vector machine, are not friendly to larger inputs and features. This paper introduces a hybrid of principle component analysis (PCA), guided filtering, deep learning architecture into hyperspectral data classification. In detail, as a mature dimension reduction architecture, PCA is capable of reducing the redundancy of hyperspectral information. In addition, guided filtering provides a passage to spatial-dominated information concisely and effectively. According to the stacked autoencoders which is a efficient deep learning architecture, deep-level multi-features are not in mystery. Two public data set PaviaU and Salinas are used to test the proposed algorithm. Experimental results demonstrate that the proposed spectral---spatial hyperspectral image classification method can show competitive performance. Multi-feature learning based on deep learning exhibits a great potential on the classification of hyperspectral images. When the number of samples is 30 % and the iteration number is over 1000, the accuracy rates for both of the two data set are over 99 %.
Journal Article•10.1007/S00500-015-1989-6•
Soft consensus measures in group decision making using unbalanced fuzzy linguistic information

[...]

Francisco Javier Cabrerizo1, Rami Al-Hmouz2, Ali Morfeq2, Abdullah Saeed Balamash2, M. A. Martínez3, Enrique Herrera-Viedma2 •
National University of Distance Education1, King Abdulaziz University2, University of Granada3
1 Jun 2017
TL;DR: The aim of this paper was to study how to adapt the existing approaches obtaining soft consensus measures to handle group decision-making situations in which unbalanced fuzzy linguistic information is used.
Abstract: An important question in group decision-making situations is how to estimate the consensus achieved within the group of decision makers. Dictionary meaning of consensus is a general and unanimous agreement among a group of individuals. However, most of the approaches deal with a more realistic situation of partial agreement. Defining a partial agreement of decision makers as a consensus up to some degree, the following question is how to obtain that soft degree of consensus. To do so, different approaches, in which the decision makers express their opinions by using symmetrical and uniformly distributed linguistic term sets, have been proposed. However, there exist situations in which the opinions are represented using unbalanced fuzzy linguistic term sets, in which the linguistic terms are not uniform and symmetrically distributed around the midterm. The aim of this paper was to study how to adapt the existing approaches obtaining soft consensus measures to handle group decision-making situations in which unbalanced fuzzy linguistic information is used. In addition, the advantages and drawbacks of these approaches are analyzed.
Journal Article•10.1007/S00500-015-1820-4•
A dynamic multi-objective evolutionary algorithm using a change severity-based adaptive population management strategy

[...]

Radhia Azzouz1, Slim Bechikh1, Lamjed Ben Said1•
Tunis University1
1 Feb 2017
TL;DR: This work proposes an adaptive hybrid population management strategy using memory, local search and random strategies, to effectively handle environment dynamicity for the multi-objective case where objective functions change over time.
Abstract: In addition to the need for simultaneously optimizing several competing objectives, many real-world problems are also dynamic in nature. These problems are called dynamic multi-objective optimization problems. Applying evolutionary algorithms to solve dynamic optimization problems has obtained great attention among many researchers. However, most of works are restricted to the single-objective case. In this work, we propose an adaptive hybrid population management strategy using memory, local search and random strategies, to effectively handle environment dynamicity for the multi-objective case where objective functions change over time. Moreover, the proposed strategy is based on a new technique that detects the change severity, according to which it adjusts the number of memory and random solutions to be used. This ensures, on the one hand, a high level of convergence and on the other hand, the required diversity. We propose a dynamic version of the Non dominated Sorting Genetic Algorithm II, within which we integrate the above-mentioned strategies. Empirical results show that our proposal based on the use of the adaptive strategy is able to handle dynamic environments and to track the Pareto front as it changes over time. Moreover, when confronted with several recently proposed dynamic algorithms, it has presented competitive and better results on most problems.
Journal Article•10.1016/J.ASOC.2017.01.037•
Optimal coordination of directional overcurrent relays using a modified electromagnetic field optimization algorithm

[...]

H.R.E.H. Bouchekara, Mohamed Zellagui1, M. A. Abido2•
University of Batna1, King Fahd University of Petroleum and Minerals2
1 May 2017
TL;DR: A modified version of the Electromagnetic Field Optimization (EFO) algorithm referred to as MEFO, inspired by the behaviour of particles of electromagnets with different polarities, is developed for the optimal coordination of Directional Overcurrent Relays.
Abstract: Display Omitted We solved the Directional Over Current Relays (DOCRs) optimal coordination problem.We used the Electromagnetic Field Optimization Algorithm (EFO).We improved the EFO algorithm for the optimal coordination of DOCRs.The proposed algorithm is better than other optimization algorithms. The optimal coordination of Directional Overcurrent Relays (DOCRs) is of paramount importance for power systems protection. The optimization model of this problem is non-linear and highly constrained. The main objective of this paper is to develop a modified version of the Electromagnetic Field Optimization (EFO) algorithm referred to as MEFO for the optimal coordination of DOCRs. The EFO is inspired by the behaviour of particles of electromagnets with different polarities where attractionrepulsion forces among these electromagnets lead particles toward global minima. It uses also the golden ratio. The proposed algorithm has been applied to three test systems including the 8-bus, the 9-bus and the 15-bus test systems. Furthermore, the results obtained using the proposed MEFO are compared with those obtained using the traditional EFO and a number of well-known algorithms. The obtained results show the effectiveness of the proposed MEFO to minimize the relay operating time for the optimal coordination of DOCRs.
Journal Article•10.1016/J.ASOC.2017.01.012•
A novel fuzzy adaptive configuration of particle swarm optimization to solve large-scale optimal reactive power dispatch

[...]

Ehsan Naderi1, Hossein Narimani2, Mehdi Fathi2, Mohammad Rasoul Narimani3•
Razi University1, Islamic Azad University2, Missouri University of Science and Technology3
1 Apr 2017
TL;DR: A novel Fuzzy Adaptive Heterogeneous Comprehensive-Learning Particle Swarm Optimization algorithm with enhanced exploration and exploitation processes is proposed to solve the Optimal Reactive Power Dispatch (ORPD) problem and a comparison proves the supremacy of the proposed algorithm in solving the complex optimization problem.
Abstract: Display Omitted Introducing a novel heuristic algorithm with extra exploration and exploitation processes namely FAHCLPSO in order to solve the ORPD problem.Applying the advantages of Fuzzy Logic (FL) and Fuzzy Interface System (FIS) for dynamic adopting the inertia weight of particles in the proposed algorithm.Considering active power transmission losses as well as voltage deviation of the system.Reporting the simulation results related to three different types of power systems such as IEEE 30-bus, 118-bus and 354-bus for small-, medium- and large-scale test systems. Management and scheduling of reactive power resources is one of the important and prominent problems in power system operation and control. It deals with stable and secure operation of power systems from voltage stability and voltage profile improvement point of views. To this end, a novel Fuzzy Adaptive Heterogeneous Comprehensive-Learning Particle Swarm Optimization (FAHCLPSO) algorithm with enhanced exploration and exploitation processes is proposed to solve the Optimal Reactive Power Dispatch (ORPD) problem. Two different objective functions including active power transmission losses and voltage deviation, which play important roles in power system operation and control, are considered in this paper. In order to authenticate the accuracy and performance of the proposed FAHCLPSO, it applied on three different standard test systems including IEEE 30-bus, IEEE 118-bus and IEEE 354-bus test systems with six, fifty-four and one-hundred-sixty-two generation units, respectively. Finally, outcomes of the proposed algorithm are compared with the results of the original PSO and those in other literatures. The comparison proves the supremacy of the proposed algorithm in solving the complex optimization problem.
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