A novel case adaptation method based on an improved integrated genetic algorithm for power grid wind disaster emergencies

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Contents lists available at ScienceDirect

Expert Systems with Applications journal homepage: www.elsevier.com/locate/eswa 5 6

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A novel case adaptation method based on an improved integrated genetic algorithm for power grid wind disaster emergencies

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Baishang Zhang ⇑, Xiangyang Li, Shiying Wang

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School of Management, Harbin Institute of Technology, Harbin 150001, China

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9 10 1 2 2 3 13 14 15 16 17 18 19 20 21 22

a r t i c l e

i n f o

Article history: Available online xxxx Keywords: Case-Based Reasoning Case adaptation Grey relational analysis Multi-objective genetic algorithms D/S evidence theory Wind disaster emergencies

a b s t r a c t Case adaptation is a challenging and crucial process of Case-Based Reasoning (CBR) for power grid wind disaster emergencies. The statistical adaptation method is a traditional method that is independent of domain knowledge, is easy to implement, but is not proper for the complex system problem. Therefore, the aim of this paper is to propose a novel case adaptation method to address this problem by integrating the multi-objective genetic algorithm with gray relational analysis, called the grey relational analysis-multi-objective genetic algorithms method (GRAMOGA). Compared with the traditional method, GRAMOGA is performed in terms of corresponding relations between the case similarity and emergency plan, indicating a new idea for case adaptation. To improve adaptation accuracy, this paper improved the multi-objective genetic algorithm by using a selection method based on the fitness function. Furthermore, the frame theory is expanded by combining it with the D/S evidence theory, providing a novel method for case description and retrieval with incomplete information. A practical example from the south of Jiangsu demonstrates that GRAMOGA achieves better adaptation performance for power grid wind disaster emergencies. In addition to the practical applications in case adaptation, GRAMOGA can be used as a novel method for expanding the case base. Ó 2015 Published by Elsevier Ltd.

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1. Introduction

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In recent years, typhoons have hit the power grid of China many times, which not only greatly harms to economic development but also affects social stability. It has been critical subject for decision makers to make fast decisions according to scenario features and implement rescue and repair work. However, mathematics analysis and statistics methods cannot work perform perfectly during power grid wind disaster emergencies because the problem involves many complex factors and incomplete information. CBR is a type of intelligent decision-making method that features implicit reasoning according to the current state, which gives the method a very strong learning ability and can provide decision support for the problem. However, it is still a challenging task for CBR researchers to accomplish case adaptation. Therefore, the design of a scientific case adaptation method is an important issue for applying CBR to power grid wind disaster emergencies. Case adaptation of wind disaster emergencies belongs to the typical calculation method of case adaptation methods because it needs to work out the types and numbers of emergency workers

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⇑ Corresponding author. Tel.: +86 18946039253. E-mail addresses: [email protected] (B. Zhang), [email protected] (X. Li), [email protected] (S. Wang).

and resources. The calculation method for case adaptation can be divided into the indirect case adaptation method and indirect case adaptation method according to the calculation approach (Henrieta, Lenia, Laurenta, & Salomonb, 2014). The former obtains results through adjusted models or formulas (Hu, Qi, & Peng, 2015; Qi, Hu, & Peng, 2015); the latter makes case adaptation a reality with genetic algorithms (Liao, Hannam, Xia, & Zhao, 2012a) neural networks (Callow, Lee, Blumenstein, Guan, & Loo, 2013) and k-NN (Qi, Hu, & Peng, 2012). Among them, the k-NN adaptation method is independent of domain knowledge and easy to implement, but has low-accuracy adaptation results. Although the accuracy of the neural network adaptation method is high, the method needs to create a model in advance. Thus, this method is not suitable for power grid wind disaster emergencies that involve many complex models. Power grid wind disaster emergencies involve many scenario features, of which the comprehensive effect on decision results is calculated through formulas. Therefore, it is very hard to address this problem with simple genetic algorithms (SGA). Motivated by these observations, in this paper, we propose GRAMOGA to accomplish case adaptation in the CBR for power grid wind disaster emergencies. In GRAMOGA, the multiple object functions include the case similarity function (CSF) and grey relational difference function (GRDF). Among them, CSF is used to ensure that the adapted case (which is the result of GRAMOGA) has a high

http://dx.doi.org/10.1016/j.eswa.2015.05.042 0957-4174/Ó 2015 Published by Elsevier Ltd.

Please cite this article in press as: Zhang, B., et al. A novel case adaptation method based on an improved integrated genetic algorithm for power grid wind disaster emergencies. Expert Systems with Applications (2015), http://dx.doi.org/10.1016/j.eswa.2015.05.042

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similarity with the object case (current emergency case); GRDF is designed to ensure that the grey relational coefficients of the scenario features and decision features in the adapted case are similar to those of similar cases (which have been retrieved from similar cases for adaptation from CBR cases). These two functions can ensure that the adaptation result is a satisfactory and is based on current scenario features. The main contributions of this paper are (see Figs. 1 and 2): (1) We propose a novel and efficient case adaptation method based on GRAMOGA in CBR for power grid wind disaster emergencies. (2) We improve multi-objective genetic algorithms by using selection method based on the fitness function and improve the adaptive genetic algorithm, which has been proven to be more effective. (3) We combine D/S evidence theory with frame theory for more precise case descriptions and retrievals to decrease the disturbance of incomplete information.

Build object functions, including CSF and GRDF, and transform them into fitness functions

Determine the coding method that can transform values from the search space

Determine the population size and GA operators

Choose the initial population

Iterate for the optimal solution

Decode Fig. 1. The flow chart of GRAMOGA.

terrain

precipitation

F1

F2

each decision

wind power

F3

feature

F19 damaged towers of 750kv lines Fig. 2. Functions between scenario features and decision features.

(4) Because GRAMOGA is effective and efficient, it can be treated as another method for expanding the case base of CBR.

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The rest of this paper is organized as follows. Section 2 reviews the related work. Section 3 details CBR for power grid wind disaster emergencies, including case representation, case retrieval and the case adaptation method that is based on the improved adaptive genetic algorithm. Section 4 describes extensive experiments to evaluate our proposed algorithm. Section 5 presents discussions and ideas for future improvements. Finally, Section 6 presents the conclusions.

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2. Related work

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2.1. Case adaptation of CBR

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CBR, which was put forward by Schank, is a type of intelligent reasoning method that guides actions based on past experience. Compared with Rule-Based Reasoning and Model-Based Reasoning, CBR focuses more on the implicit reasoning of empirical knowledge and has more practicability (Schank, 1982). A complete CBR process includes case representation, case retrieval, case adaptation and case saves (Ping & et al., 2015; Pla, López, Gay, & Pous, 2013). Most of the papers on CBR focus on case representation (Teodorovic´, Šelmic´, & Mijatovic´-Teodorovic´, 2013), case retrieval (Hong, Koo, & Park, 2012; Vukovic, Delibasic, Uzelac, & Suknovic, 2012) and feature-weights learning (Yeow, Mahmud, & Raj, 2014), because case adaptation is still a challenging process in CBR. In recent years, few studies have focused on case adaptation. At present, there are three types of adaptation styles according to the problem presentation style, including pictures, words and data. Adaptation for pictures is usually applied during physician examinations, transportation and photo taking. An example is that of Esmat, Hossei and Saeid, who employed case adaptation for modifying retrieved images in relevance feedback (Esmat, Hossein, & Saeid, 2014). This type of adaptation involves color design and intelligent calculation. The second type of adaptation aims to address sematic words or processes presented by words. Reyes, Negny, Robles and Lann presented a new methodology for the process engineering domain. In their paper, constraint satisfaction problem algorithms were integrated for adaption, and the modification of the adaptation loop was used for improving performance. This method is appealing, although specific adaptation methods need to be built for the problem that is addressed. The case adaptations for data are applied in more fields because many natural phenomena and societal problems can be presented though data that is helpful for predictions or judgments. The process of this adaptation style can be performed in two ways: classification and computation. The case adaptation based on classification is often applied to diagnoses, predictions and so on. It compares the object case with the base cases and distinguishes the sample, which belongs to one type or another, following the principle of taking a decision task as a classification task (Amailef, & Lu, 2013). Researchers often achieve case adaptation objects by integrating CBR with intelligent algorithms or technologies, especially data mining (Zhu, Hu, Qi, Ma, & Peng, 2014), supporting vector machines (Pinzón et al., 2013), neural networks (Planton, Dehkordi, & Martel, 2015) and GA (Koo & Hoo, 2015). Although there are many differences in the processes and methods for the classification of these smart technologies, one common characteristic of these processes and methods is determining which values of the object case fall into which category after conducting data analysis and then performing qualitative analysis (Chang, Lin, & Liu, 2012). Computation is another important way to achieve case adaptation. Case adaptations based on computation

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can be divided into case adaptations for a single numerical adaptation and case adaptations for data sets according to the forms of the solutions. Case adaptations based on computation can be divided into case adaptations for a single numerical adaptation and case adaptations for data sets according to the forms of the solutions. The former is usually used to estimate the whole probability of events; the latter is often applied to resolve two problems: overall situation estimations of events at different stages and state estimations of events on different sides at the same stage (Pinzón et al., 2013; Toro, Meire, Gálvez, & Fdez-Riverola, 2013). The mechanism of this case adaptation is built by outputting the corresponding results by comparing feature values that are realized by the KNN strategy. Some studies accomplish the KNN strategy with a traditional similarity calculation. For example, Lv, Liu, Zhao and Wang realized the case adaptation method based on the KNN strategy by considering community distributions and similarities (Lv, Liu, Zhao, & Wang, 2015). Furthermore, Danielle, Maria, Daniel and Elena designed a case adaptation method for a proposed new solution by calculating weighted similarities (Danielle, Maria, Daniel & Elena, 2015). Because intelligent optimization technology, such as GA, has the ability to search for more satisfactory solutions, traditional statistical computation methods are used instead by intelligent computation technologies when the KNN strategy is applied. Yan, Shao and Wang proposed a case adaptation method based on GA and group decision making in which GA was mainly used for adaptation and group decision making aimed to improve the solution quality for wastewater treatment (Yan, Shao, & Wang, 2014). Most case adaptations for data consider the feature differences between the target case and similar cases and focus less on the complex effect of features on adaptation results. Different from the previous methods, this paper adopts the idea of a corresponding relations mechanism in terms of the corresponding relations between feature similarity and emergency plans, providing a new perspective for case adaptation in a complex system where many feature factors have a combined effect on the results.

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2.2. Genetic algorithm

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A genetic algorithm (GA) is a type of optimization technique for imitating the evolution process of an animal chromosome; the optimal solution is obtained by searching for a feasible solution space in iterative ways under the guidance of genetic optimization ideas (Holland, 1975). This method can transform the solution space to the form of chromosomes and search for an optimal solution based on probability rather than explicit rules (Wang, Ma, Xu, Liu, & Wang, 2015). GAs have been applied in many fields due to their strong intelligent computation and parameter optimization abilities (Kuo, Huang, Ma, & Fanjiang, 2013; Lam, Choy, Ho, Kwong, & Lee, 2013; Wang & Yang, 2012; Wendt, Cortés, & Margalef, 2013). GA is composed of five elements: coding, population initialization, fitness function, genetic operators and control parameters (Zhang & WongKoo, 2015). Although genetic algorithm has strong parallelism and robustness, it has defects in premature and local convergence (Faghihia, Reinschmidta, & Kang,2014). Therefore, researchers have proposed many methods to improve its performance. Among the methods, most of improvements concentrate on coding, individual selection, crossover probability, mutation probability and control parameter adjustment (Binu, 2015; Bukharov & Bogolyubov, 2015; Chena, Liub, Chou, Tasif, & Wang, 2015; Chou, Cheng, Wu, & Pham, 2014; Liao et al., 2012a). Previous improved GA mainly improve searching solution performance by selecting genetic individuals and setting crossover and mutation operators. Some studies focused on improving methods of genetic individuals for better performance, because genetic

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individuals have great effect on advantage and diversity of offspring. Traditional chromosome reproduction technologies usually include the roulette wheel selection (RWS) and the tournament selection (TS). RWS involves heavy computation, decreasing the involution speed. TS can be operated based on competition of fitness function, but this method is straightforward, missing some potential chromosomes. Chuanga, Chena, and Hwangb developed a parallel-structured real-coded GA by integrating the Ranking Selection for evolution process, what reaps the benefits of RWS and TS (Chuanga, Chena, & Hwangb, 2015). Most papers aimed to find more better performance for GA by modifying crossover operators and mutation operators because these operators have more great effect on evolution performance based on individual selection. In these studies, some papers focused on accelerate evolution speed. Janeš and Car suggested that crossover operator should be set based on the fitness evaluation of just part of the genome. And the test results suggest that this method could accelerate evolution speed because of less genetic individuals (Janeš & Car, 2015). Akgüna and Erdog˘musßb developed a new GA by using graphical processing units, being able to accelerate training process (Akgüna & Erdog˘musßb, 2015). Most of research on modifying crossover operators and mutation operators tried to obtain more performance method. In Kima, Lee and Baik’s study, heuristic crossover and non-uniform mutation was used for improving the accuracy and performance of the parameter estimation with GA (Kima, Lee & Baik, 2015). Wang, Huang, Ma, and Chen improved partheno genetic algorithm (IPGA) for resolving the MOED problem in hydropower energy systems based on the non-uniform mutation operator. In the method, the crossover operator was removed and only mutation operation was made, making it simpler than GA in the genetic operations and not generated invalid offspring during evolution (Wang, Huang, Ma, & Chen, 2015). Qu, Xing, and Alexanderb presented a Co-evolutionary Improved Genetic Algorithm by employing a co-evolution mechanism together with an improved GA. This improved GA presented an effective and accurate fitness function, improved genetic operators of conventional Gas. Compared with conventional GAs, this method is better at avoiding the problem of local optimum and has an accelerated convergence rate (Qu, Xing, & Alexanderb, 2013). Hu, et al. proposed a self-adaptive GA-aided multi-objective ecological reservoir operation model where an improved self-adaptive GA was employed through incorporating simulated binary crossover and self-adaptive mutation (Hu & et al., 2014). From above researches, we can conclude that previous improved method for GA in the view of individual selection focused on only one aspect of diversity and competition, less considering them at the same time. This paper will design a new mechanism for individual selection based on values of fitness function. For previous studies on modifying crossover operator and mutation operator, crossover and mutation were only conducted according to fitness above or below average fitness, causing coarse partition; optimal fitness evolving with evolution generations wasn’t taken into account. This paper taking a new method for crossover and mutation, taking into account of the effect of evolutional generation on crossover probability and mutation probability for accelerating convergence rate and avoiding prematurity.

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2.3. Grey relational analysis

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Deng proposed grey system theory in 1982 to address problems involving incomplete information and less data samples (Deng, 1989). Grey relational analysis is an important part of the grey system theory. This method is mainly applied to find the correlation between the behavioral sequence of system features and behavioral sequence of influencing factors in complex discrete systems with high degrees of randomness (Chuang, 2013; Tang, 2015).

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Compared with other methods, grey relational analysis has more advantages, such as fewer samples and a small number of calculations (Xing, Ding, Chai, Afshar, & Wang, 2012). Moreover, this method does not require data in a typical distribution, which is helpful to characterize the correlation degree between objects (Gu, Liang, Bichindaritz, Zuo, & Wang, 2012). Therefore, this method has been applied in agriculture, industry, transportation, commerce, culture, education, and many other fields, with fewer applications in emergency management (Ai, Hu, & Chen, 2014; Jiang, Yu, & Zhao, 2012; Wang, Meng, Zhai, & Zhu, 2014;). Grey relational analysis is composed of the following steps: (1) Data preprocessing. Raw data with different dimensions cause unified comparative analysis to fail. Therefore, non-dimensional methods, such as range transforms, should be used before beginning any work. (2) Determining main the sequence X 0 and subsequences X i . (3) Computing the absolute value of the difference between the main sequence and subsequence at different times D0i ðtj Þ ¼ jX 0 ðtj Þ  X i ðt j Þj. (4) ) Determining the max value Dmax and the min value Dmin of the values determined by (3). (5) Determining the connection relational coefficients between the main sequence and subsequences L0i ðtj Þ ¼

Dmin þDmax . D0i ðtj ÞþDmax

(6) Computing the mean value of the connection relational coefP ficients c0i ¼ 1n nj¼1 L0i ðtj Þ.

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A higher correlation rate shows that the main sequence is more similar to the subsequences, which is characterized by a similar collection of curve shapes.

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2.4. D/S evidence theory

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There is a great deal of multi-source information and incomplete information in the real world, which affects decision-making efficiency. D/S evidence theory has two great advantages in dealing with uncertain information: one advantage is that it can be used to analyze random information and fuzzy uncertain information, while the other is that it does not need to determine the prior probability and conditional probability of the factors affecting decisions in advance (Aliev et al., 2012). This theory has been successfully applied to target recognition, behavioral decisions, collective assessment and so on (Dong & Liu, 2014; Ghasemi, Ghaderi, Karami Mollaei, & Hojjatoleslamiet, 2013). In this theory, assume that U is a discernment frame of a complete set for incompatible events, which can be presented as:

336 338

U ¼ fh1 ; h2 ; . . . ; hj . . . ; hN g

324 325 326 327 328 329 330 331 332 333 334

339 340 341 342 343 344 345 346 347

in which, hj is an element of the discernment frame, j = 1, 2 ,. . ., N; the set composed of all of the subsets of the discernment frame is called the power of U, which can be recorded as 2U . Thus, we can obtain two definitions: Definition 1. Belief function Bel(A) is a mapping from a set to [0, 1]. If U includes two subsets A and B, B # A # U, then P BelðAÞ ¼ B # A mðBÞ in which, mðBÞ is the basic probability assignment function of B; Bel(A) is the belief function of A, denoting the extent to which A is true.

348

Definition 2. Likelihood function P*(A) is a mapping from set 2U to

349

[0, 1], where A is a subset of 2U and satisfies P*(A) = 1-Bel(A).

Thus, we can obtain the combination rules of incomplete information in wind disaster emergencies of the power grid according to these definitions: mðAÞ ¼ m1 ðAÞ  m2 ðAÞ     mn ðAÞ

mðAÞ ¼

8 X m1 ðAi Þm2 ðBj Þ þ DA <

A–;

:

A¼;

352

353

355

in which,

DA ¼

351

ð1Þ

Ai \Bi ¼A

0

350

356

X

qðA; Bj Þ þ

A\Bj ¼;

(

rðA; Ai Þ ¼

357

rðA; Ai Þ

ð2Þ 359

A\Ai ¼;

(m

qðA; Bj Þ ¼

X

360 1 ðAÞm1 ðAÞm2 ðBj Þ

m1 ðAÞþm2 ðBj Þ

m1 ðAÞ þ m2 ðBj Þ > 0

0

m1 ðAÞ þ m2 ðBj Þ ¼ 0

m2 ðAÞm2 ðAÞm1 ðAi Þ m2 ðAÞþm1 ðAi Þ

m2 ðAÞ þ m1 ðAi Þ > 0

0

m2 ðAÞ þ m1 ðAi Þ ¼ 0

ð3Þ 362 363

ð4Þ 365

3. Theory and methodology

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3.1. Theory

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A power grid wind disaster emergency can be expressed as C = (S, P), in which C denotes a complete power grid wind disaster emergency (S ¼ ðs1 ; s2 ; . . . si Þ); and P denotes its emergency plan (P ¼ ðpiþ1 ; piþ2 ; . . . ; pm Þ). Therefore, N cases constitute a matrix (Z mn ). In the matrix, there is a Function F: P = F(S) in which numbers of S are independent variables and those of P are dependent variables because the P values of the emergency personnel and emergency equipment are calculated according to the terrain, temperature, precipitation and damage situations of the power grid. However, because changes of the S attributes affect the function and there are many attributes of S and P, Function F cannot be described with a mathematical formula directly. As an intelligent method for solving problems based on empirical data, CBR is suitable for dealing with complex problems that cannot be expressed with mathematical formulas. Assuming that the numbers of S0 are scenario features in a power grid wind disaster emergency, policymakers have to make decisions according to the situations through obtaining P0 . Decision-making based on CBR for power grid wind disaster emergencies mainly includes three steps: obtaining and inputting the scenario features into a prototype system; determining the scenario features and the emergency plan of cases similar to the current emergency case through retrieval; comparing the scenario features of the object case to those of similar cases and obtaining the emergency plan of the object case. This paper accomplished case adaptation with multiple-object genetic algorithms to solve problems involving many variables and models in power grid wind disaster emergencies. The main ideas of this paper are as follows: The essence of this method is that the designed algorithm does not stop searching for optimization solutions under the guidance of the proposed target until it finds a satisfactory solution. In this method, object functions consist of CSF and GRDF. CSF aims to compute the similar degree of object cases to cases generated by the multiple-objects genetic algorithm, ensuring that the case generated by this algorithm is most similar to the object case. GRDF is designed to compute the grey relational coefficients of scenario features and decision features in the generated case and similar cases, ensuring that the grey relational coefficients of the scenario features and the decision features in the generated case are similar to those in similar cases. These two object functions can provide

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guidance for the optimal decision values and ensure that the adaptation results are more correct.

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3.2. Methodology

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3.2.1. Case representation method for power grid wind disaster emergencies The common case representation method includes the XML method, ontology method, tree structure method and frame method. Frame representation has both a good structure and a clear logic, meeting the demand for the quantification and structure of a power grid wind disaster emergency (Xie, Lin, & Zhong, 2013). However, because power grid wind disaster emergencies are characterized by urgency and incomplete information, policymakers have to estimate the scenario features according to the relevant information and parameters. Therefore, this paper combines the frame method with D/S evidence theory, which addresses incomplete information to represent power grid wind disaster emergencies under the condition of incomplete information. An example of transmission line repairs is used to illustrate the application of representing a case with this novel method. This instance represents transmission line repairs with nested frames; a scenario features sub-frame, emergency plan sub-frame and emergency effectiveness sub-frame are nested in the mainframe of the transmission line repairs in the form of slots. Among these sub-frames, the scenario features sub-frame includes three slots: time, affected area and scenario description; the emergency plan sub-frame includes four slots: personnel, equipment, logistics and devices; and the emergency effectiveness sub-frame includes three slots: result, deficiency and evaluation. Each slot is divided into several sides according to practical situations. Decision makers have to grasp the decision according to incomplete information due to event urgency, increasing the decision-making risk. To decrease this risk, this paper adds the basic probability assignment function m(A) to scenario features for describing reliability. Therefore, this paper represents the case as tables, Tables 1–4.

409

Table 2 The scenario features sub-frame. Frame name:< Scenario features >

413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451

3.2.2. Retrieval method for power grid wind disaster emergencies The nearest neighbor method is a method that classifies the most similar samples in a feature space and has high accuracy and is readily applicable in computing the similarity of cases (Jamshidia & Kaburlasos, 2014). This paper takes transmission line repairs as an example to depict the application of the nearest neighbor method in case retrieval. This method consists of two steps: computing local similarity and computing global similarity.

457

3.2.2.1. Local similarity calculation. For the first property, if the scenario features of a similar case are consistent with those of the object case, the local similarity can be calculated with the formula: 1  jmðAÞ01  mðAÞi1 j, otherwise, the value of local similarity is 0. The similarity of the rest attributes can be calculated through the following formula:

460

   jf 0j  f ij j   simj ¼ 1    jmðAÞ0j  mðAÞij j  maxðf 0j ; f ij Þ

452 453 454 455 456

458

Table 1 The main frame of transmission line repairs. Frame name:< transmission line repairs > Slot1: < scenario features > Slot2: < emergency plan > Slot3: < emergency effectiveness >

ð5Þ

Slot 1: Time Slot 2: disaster area Slot 3: scenario description Face 31: terrain Face 32: rainfall Face 33: wind power Face 34: broken wires of 10 kv lines Face 35: damaged towers of 10 kv lines Face 36: broken wires of 35 kv lines Face 37: damaged towers of 35 kv lines Face 38: broken wires of 66 kv lines Face 39: damaged towers of 66 kv lines Face 310: broken wires of 110 kv lines Face 311: damaged towers of 110 kv lines Face 312: broken wires of 220 kv lines Face 313: damaged towers of 220 kv lines Face 314: broken wires of 330 kv lines Face 315: damaged towers of 330 kv lines Face 316: broken wires of lines Face 317: damaged towers of 500 kv lines Face 318: broken wires of 750 kv lines Face 319: damaged towers of 750 kv lines

Value Value

m(A) m(A)

Value Value Value Value Value Value Value Value Value Value Value Value Value Value Value Value Value Value Value

m(A) m(A) m(A) m(A) m(A) m(A) m(A) m(A) m(A) m(A) m(A) m(A) m(A) m(A) m(A) m(A) m(A) m(A) m(A)

Table 3 The Emergency plan sub-frame. Frame name:< Emergency effectiveness > Slot 1: personnel Face 11: maintenance staff Face 12: support staff Face 13: transportation personnel Slot 2: equipments Face 21: emergency clothes Face 22: hiking shoes Face 23: cotton gloves Face 24: backpacks Face 25: alpenstocks Face 26: helmet Face 27: safety belts Face 28: interphones Face 29: telescopes Face 210: rope pistols Face 211: climbing rope Face 212: bottles Face 213: explosion-proof torch Face 214: explosion proof searchlight Face 215: first-aid cases Slot 3: logistics Face 31: ship biscuits Face 32: self-heating food Face 33: tents Face 34: cooking utensils Face 35: drinking water Slot 4: devices and tools Face 41: alternators Face 42: electric saws Face 43: lights Face 44: recovery trucks Face 45: pumpers Face 46: steam boats Face 47: electric tools

10,474 579 1320 3165 0 10,567 73,338 0 10,570 3165 103 308 0 0 10,474 2637 349 1055 2147 30.2 1114 109 40 201 309 364 103 2 14 4215

In this formula, f 0j denotes the attribute values of the object case; f ij denotes the attribute values of the cases generated by GRAMOGA; mðAÞ0j denotes the basic probability assignment function of the scenario features in the object case; mðAÞij denotes the basic probability assignment function of the scenario features in the cases generated by GRAMOGA.

Please cite this article in press as: Zhang, B., et al. A novel case adaptation method based on an improved integrated genetic algorithm for power grid wind disaster emergencies. Expert Systems with Applications (2015), http://dx.doi.org/10.1016/j.eswa.2015.05.042

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500 501 502 503 504

505

f1 ¼

j01 ¼ ji1

> 19 > X > > > wj simj > :

j01 –ji1

j¼2

507

ð6Þ

508

in which, x1 2 ½1; 3; x2 2 ½0; 1055; x3 2 ½0; 16; x4 2 ½0; 300; x5 2 ½0; 300; x6 . . . x19 2 ½0; 150, and all of the variables are positive integers.

509 510

0.0554 0.0554

x18 x16

0.0554

x19

8 19 X > > > wj simj > 0:0330  j1  jmðAÞ01  mðAÞi1 jj þ > > < j¼2

x8 x7 x6

499

x5

498

x4

497

x3

496

0.0396

495

x2

494

We can obtain this formula based on the assignment principle: r2 ¼ x4 =x5 ¼ 1:0, similarly, r 3 ¼ r4 ¼ r5 ¼ r 6 ¼ r 7 ¼ r 8 ¼ r9 ¼ r10 ¼ r 11 ¼ r12 ¼ r13 ¼ r 14 ¼ r 15 ¼ r16 ¼ r18 ¼ 1:0; r 17 ¼ x19 =x2 ¼ 1:4; r19 ¼ x3 =x1 ¼ 1:2: At the same time, we have r2 r3    r 19 ¼ 1:68; r 18 r19 ¼ r 19 ¼ 1:2, and the remaining continued products of r is 1.68. Because all of the continued products sum to 29.28, we can obtain P Qm 1 x19 ¼ ð1 þ m ¼ ð1 þ 29:28Þ1 ¼ 0:0330; similarly, the k¼2 i¼k r i Þ remaining values from x17 to x1 can, in turn, be calculated. Therefore, the weights of the attributes from x1 to x19 are obtained in Table 5. This paper obtains the formula of case global similarity based on the above analysis:

0.033

493

x1

492

¼ x16 ¼ x17 ¼ x18 ¼ x19 > x2 ¼ x3 > x1

Table 5 The weights of attributes.

491

x9

x4 ¼ x5 ¼ x6 ¼ x7 ¼ x8 ¼ x9 ¼ x10 ¼ x11 ¼ x12 ¼ x13 ¼ x14 ¼ x15

0.0554

x15 x14

489

0.0554

x17 478

x13

477

x12

476

x11

475

x10

474

0.0554

473

0.0554

472

0.0554

470 471

0.0554

469

3.2.2.2. Global similarity calculation. The attribute weights of the scenario features should be determined before building the case similarity function. Analytic hierarchy process (AHP) is a common method combining qualitative analysis with quantitative analysis to determine attribute weights and has been applied in many fields. However, this method does not work in situations where there are more than nine indexes. Moreover, the judgment matrix of this method generally does not satisfy consistency conditions (Shi, Shuai, & Xu, 2014). It is exciting that the G1 method can overcome the above problems. Therefore, this paper determines attributes weights with the G1 method. In the G1 method, it is assumed that there is a sequence relation composed of x1  x2      xk , k = m, where  denotes the greater importance of one attribute than the attributes and where the attributes are sequenced in descending order according to their importance. The xk1 /xk ratio estimated by experts can be represented as r k ¼ xk1 =xk , k = m, m1, . . ., 2. In general, the value of rk can be one number from the dataset f1:0; 1:1; 1:2; P Qm 1 1:3; 1:4; 1:5; 1:6; 1:7; 1:8g. Then we have xm ¼ ð1 þ m k¼2 i¼k r i Þ and xk1 ¼ r k xk , k = m, m1, . . ., 2, in which xk is the weight of xk . The order of the relation of the 19 scenario features determined by experts in transmission line repairs is:

0.0554

468

0.0396

467

0.0554

Value Value Value Value Value Value Value

0.0554

Slot 1: result of transmission line repairs Slot 2: deficiency of emergency plan Face 21: deficiency 1 Face 22: deficiency 2 ... Face 2n: deficiency n Face 3: evaluation on transmission line repairs

0.0554

Frame name:< Emergency effectiveness >

0.0554

Table 4 The emergency effectiveness sub-frame.

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0.0554

6

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3.2.3. GRAMOGA method Because this method makes emergency plans for the object case according to similar cases’ plans, two aspects should be ensured: one, the scenario features of the adaptation results have high similarity compared to those of the object case; two, the emergency plan of the adaptation results should be worked out based on those of similar cases. Therefore, the object functions include two functions: CSF (for ensuring high similarity) and GRDF (for ensuring high feasibility). (3) CSF

521 522 523 524

525

This function aims to ensure that the scenario features of the generated case are more similar to those of the object case. The calculation of this function is as the calculation in Section 3.2.2.2.

f1 ¼

8 19 X > > > 0:0330  j1  jmðAÞ01  mðAÞi1 jj þ wj simj > > < j¼2 19 > X > > > wj simj > :

j01 ¼ ji1 j01 –ji1

j¼2

527

ð7Þ

528

in which, x1 2 ½1; 3; x2 2 ½0; 1055; x3 2 ½0; 16; x4 2 ½0; 300; x5 2 ½0; 300; x6    x19 2 ½0; 150, and all of the variables are positive integers.

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(2) GRDF This function ensures that the decision features are worked out according to the corresponding scenario features. It works on the principle that there exists a function F that can be represented as a grey relational coefficient between each decision feature and each scenario feature and that each decision feature is the combined effect of all of the scenario features. If the combined grey relational coefficient between the decision features and scenario features in the generated case is consistent with those in similar cases, it shows that the decision features in the generated case are worked out according to scenario features. This paper accomplishes this goal through the following steps:

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(1) Forming a 3  20 matrix with 19 scenario features and one decision feature and conducting data preprocessing such that the numbers in each column are divided by those in column 1. (2) Determining the main sequence X 0 and subsequences X i . The former consists of the numbers of one decision feature, and the latter consists of the 19 scenario features. (3) Computing the absolute value of the difference between the main sequence and subsequence at different times Dij ¼ jX 0j  X ij j. (4) Determining the max value Dmax and min value Dmin of the values determined by (3). (5) Working out the connected relational coefficients between

558

þ0:5Dmax the main sequence and subsequences rij ¼ DDminþ0:5 . Dmax

545 546 547 548 549 550 551 552 553 554 555 556

559 560 561 562 563 564 565 566 567 568 569

ij

Because grey relational analysis is used to compute the relational coefficient between the 19 scenario features and one decision feature in this paper, there are 19 relational coefficients, ri1    r i19 , for one decision feature. (6) Computing all of the correlation coefficients in the matrix by the above steps. (7) Adding the case generated by GRAMOGA to this matrix and establishing a 4  20 matrix. Computing all of the grey correlation coefficients, sij , by following steps (1)–(7). (8) Working out the sum of the differences between the two matrixes.

7

(3) Multiple object functions

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The adapted case must have the highest similarity with the object case for the scenario features and least sum of the difference between the correlation coefficients and those of similar cases. Therefore, we can obtain multiple object functions:

8 max f 1; > > > > > min f 2; > > > < s:t:x 2 ½1; 3; x 2 ½0; 1055; 1 2 > 2 ½0; 16; x 2 ½0; 300; x 3 4 > > > > > x 2 ½0; 300; x . . . x19 2 ½0; 150; > 5 6 > : x20 . . . x49 2 ½0; 50000; all positive integers

572 573 574 575

576

ð8Þ

578

3.2.3.1. Coding method. Because the values of the scenario feature vary in a small scope and the values of the decision features have a large scope, using the same coding method would result in a large waste of storage and search space. The multi-parameter cascade coding method is suitable for value ranges of variables that are different because this method encodes each variable in a different coding method and arranges them in a certain form, leading to a new chromosome code (Homayouni, Tang, & Motlagh, 2014). This paper chooses the multi-parameter cascade coding method for encoding variables, in which binary code is used to encode the scenario features because of their small value range and real-number code is applied to encode the decision features due to their large value range.

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3.2.3.2. Initial population. Because case adaptation is a process of case modification and grey relational analysis works under the conditions of the least of the three cases, this paper chooses three similar cases that were retrieved from the case base as the initial population.

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3.2.3.3. Selection. In the selection method of SGA, each individual has the same opportunity to be copied, which cannot reflect competitive advantage of an better individual (Motta Toledo, Oliveira, Freitas Pereira, França, & Morabito, 2014). This paper proposes a selection method based on the values of fitness, as follows:

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(1) Sorting individuals by their values of fitness in descending order. (2) Computing the average fitness as a threshold and choosing individuals whose fitness is greater than the average fitness. (3) Computing the similarity (if the same characters are in the same position for two individuals, then the numbers of those same characters are defined as the similarity degree) and deleting individuals that are similar to the individual with the highest similarity degree. (4) Taking individuals with high fitness as templates and choosing these templates to constitute the population. In this process, templates with high fitness are copied three times; templates with medium fitness are copied twice; and templates with low fitness are copied once. (5) Judging whether the number of individuals amounts to population size. If the number of individuals satisfies the population size, then this method will conduct the next crossover and mutation; otherwise, the population should be completed in the following way: if the number of individuals is greater than the population size, then remove one of the individuals that were copied twice (in ascending order of fitness) until the population size satisfies the conditions; if the number of individuals is smaller than the population size,

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then add the removed similar case to the population (in descending order of fitness) until the population size satisfies the conditions.

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This method can avoid individuals with high fitness occupying populations at the beginning of evolution and avoid evolution stopping because of a similar fitness later in the process.

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3.2.3.4. Crossover. To some extent, the adaptive genetic algorithm has solved the problem of the prematurity and convergence of SGA by adjusting the crossover probability and mutation probability (Víctor, Francisco Gomez-Gilb, Jaime, & Ruben, 2015). However, there are still some problems in the adaptive genetic algorithm: crossover is only conducted according to fitness above or below an average fitness, causing a coarse partition; optimal fitness evolving with evolution generations is not taken into account. In consideration of the effect of the above problems on efficiency, this paper makes some improvements to the adaptive genetic algorithm as follows:

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8 ðp p Þðf 0 f Þ f þf 0 pc1 þpc2 > >  c1 f c2 f av g ; max 2 av g 6 f 6 f max > 2 max av g > < 0 pc ¼ pc1 þpc2  ðpc1 pc2 Þðf f av g Þ ; f min þf av g < f 0 < f max þf av g 2 2 2 2ðf max f av g Þ > > > > f min þf av g 0 : pc1 þpc2 ; f 6 2 2

646

1 in which pc1 ¼ 2þlg þ / (N is evolutional generation); pc2 = 0.9 is the N

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643

647 648 649 650 651

652

ð9Þ

respective maximum fitness of chromosomes for crossover; and f max ; f av g ; f min is maximum fitness, average fitness, minimum fitness of chromosomes in the current generation, respectively. 3.2.3.5. Mutation. Some improvements for mutation have been made, as follows:

8 ðp p Þðf 0 f Þ f þf 0 pm1 þpm2 > >  m1 f maxm2f av g av g ; max 2 av g 6 f 6 f max > > < 2 0 pm ¼ pm1 þpm2  ðpm1 pm2 Þðf f av g Þ ; f min þf av g < f 0 < f max þf av g 2 2 2 2ðf max f av g Þ > > > > f min þf av g 0 : pm1 þpm2 ; f 6 2 2

ð10Þ

0:1 in which pm1 ¼ 2þ0:7 þ u (N is evolutional generation); pm2 = 0.1 is lg N

654 655

the respective maximum fitness of chromosomes for mutation; and f max ; f av g ; f min is maximum fitness, average fitness, minimum fitness of chromosomes in the current generation, respectively. The above improvement is beneficial for dividing chromosome groups into more specific spaces, increasing the solution diversity and avoiding trapping in the local optimum. More importantly, this method takes into account the effect of evolutional generation on the crossover probability and mutation probability, accelerating the convergence rate and avoiding prematurity.

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3.2.3.6. Stop condition. This method sets a stop condition with evolutionary stagnation: if the average fitness stops for 50 generations, then this algorithm will stop.

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4. Application and analysis

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A prototype system based on CBR for power grid wind disaster emergencies is developed on the basis of the above theory and methodology. This section validates the correctness and effectiveness of GRAMOGA through a practical example.

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4.1. Application example

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This paper takes the case of when the Severe Tropical Storm Fitow hit transmission lines in southern Jiangsu of China on

674

Fig. 3. Case representation of power transmission line repairs.

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Fig. 4. Adaptation results.

Fig. 5. Application analysis.

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October 6, 2013, as an example to validate the effectiveness of this method.(Wen, Wei, & Zhang,2014). The scenario features should be obtained through information sources, and the basic belief probability function should be calculated before case representation. According to two survey reporting units, the information related to broken wires of 10 kv lines is (187, 0.9), (159, 0.9); the information related to damaged towers of 10 kv lines is (1, 0.9), (109, 0.6); and the information related to broken wires of 35 kv lines is (130, 0.7), (3, 0.8). The basic belief probability functions of the remaining scenario features are all 1. We process the reported data with an uncertain information model, as follows:

690

0:9  0:9  0:6 0:9  0:9  0:4 mðaÞ ¼ 0:9  0 þ þ ¼ 0:5732 0:9 þ 0:6 0:9 þ 0:4

ð11Þ

0:9  0:6  0:6 0:6  0:6  0:1 þ ¼ 0:2674 0:9 þ 0:6 0:6 þ 0:1

ð12Þ

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688

value of object function 1 amounts to 1 at generation 300, demonstrating that the scenario features of the adaptation case are extremely similar to those of similar cases. The value of object function 2 is 127 at that generation, also producing a satisfactory result. The reason is that the lower the value of object function 2, the more similar the grey correlation coefficient of the adaptation case to that of similar cases. Because there are 19 grey correlation coefficients for each scenario feature and 30 scenario features exist in the case in total, if the adaptation results are completely invalid, then the value of object function 2 will be 30  19 = 570. Based on the above analysis, we can obtain the application of this method as (1–127/570) = 0.778, which has higher accuracy. Globally, we can also compute the global application, which can be calculated as (1 + 0.778)/2 = 0.889.

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4.2.2. Convergence analysis Convergence analysis can reflect the performance of the method to search for the optimal solution. To test the convergence of this

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736 737 738 739 740 741 742 743 744 745 746 747 748

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mðbÞ ¼ 0:6  0 þ

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0:1  0:6  0:6 0:4  0:4  0:9 mðcÞ ¼ 0:1  0:4 þ þ ¼ 0:1594 0:1 þ 0:6 0:4 þ 0:9 696

ð13Þ

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In the prototype, power transmission line repairs are represented as Fig. 3. Decision makers can input the values of the scenario features into this system to retrieve similar cases. This paper uses the most similar case to illustrate how the system computes the case similarity degree. At first, the local similarity degree is calculated:

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704 706 707 709

710 712 713 715 716 717 718 719

720

sima ðc1 ; t 1 Þ ¼ 1  j1  1j ¼ 1

ð14Þ

   j170  150j sima ðc2 ; t 2 Þ ¼ 1  j1  j1  1jj ¼ 0:957 j546  80j 

ð15Þ

   j14  10j sima ðc3 ; t 3 Þ ¼ 1  j1  j1  1jj ¼ 0:5 j16  8j 

ð16Þ

   j190  187j sima ðc4 ; t 4 Þ ¼ 1  j1  j1  0:5732jj ¼ 0:565 j204  0j 

ð17Þ

Similarly, other local similarity degrees can be calculated in the same way: 0.542, 0.525, 1, 1, 1, 0.998, 1, 1, 1, 1, 1, 1, 1, 1, 1. Then, the G1 method (introduced in 3.2.2.2) is applied to compute the global similarity degree:

Fig. 6. The convergence of object function 1 in SGA.

1  0:0330 þ 0:957  0:0396 þ 0:5  0:0396 þ 0:565  0:0554 þ 0:542  0:0554 þ 0:525  0:0554 þ 1  0:0554 þ 1  0:0554 þ 1  0:0554 þ 0:998  0:0554 þ 9  1  0:0554 722

¼ 0:9012

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The other two global similarity degrees can also be obtained in this way, producing 0.9001 and 0.8993. The prototype system can generate adaptation results, as shown in Fig. 4, based on GRAMOGA.

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4.2. Effectiveness analysis of the results

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The effectiveness analysis of the results for this method mainly includes application analysis and convergence analysis.

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4.2.1. Application analysis We conduct the application analysis, as shown in Fig. 5, from this prototype system as follows. Application analysis is an important indicator that reflects whether the decision results are feasible. Fig. 5 shows that the

Fig. 7. The convergence of object function 2 in SGA.

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Fig. 8. Performance of the sum of the object functions in SGA.

Fig. 9. Performance of the sum of the object functions in GRAMOGA.

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algorithm, this paper also compares the performance of GRAMOGA with that of SGA for the aspects of object function 1, object function 2 and the sum of the object functions. Comparing Figs. 6 and 7 to 5, we can observe that object function 1 of SGA cannot converge and that its optimal solution is 0.96; GRAMOGA can achieve convergence at a certain generation, and the value of the optimal solution is 1, showing better performance. At the same time, object function 2 of SGA cannot accomplish convergence either, and its optimal solution is 137; GRAMOGA can converge after a short amount of time, and the value of its optimal solution is to 126, increasing the correlation between scenario features and decision features. Then, we also analyze the performance differences of the sum of the object functions in these two methods, the results of which are shown in Figs. 8 and 9. According to these figures, we can observe that the sum of the object functions in SGA cannot accomplish converge either and that its optimal solution is 138; GRAMOGA can converge, and the value of its optimal solution is 127, which has a global advantage.

11

It can be observed that GRAMOGA is better than SGA for convergence and optimization performance based on the above analysis.

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5. Discussion

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There are dozens of scenario features and decision features that have functions that cannot be described with mathematical models in power grid wind disaster emergencies. CBR solves practical problems based on past experience and is suitable for dealing with complex problems that cannot be solved with a conventional decision making method. However, less emergency cases for power grids exist in reality, thus affecting the performance of CBR. Therefore, application cannot be ensured when only CBR is applied in decision making for power grid wind disaster emergencies. Grey system theory has a large advantage for solving small sample problems because it can ensure high accuracy with small samples. Integrating CBR with grey relational analysis can remedy the defect of fewer cases of power grid wind disasters emergencies, improving the performance of CBR. SGA has defects, such as in prematurity and local optimum, that cause the search for the optimal solution to fail. GRAMOGA, proposed in this paper, conducts genetic operations by using a selection method based on fitness. Moreover, GRAMOGA adjusts crossover probability and mutation probability adaptively according to the evolution generation. The experimental results show that the improved adaptive multi-objective genetic algorithm is better than SGA in convergence and optimization. This method of case adaptation can be applied to extending the case base, which is usually needed for solving problems in fields with fewer cases. At present, the expansion of the case base includes an expansion method based on rules and the Monte Carlo method. The expansion method based on GRAMOGA can ensure the interconnection between indexes and has a large great advantage according to facts. This method can fuse information from two information sources to calculate the probability of scenario features by dealing with uncertain information with the D/S evidence theory, improving the availability to a great extent. However, this method only considers the situation of two information sources and does not consider multiple information sources, which is very common and complex. Thus, our further research will be to determine how to calculate the probability of information fusion under the condition of multiple information sources.

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6. Conclusion

812

Based on the grey relational analysis-multi-objective genetic algorithm, the aim of this study is to propose a novel case adaptation method in the CBR for power grid wind disaster emergencies. Previous studies performed case adaptations by calculating the similarity values of the features rather than considering the complex effect of the features on the adaptation results. To focus on the complex effect of the features on the adaptation results, this paper designs GRAMOGA by integrating the genetic algorithm with grey relational analysis. At the same time, the SGA has been improved by using a selection method based on fitness and improving adaptive operations. Furthermore, considering that a great deal of incomplete information exists related to power grid wind disaster emergencies, the frame representation method is combined with D/S evidence theory to address information fusion. To describe the possibilities of this methodology, it is tested in the case of a transmission lines emergency in southern Jiangsu, China. From the adaptation results, we can draw the conclusion that compared with the previous methods, this novel case adaptation method can achieve better adaptation performance in a complex

813

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system problem with incomplete information. Moreover, this method can be used for expanding the case base by constructing new, similar cases. The major contribution of this paper, we believe, are (i) Compared with the previous methods, this paper adopts the idea of a corresponding relations mechanism in terms of corresponding relations between the case similarity and emergency plan, providing a new perspective for case adaptation in complex systems where many feature factors have a combined effect on the results, (ii) by using a selection method based on fitness and improved adaptive operations, SGA has been improved to overcome prematurity and convergence, proposing a new method for improving SGA, (iii) the frame representation method is combined with D/S evidence theory to address information fusion, enriching case presentation theory, especially for situations with incomplete information. Although the comparison results demonstrate that GRAMOGA can achieve a better adaptation performance, a number of limitations need to be considered. First, this paper only studied information fusion from two data resources regarding the combination of the frame representation method with D/S evidence theory and did not consider situations with incomplete information from multi-resources. Second, this study focused on using accuracy data rather than fuzzy data for emergency plans, although there is some fuzzy information related to power grid wind disaster emergencies. Third, the method proposed is mainly used on a computer without consideration its use on mobile devices. This research can be extended. In the future, we will pay attention to the integrated modified D/S theory with the frame case presentation to deal with incomplete information from multi-resources. Fuzzy set theory will also be used for the precision of fuzzy information. Moreover, mobile technology will be studied to enhance time and place convenience for decision making. Furthermore, the integration of an emergency system with other management information systems, such as a transportation information system, will be a future research interest because it may be able to improve the emergency effect.

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7. Uncited references

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Liao, Mao, Hannam, and Zhao (2012b) and Wang, Wang, and Ai (2014).

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Acknowledgements

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This work is supported by the National Natural Science Foundation of China (Nos. 91024028, 91024031, 91324018).

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