【正文】 nt linearity arithmetical crossover and utilized it to select the value of ? 。 it can greatly improve the speed 中英文資料 21 of crossover and mutation. The steps of the improved decimalcode representation scheme are as follows: （ 1） Coding： Suppose ? ?0,1?? is a binary string of C bits, then let every n bits transform a decimal from right to left.(nC, the values of n and C are ensured by precision) （ 2） Randomize population: Select one integer M as the size of the population, and then select M points stochastically from the set ? ?0,1 ,as ? ?? ?, 0 1, 2 , ,i i M? ??, these points pose the individuals of the original population, the sequence is defined as: ? ? ? ? ? ? ? ?? ?0 1 , 0 , 2 , 0 , , , 0PM? ? ??? （ 3） Evaluate the fitness: In the selection step,individuals ? ?,ik? are chosen to participate in the reproduction of new individuals. The individual ? ?,ik? with the highest fitness F（ ? ?,ik? ） has the priority and advances to the next generation. The fitness function is ? ?? ? ? ?? ? ? ?? ? ? ? ? ?? ? ? ?? ? 200m a x m a x 1, , , ?,0, n iiic f i k f i k cF i k X i k X???? ?? ???? ? ???? ?其 它 and ? ? ? ?? ?0? ,iX i k? is the value of forecasting which is gained by the individual ? ?,ik? . maxc is the maximum of the sum of iterative squares. Step4: Selection: In this paper, we calculate individual selected probability ? ? ? ?? ? ? ?? ?1,k miiF I KpF i k???? ? respectively according to their fitness functions ? ?? ?,F i k? , then we adopt the roulette wheel selection scheme, so that the propagated probability of respective individual is p(k) ,after that we take the inborn individual to pose the next generation p(k +1). Step5: Crossover and Mutation: Coding and crossover are correlative。 we utilized the decimalcode representation, so we propose a new crossover operator “onepoint linearity arithmetical crossover” 1) Select the fit two individuals with probability of crossover cp . 2)For the two selected individuals, we still adopt the random selection means to ensure the crossover operator. For example: ? ?? ?12 1:,i i i ik ilikz z z z z z??? ? ?? ?12 1:,j j j jk jljkz z z z z z??? 3)crossover: ① We exchange their right strings each other. ② The bit on the left of crossover can be calculated through the following algorithm: a: Gene analysis: 中英文資料 22 ? ?* 1 *ik ik ikz z z??? ? ? ? ?* 1 *jk jk jkz z z? ? ? b: Exchange the back gene: ? ?* 1 *ik ik jkz z z??? ? ? ? ?* 1 *jk jk ikz z z? ? ? The ? ?0,1?? is called crossover coefficient, it is chosen each time by random crossover operation. 4)Mutation: There is a new mutation operation:when the mutation operator was chosen, the new gene value is that a random number within the domain of weight, which is operated into a weighted sum with original gene value. If the value of mutation operator is Zi , the mutation value is: ? ?* 1 *iiz r z??? ? ? And ? is the mutation coefficient, ? ?0,1?? . r is a random number, min max,i ir z z????? .It is selected randomly every time when mutation operation is happening. Therefore, the new offspring can be created through crossover and mutation operations. Step6: Quit principle: Select the remaining individuals in the current generation to reproduce the individuals in the next generation, then evaluate the fitness value and judge whether the algorithm fulfils the quit condition. If it is certifiable, in this case the ? value is optimal solution, else repeat from Step 4 until all individuals in population meet the convergence criteria or the number of generations exceeds the maximum of 100. 4. Load prediction example 中英文資料 23 In this section, we try to evaluate the performance of GM(1, 1)connection improved geic algorithm. First: The daily load data sequences of m days are defined as ? ?? ?1, 2, ,x k k n??, we measured the power load each hour, and the load sequence vector is a twentyfourdimensional data. 01 the time of day: ? ?? ?0 1 0 1 1 , 2 , ,X x i i m? ? ? 02 the time of day: ? ?? ?0 2 0 2 1 , 2 , ,X x i i m? ? ? j the time of day: ? ?? ?1, 2 , ,jjX x i i m? ? ? 24 the time of day: ? ?? ?2 4 2 4 1 , 2 , ,X x i i m? ? ? Where m is the number of modeling days, X j is the daily load data sequence of the jth time of day. Fig 1. Original data and forecasting value Second: We utilize improved geic algorithm to select the value of ? for respective load datasequence X j . After that, we can calculate a and b, then we utilize GM(1,1)IGA to predict the load forecasting of the jth time of the (m+1)th day, so we could get X j(m+1), and the twentyfour forecasting values of the (m+1)th day structure the load data sequence ? ?? ?1 1, 2 , , 2 4jx m j? ? ?. 中英文資料 24 There was an example of GM(1,1)connection improved geic algorithm(GM(1,1)IGA), both the two forecasting daily load data curves (July26) and the original daily load data curve were drawn simultaneously on Fig 1. Thirdly: We can use four indexes of this GM(1,1)GA to verify the precise, including of the relative error,the ratio of mean square error, the micro error probability and the relevance degree. The accuracy verification of GM(1,1)GA is better if the relative error and the ratio of mean square error is lower, or the micro error probability and the relevance degree is larger[16]. Set the simulated residual of x(0)(k) is ? ? ? ? ? ? ? ? ? ?00?k x k x k? ?? k=1， 2，?， n Set the simulated relative residual is ? ? ? ? ? ? ? ?0 ,k k x k??? k=1， 2，?， n Set the mean of x(0) is ? ?? ?011 nkx x kn ?? ? Set the variance of x(0) is ? ? ? ?? ?2021 11nkS x k xn ????1 Set the means of residual error is ? ?11 nk kn???? ? Set the variance of residual error is ? ?? ?222 11nkSkn ?????? So the check value of thi