【正文】 (STLF) problems in power system. The traditional GM (1, 1) forecasting model often sets the coefficient ? to , which is the reason why the background value z(1)(k) may be unsuitable. In order to overe the abovementioned drawbacks, the improved decimalcode geic algorithm was used to obtain the optimal coefficient ? value to set proper background value z(1)(k).What is more, the onepoint linearity arithmetical crossover was put forward, which can greatly improve the speed of crossover and mutation so that the proposed GM(1,1)IGA can forecast the shortterm daily load successfully. The paper is anized as follows: section 2 proposes the grey forecasting model GM(1,1): section 3 presents Estimate ? with improved geic algorithm:section 4 puts forward a shortterm daily load forecasting realized by GM(1,1)IGA and finally, a conclusion is drawn in section 5. 2. Grey prediction model GM (1,1) 中英文資料 18 This section reviews the operation of grey forecasting in details. The grey model GM(1,1) is a time series forecasting model. It has three basic operations: (1) accumulated generation, (2) inverse accumulated generation, and (3) grey modeling. The grey forecasting model uses the operations of accumulated to construct differential speaking, it has the characteristics of requiring less data. The grey model GM(1,1), ., a single variable firstorder grey model, is summarized as follows: Step1: Denote the initial time sequence by ??0x = ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?? ?0 0 0 01 , 2 , 3 , ... ,x x x x n x(0) is the given discrete nthdimensional (0)(m) is the time series data at time m , n must be equal to or larger than 4. On the basis of the initial sequence x(0) , a new sequence x(1) is set up through the accumulated generating operation in order to provide the middle message of building a model and to weaken the variation tendency, so x(1) is defined as: ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?? ?1 1 1 1 11 , 2 , 3 , . . .x x x x x n? Where ???? ????1011xx? ， and ? ? ? ? ? ? ? ?101 , 2 , 3kmx k x m k n?? ? ?? and ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?? ?1 , 2 , 3 , . . .r r r r rx x x x x n? is the r times accumulated series. Step2: To set the ? value to fine z(1)(k) According to GM (1, 1), we can form the following firstorder grey differential equation: ? ? ? ?1 1dx a x bdt ?? And its difference equation is ? ? ? ? ? ? ? ?01x k az k b??.Where a was called the developing coefficient of GM,and b was called the control variable. Denoting the differential coefficient subentry in the form of difference, we can get: ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?111 111 11x k x kdx x k x kd t k k??? ? ? ??? Before a grey GM (1, 1) model was set up, a proper ? value needed to be assigned for a better background value z(1)(k). The sequence of background values was defined as: ? ? ? ? ? ? ? ? ? ? ? ? ? ?? ?1 1 1 11 , 2 ,z z z z n? ?? Among them ? ? ? ? ? ? ? ? ? ? ? ? ? ?1 1 1* 1 * 1 , 2 , 3 , 0 1z k x k x k k n? ? ?? ? ? ? ? ? ? ? 中英文資料 19 For convenience, the ? value was often set to ,the z(1)(k) was derived as: ? ? ? ? ? ? ? ? ? ? ? ?111 12x k x kzk ??????? However, this constant ? might not be optimal because the different questions might need different ? value. And, both developing coefficient a and control variable b were determined by the z(1)(k). The process of the original grey information for whitening may be suppressed resulted from the coefficient ? was constant. Hence, the accuracy of prediction value x?(0)(k) in GM (1, 1) model would seriously be decreased. In order to correct the defect, the coefficient ? must be a variable based on the feature of problems,so we estimate ? by geic algorithms. Step3: To construct accumulated matrix B and coefficient vector X n . Applying the Ordinary Least Square (OLS) method obtains the developing coefficient a , b was as follows: ? ? ? ?? ? ? ?? ? ? ?11121311zzBzn???????????????? and ? ? ? ? ? ? ? ? ? ? ? ?0 0 02 , 3 , , Tnx x x x n???? So ? ? 1??, * * *T TTna b B B B X??? ??? Step4: To obtain the discrete form of firstorder grey differential equation, as follows: The solution of x(1) is ? ? ? ? ? ? ? ?10 ?? ?? 1 1 *? ?akbbx k x eaa???? ? ? ????? And the solution of x(0) is ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?0 1 1 0 ??? ? ?1 1 1 * 1 *?a a kbx k x k x k e x ea????? ? ? ? ? ? ????? 3. Estimate ? with improved GA 中英文資料 20 In order to estimate the accuracy of grey mode GM(1, 1), the residual error test was essential. Therefore,the objective function of the proposed method in this paper was to ensure that the forecasting value errors were minimum. The objective function was defined as mean absolute percentage error (MAPE) minimization as follows: ? ?1m in nkM A P E e k?? ? Where， ? ? ? ? ? ? ? ? ? ?? ? ? ?000? 100%x k x kekxk??? x(0)(k) is original data, ? ?? ?0?xkis forecasting value,n is the number of sequence data. However, from the above description of the establishment of GM (1, 1), we can get: In GM (1, 1), the value of parameter ? can determine z(1) , and, both developing coefficient a and control variable b were determined by the z(1)(k).What is more, the solution of x(0) was determined by a and b,so the key part of the whole model selecting process was the value of ? .There is kind of plicated nonlinear relationship between ? and residual errors,and this nonlinearity was hard to solve by resolution, so the optimal selection of ? was the difficult point of GM（ 1,1） . Geic algorithm is a random search algorithm that simulates natural selection and evolution. It is finding widespread application as a consequence of two fundamental aspects: the putational code is very simple and yet provides a powerful search are func