A Hybrid Generic Algorithm for Dynamic Data Mining in Investment Decision Making
Kangzhi Yu1, Yufang Li2, Zhengying Cai1, *
1College of Computer and Information Technology, China Three Gorges University, Yichang, China
2College of Economics and Management, China Three Gorges University, Yichang, China
To cite this article:
Kangzhi Yu, Yufang Li, Zhengying Cai. A Hybrid Generic Algorithm for Dynamic Data Mining in Investment Decision Making. International Journal on Data Science and Technology. Vol. 2, No. 6, 2016, pp. 62-71. doi: 10.11648/j.ijdst.20160206.12
Received: October 16, 2016; Accepted: November 8, 2016; Published: December 9, 2016
Abstract: To solve the risks and uncertainty problem in investment decision-making, a dynamic data mining architecture is introduced here. First, the investment decision-making process is examined and the involved risks are analyzed. Accordingly, dynamic data mining architecture is proposed here with the dynamic search ability of the generic algorithm. Second, a hybrid algorithm with dynamic learning ability is submitted to overcome the local minima problem prevalent in dynamic data mining. Whenever new data are generated, the data mining algorithm can dynamically collect the original input data without any reconstruction, to realize the dynamic update for investment decision-making. Last, an example is illustrated to verify the proposed model, and the solution provides us an effective model to improve the robustness of investment decision-making under risk environment.
Keywords: Dynamic Data Mining, Investment Decision, Hybrid Genetic Algorithms, Risk Management
The investment decision-making problem is very important in modern economy, but the risks in investment environment increased the difficulty to make a right decision. To solve this risk problem, data mining is introduced in all decision making support systems. Zanin (2016) made a deep analysis on the combination of complex network analysis and data mining, and describes how to extract information from the complex system, and finally create a new compact quantitative representation in combining complex networks and data mining . Heinecke (2016) showed us the optimization of data mining algorithms to solve the regression and classification problems in a broad data set in Data mining on vast data sets as a cluster system benchmark . Garcia (2016) summarized the most influential data preprocessing algorithms, the impact of each algorithm is discussed, and the current research and further research is reviewed in Tutorial on practical tips of the most influential data preprocessing algorithms in data mining . An approximate method for dynamic maintenance of objects and attributes was proposed by Chen (2015) in a decision-theoretic rough set approach for dynamic data mining . Chen (2015) discussed the production and development of the logistics fee policy in toll policy for load balancing research based on data mining in port logistics. It studied the impact of the charges on the consumer's choice of logistics, and even the choice of departure time .
Moreover machine learning and artificial intelligence are applied in data mining to improve its performance. A set of unsupervised machine learning techniques was proposed and applied by Gajowniczek (2015) in data mining techniques for detecting household characteristics based on smart meter data to reveal the specific usage patterns . Morro (2015) achieved a similar search of the data with respect to different pre stored categories in ultra-fast data-mining hardware architecture based on stochastic computing . Zheng (2015) conducted a systematic survey, the main research on the trajectory of data mining, to provide a panoramic view of the field, as well as the scope of its research topics in trajectory data mining with an overview . Li (2015) published a paper entitled distributed data mining based on deep neural network for wireless sensor network, and this paper proposed a distributed data mining method based on deep neural network (DNN), divided by the deep neural network into different levels, and put them into the sensor . Boland (2015) discussed the future development trends of business intelligence and data mining in business intelligence, data mining, and future trends . Li (2014) researched integrates three data mining techniques, k- means clustering, decision tree and neural network to predict the travel time of non-recurrent congested highways in a data mining based approach for travel time prediction in freeway with non-recurrent congestion .
With the further development of the complexity of human activities, the diversity of information, began showing explosive growth, in order to fully grasp the new information on the dynamic data source (database, sequence data, streaming data etc.) data mining becomes inevitable. An advanced process management method, called "program tree" (PT), was proposed for radio frequency identification data mining by Kwon (2014) in a real time process management system using RFID data mining . Itzama (2014) introduced a new association model of time series data mining, which is based on gamma classifier in a novel associative model for time series data mining . The classification of proton transfer events using artificial neural networks was evaluated in pattern recognition and data mining software based on artificial neural networks applied to proton transfer in aqueous environments by Tahat (2014) . Hassani (2014) described a thorough review of the published work on the date of data mining applications in official statistics, and identifies the technology that has been explored in data mining and official statistics form the past, the present to the future . The main focus of the work described in experimental analysis on the normality of pi, E, phi, root 2 using advanced data-mining techniques by Xylogiannopoulos (2014) was to examine whether the well-known mathematical constants of phi, E, phi, and root 2 are normal figures . A survey by Tsai (2014) first discussed the Internet of Things, and then briefly reviewed the "Internet of Things" and "Internet of Things data mining" function. Finally, the future development trend of this field is discussed . Mirco (2014) published a paper entitled with big mobile data mining from good or evil . Xu (2014) discussed the privacy security issues under the big data in his information security in big data from privacy and data mining . Wu (2014) proposed a kind of theorem, the characteristics of the big data revolution, put forward a large data processing model, from the point of view of data mining in data mining with big data . Lima(2016) put forward a hybrid neural evolutionary algorithm (NEA) using a compact indirect encoding scheme (IES) said its genotype, but also by the genotype and the automatic construction of modular, hierarchical recursive neural network in optimization of neural networks through grammatical evolution and a genetic algorithm .
To diminish the risk and uncertainty problem, dynamic data mining is especially presented. Yuregir (2016) used modern data mining methods (SOM and k- mean) and the official statistics of the city cluster according to their consumption characteristics, welfare level and growth rate, and compare them with the help of renewable resource potential rapid mine in solar energy validation for strategic investment planning via comparative data mining methods with an expanded example within the cities of Turkey . A decision-theoretic rough set approach for dynamic data mining by Chen (2015) described an approximate dynamic maintenance method for objects and attributes, and the decision theory of rough set theory (DTRS) is proposed . Composite rough sets for dynamic data mining was proposed by Zhang (2014), with a composite relationship of multiple different types of attributes, and the upper approximation and lower approximation of the composite rough set were re-defined . The dynamic data mining and traditional data warehouse based on data mining very different from traditional data mining is mining based on historical data, extract the knowledge hidden in them, and dynamic data mining is in the past, present and future in the development of knowledge extraction process.
This paper presents a solution for dynamic data mining with high precision. It is focused on the state feedback and dynamic adjustment of parameters, and then a set of investment decision rules, and a set of neural network weights will be gotten. For each network, a genetic algorithm is used to foster a more healthy weight and update its feedback rule. Genetic algorithm is used to optimize the weights of neural network, which solves the problem of slow convergence speed of the traditional algorithm.
In any given generation, data mining starts from a fixed initial state, and then updates the relevant parameters and weights with the addition of more dynamic data. Because it is important to look for a fixed feedback rule and the same neural network weights, so it is to avoid the dependence on the initial conditions to accelerate the learning speed of genetic algorithm from the initial state to do data mining, thus.
In essence, every data mining algorithm will update the investment data with the new and more accurate and excellent neural network. Initially, GA starts a searching based on the initial data set. However, with the continuous data and updating for each investment decision-making network training, any other policy rules will gradually be made to achieve the most appropriate weight. According to the updated weights, each decision maker can better predict the best return on an investment plan.
The structure of this paper is as follows. In the 2nd section, some basic concepts of investment decision making and dynamic data mining are briefly discussed. In the 3rd section, a brief introduction is given on the neural network and genetic algorithm, and then a hybrid algorithm of GA optimized BP is proposed. In the 4st section, a simple test of the performance of the hybrid algorithm is made based on the background of the investment decision example.
2. Dynamic Data Mining for Investment Decision Making
2.1. Investment Decision-Making Process
The investment decision-making with risks is a complex process, as shown in figure 1. To determine the investment target is the premise of investment decision-making, in the specific investment objectives. To further develop the investment direction, the dynamic data mining system was then used, from the dynamic DDS (dynamic data source) where extracted data were analyzed according to the results of the analysis, to the investment plan where the feasibility of the scheme evaluation was demonstrated in detail. The investment plan is mainly to evaluate the investment risk and return analysis, thus determining the reliability of investment decision. The investment plan can adjust the original decision according to the changing environment and needs, making the investment decision more scientific and reasonable.
In the investment decision-making process, it is important to solve the dynamic acquisition of effective data and dynamic processing of them.
As the current time point T, there is a number , in the DDS before the moments when the formation of all the composed of the data set will become a historical data set, denoted as .
As the current time point T, existing number , in the DDS from the time to the time T is to generate all the composing of the data set to become the current data set, denoted as .
As the current time point T, existing number , in the DDS after the T moments when the formation of all the compose of the data set to become the subsequent data set, denoted as .
2.2. Dynamic Data Mining Architecture
With the further development of the complexity of human activities, the diversity of information began showing explosive growth. In order to fully grasp the new information on the dynamic data source (database, sequence data, streaming data etc.), data mining becomes inevitable. The dynamic data mining and traditional data warehouse based on data mining are very different from each other. Traditional data mining is to mine data based on historical data, extract the knowledge hidden in them, whereas dynamic data mining is based on the past, present and future data in the development of knowledge extraction process.
Dynamic data mining is mainly embodied to dynamically extracted data from DDS (dynamic data source) for analysis to find out the knowledge and planning, and it is more popular for the enterprises and institutions or management departments to provide decision-making plan. The dynamic data mining process can be divided into dynamic data acquisition, data processing, data mining, the evaluation process of dynamic data mining. The key is to solve the problems of dynamic acquisition of subsequent data sets and dynamic processing.
The data sources used in investment decision making will be divided into three data sets. First, historical data set for long-term investment information, and its updating time is generally a quarter or year. Second, updating data set for the real-time data is related to investment projects, and these data will fine tune the weights for the data network, where the updating time is in accord with the importance of the new data and can be automatically adjusted by the decision makers or by customs. Third, the buffered data set is a collection of rough and original data. The hybrid algorithm proposed in this thesis will use the dynamic data source to be continuous to optimize the proposed method with the survival of the fittest structure according to the actual needs of the problem, to obtain a set of rules for investment decision and investment decision support.
Dynamic data mining (DDM) is mainly embodied in it can dynamically extract data from DDS (dynamic data source) for further analysis to find out the knowledge and planning, to provide decision-making plan.
The following is the system structure of dynamic data mining:
As we can see, in DDS, according to the data di ( for the data identification number, ), the generation time is divided into the window size of ( for the time period, and and ) with the data segment Dk, where each data segment is for a data window, and is for the data threshold value.
For an integer , , for a time T, a data set in the window size of the window SW can be gotten every time to move forward the location of the s data window size, where the window SW can be called as a sliding window.
2.3. Dynamic Data Processing with General Neural Network Algorithm
The neural network can be used for classification, clustering, and prediction. Historical data can be acquired to form a certain amount of historical data, then the network can learn the hidden knowledge in the data through training. In this case, some characteristics of the dynamic data processing is to find some further problems, and the corresponding evaluated can be used to train the neural network.
If you are using a simple BP algorithm to train the neural network, there will be some problems, such as, BP learning algorithm is very slow. The possibility of failure of network training is great. The application examples of problems are difficult to solve the contradiction between the scale of problem and the scale of the network. This involves the relationship between the possibility and feasibility of network capacity, namely learning complexity. The selection of network structure is not a unified and complete theoretical guidance, and it is general only selected by experience. Therefore, the selection of neural network structure is known as a kind of art. But the network directly affects the structure of neural network and many extended properties. Therefore, the application of how to choose the suitable network structure is an important and difficult problem. The new sample has effect in the success of the network learning, and describes the characteristics of each number of input samples must be the same, including the contradiction between the network prediction ability and training ability. In general, for ability training, if the prediction ability is poor, to a certain extent with the ability to improve training, the prediction ability will be improved. But this trend has some limits, when it reaches a limit, the training ability and the predictive ability will decrease, which is called over-regularization phenomenon. At this time, the network learning is too much for the details of the sample to reflect the sample containing rules.
Although the BP network has been widely used, it also has some shortcomings, mainly including the following aspects. Firstly, the learning rate is fixed, so the convergence speed is slow and a longer training time is often required. For some complex problems, the BP algorithm may requires too much for the training time, mainly due to the learning rate is too small to be used to change the learning rate or adaptive learning rate for improvement. Secondly, the BP algorithm can make convergence to a certain value, but it does not guarantee its minimum value in the global error level, because the gradient descent method may produce a local minimum. For these problems, it can not be easily solved by additional momentum methods. Thirdly, in the network number of hidden layers and the unit layer selection there is no theoretical guidance, and it is generally based on experience or through repeated experiments for sure. Therefore, the network often has great redundancy, to a certain extent, also increases the burden of network learning. Finally, the learning and memory of the network are unstable. That is to say, if the learning samples increase, the trained network will be needed to start training, so there will be no memory of previous weights and the threshold can not be predicted. However, the classification or clustering needs a better weighting preservation.
3. Hybrid General Algorithm for Dynamic Data Mining
In this section, genetic algorithm (GA) is selected to train the neural network for the following reasons. First, compared with the gradient descent method, the genetic algorithm does not use gradient information. Therefore, it does not require the existence of continuity and derivation of the objective functional or state transfer function. The only limitation is that it is bounded. Of course, it can be applied to a larger class of problems. Second, the genetic algorithm is a global search algorithm, based on the historical data set from start, and then makes some adjustments according to the updated data, which can guarantee the convergence of approximate solutions to global optimal domain space and relatively better development by genetic operators. The gradient descent method, on the other hand, requires the gradient information and may stay in a local optimum or not, which depends on the initial parameters.
Compared with the traditional data mining technology, neural network provides a more flexible solution. The genetic algorithm is select to train the neural network, because the genetic algorithm guarantees the convergence to an approximate global optimum no matter what the initial parameter values are. Another feature of GA is that it has parallelism.
3.1.Introduction of Neural Network Algorithm and Genetic Algorithm
Artificial neural network is the basic element of the neural networks, and the principle can be expressed in the following figure.
In figure 3, x1~xn are the input signals from other neurons, wij represents the weights of the connections from the neuron j to the i. θ represents a threshold, or a bias. The relationship between the output and input of the neuron can be expressed as:
In the graph, the output of the neuron i is expressed by yi, the function f is called as the activation function or transfer function, and net is called net activation. If the threshold is regarded as a weight wi0 of input x0 of neuron i, then the equation above can be simplified as:
If the input vector is expressed by X, the weight vector is expressed by W, that is:
Then the output of the neuron can be expressed as a form of vector multiplication:
If the net activation of net is positive, then the neuron is in an active state or excited state, but if the net activation of net is negative, then the neuron is in a state of suppression.
In order to get better fitting, nonlinear functions are usually used, for example a) Sigmoid function bipolar S shape function: b) Bipolar S shape function: .
The main difference between bipolar S shape functions and S shape function lies in the range of the function, where shape function of Bipolar is S (-1,1), and S (0,1) is the S shape function. Because the S shape function and the bipolar S shape function are both the guide functions for continuous functions, so it is suitable to be used in the BP neural networks.
3.2. Introduction of Genetic Algorithm
An adaptive search algorithm, genetic algorithm is put forward by Michgan J.H. Holland University of the United States in 1960s with the genetic mechanism and Simulation of natural biological evolution theory and the GA algorithm. Its theoretical support comes from Darwin's theory of evolution. The theory is based on the process of biological evolution in nature, animal and plant species where every generation keeps on evolving in the constant survival process of the fittest to adapt to the new environment. Through the genetic algorithm of group encoding, selection, crossover and mutation operations, individual screening are performed to find a high degree of individual to be retained in the community. By the elimination of the fitness difference of individual, no generation inherits a same generation of information of its parents, and is better than the previous generations to meet the conditions. So far, it is to realize the simulation of the natural survival law of the fittest in natural selection.
The general genetic algorithm consists of four parts: coding mechanism, fitness function, genetic operator and control functions.
1) Coding mechanism
Genetic algorithm is not to discuss the research object directly, but through some kind of coding mechanism, where the object is given by the specific symbols according to a certain sequence. As the biological heredity is from the chromosomes, and the chromosome is a string of genes. Character set consists of 0 and 1, the code is two strings, and the general GA is not affected by this restriction. In an optimization problem, a string is corresponding to a possible solution and a string class is interpreted in classification as a rul. This is also an important reason for the wide application of GA.
2) Fitness function
Survival of the fittest is the principle of natural evolution. In the genetic algorithm, the fitness function is used to describe the degree of adaptation of each individual. To an optimization problem, the fitness function is often chosen as the objective function. The introduction of the fitness function is designed according to their fitness to assess the individual comparison, and determine the extent of the pros and cons, in order to carry out the survival of the fittest genetic operation.
3) Genetic operator
Genetic operators including the selection of reproduction operator, crossover operator, mutation operator, respectively, to simulate the natural biological reproduction, mating and gene mutation processes.
4) Control parameters
In the actual operation of the genetic algorithm, it is needed to determine the string length of the solved string to improve the effect of the selection. Here, the string length is denoted as L; the group size is denoted as size. crossover rate, that is, the probability of crossover operator is denoted as Pc; mutation rate is denoted as Pm, that is, the probability of the implementation of the compiler.
3.3. Optimization of Neural Network by Genetic Algorithm
Genetic algorithm is an adaptive search algorithm of global optimization probability, which simulates the genetic and evolutionary process of biological in the natural environment. Traditional genetic algorithm has many advantages, but there are still some problems, this paper proposes an improved genetic algorithm, based on the standard genetic algorithm to improve the 4 points:
1) Floating point code;
2) Uniform generation of initial population;
3) Using dynamic selection operation;
4) Adaptive adjustment of and . (is the exchange of probability of first generation. is the mutation probability of the generation, is a time factor.
The expression of the adaptive formula is:
In the formula, is the largest mutation probability, is the minimum one, is a constant, is an algebra and is the maximum genetic algebra.
In this paper, the main steps are: to randomly generate initial population; and then to iterate in each iteration, where each iteration is the first genetic manipulation; to select the sub elite and the training mode of corresponding parent individuals; and then to memory map the BP network and operation of the BP training; if it is successful, it will produce a small amount of individual by the GA, and a plurality of individual will extract in BP; if the BP training is not successful, then it will generate a plurality of individual BP network by GA, and extract a few individuals; finally to meet the termination conditions. When this algorithm is combined with the evolution of the learning ability of BP and GA's ability, it makes the individual evolution by studying to be more in line with the actual characteristics of biological growth.
The hybrid learning algorithm process is as shown in Figure 4.
As a three layer BP neural network, n is the number of input nodes, is the number of hidden nodes, m is the number of output nodes. The activation function of the input layer to the hidden layer is S type, and the activation function of the hidden layer to the output layer is a linear function. Given a training set, the input mode is , so the corresponding target output is , it is said a total of training samples, where is a n-dimensional vector, is a m dimension of the desired output and the actual output vector, and the vector , is available between the input and output of the network relationship:
Among them, is the connection weight between node in the implicit layer and node in the input layer, is the threshold value of the node in the hidden layer.
For the connection weights between the node in the hidden layer and the node in the output layer, is the threshold of the node in third output layer, is the actual output of node in output layer. According to the error between the actual output vector and the target output vector, a least square error function is defined.
Among them, is indicated in the first training sample training with the desired output and the actual output of the node of the output layer.
The least squares error function can be used to describe the performance of the neural network, and the optimization objective function is to optimize a network output and the minimum square error. And the requirement of network structure should be as simple as possible, namely the network nodes and their connections should be as least as possible.
In order to combine genetic algorithm with neural network, there is
The error function of the network output is the smallest when the adaptive degree of the offspring is the maximum. Its optimization function is:
is the range of the variables in the formula.
The coefficient weights and threshold values are encoded by floating point numbers, and the string length is ( is the number of input nodes, is the number of hidden nodes, is the number of output nodes). The code is concatenated into a long string according to a certain order, corresponding to .
4. Example Application and Performance Analysis
4.1. Example Explanation
Here is an example for dynamic data mining in investment decision making, as shown in Table 1. As can be seen from the table 1, the company in the three years of 2012-2014, the flow rate and speed ratio increased slightly, the asset liability ratio showed a downward trend, which shows the company's solvency has increased. Accounts receivable turnover and inventory turnover rate have growth trend, which show that the company's sales situation has a good trend.
|Asset liability ratio||0.52||0.49||0.47|
|Accounts receivable turnover rate||11.46||13.55||14.23|
|Turnover ratio of total assets||2.27||2.29||2.25|
|Net asset interest rate||33.88%||32.36%||30.35%|
|Return on shareholders' equity||64.86%||63.81%||57.18%|
|Net sales rate||17.85%||14.23%||13.43%|
Flow rate = current assets / current liabilities
Speed ratio = quick assets / current liabilities
Asset liability ratio = Total Liabilities / total assets
Accounts receivable turnover rate of credit = net income / average accounts receivable
Inventory turnover = cost of sales / inventory balance
Total asset turnover = sales / total assets
Net profit margin = net profit / total assets
Return on shareholders' equity = net profit / total stockholders' equity.
Net profit margin = net profit / net profit
However, the company's total asset turnover rate has not changed much. It is worth noting that the company's three profitability indicators are declining. According to the above analysis, although the solvency of the company enhanced, but the asset turnover rate has not accelerated, and the company's profitability is declining. Therefore, it is important to strengthen the sales work, strictly control costs and expenses, in order to reverse the trend of declining profitability of the company.
4.2. Results Analysis
The curve of mean square error is shown in figure 5. The training of a total of 800 times, with a time of 7 seconds, the average variance of the training time is 0.01, the mean variance of the training time is 0.001. The following figure for the neural network in training 800 times shows the performance of the indicators, where the three lines shown in the figure, are the actual training indicators, the best indicators of line and target line, respectively.
It can be seen from the figure that the convergence rate is very fast in the initial stage of training, but in the later period of training, the convergence rate is obviously slowed down.
The following figure shows the current gradient of the training process and calibration curve.
As the selected explanatory variables, it is clear their ability to explain the target variables, but when many variables are available, it is difficult to manual so many data of the observed variables. It is entirely possible only because of sampling error, or even just a coincidence caused, and is not caused by the nature of the overall because data mining is often faced with massive data. And automatic tools with fitting ability and strong over fitting may be very helpful. But once the transition fitting phenomenon is serious, the whole model for the prediction of the value will be greatly reduced. So it is necessary to assess the validity of the model, in order to ensure a robust and reliable model. The algorithm proposed in this paper has a high degree of fit to the data, and the error is small. The new hybrid algorithm significantly improves the adaptability of the neural network. In the initial stage of evolution, adaptation significantly improved, when the evolution is in the late period, the adaptation will not be obvious.
4.3. Further Discussion
Because the data mining model is very powerful, it is very easy for us to evaluate the resulting transition of fitting model. In order to establish a true and useful model, it is necessary to prevent the transition fit. So the effectiveness of the evaluation model must be carried on to ensure the prediction to being robust and reliable. Although the genetic algorithm can guarantee the convergence to the optimal solution in theory, it is difficult to determine the evolutionary algebra.
The comparison of investment and production are shown in figure 7. If the numerical model can predict well beyond the range of sample, this model is called "extrapolation", but a lot of models can not be extrapolated effectively because of the over-regularization. Over quasi consensus, this model can not only explain the changes which can be observed in the in general, but also explain the cause of error due to the fluctuation of the individual samples.
In order to prevent the transition in the method of data fitting, data mining is generally used in the split. The so-called split data is starting in accordance with a certain proportion of the sample data, and it is necessary to be split into three separate training data set, validation data set, test data sets, and the training data set for the fit for the selected model.
The sample data distribution map is shown in figure 8.
Using the sample data distribution map, it can be avoided to be over-regularization to the greatest extent, to ensure the stability of the model. The important point is that the data resolution is a data luxury, only when a sufficient number of samples can be used. Investment parameter list and return form is shown in Table 2.
|Actual value / million||5178||6648||7612.6|
|Predicted value / million||5016||6472.65||7578.56|
|Error rate / (%)||3.13%||2.64%||0.45%|
As can be seen from the table, the cost of rapid growth, results in a slow growth in net profit, so the company should strengthen management, and strive to do more work to diminish investment risk and loss, especially to strengthen the main business, cost control. So it will be possible to help us to make the company's net profit to be a substantial growth. Because of the data test in this part is completely independent of the modeling data set, and the samples have any modeling uncertainties taken from the same general, it should be considered to be an extrapolation of test validity of the proposed model, where the evaluation for the model results is very impressive.
A dynamic data mining scheme is introduced here for decision making problem with risks, where the hybrid model of genetic algorithm is proposed. The ingenious reasonable error function of neural network combined with the fitness function is combined for the optimization of objective function, which has dynamic topological structure to optimize the BP neural network, weights and thresholds. And the experimental study presented a set of advanced encoding technology and evolution strategy optimized by genetic algorithm to overcome the arbitrariness of the process caused by the network risks. The proposed model can not only help investors to determine the risk investment with high efficiency over traditional technologies, but also avoid the decision problem to be easy to fall into local solutions.
Future work will make further test and comparison of the practical results and apply the optimization method to international investment problems.
This research was supported by the National Natural Science Foundation of China (No. 71471102), and Science and Technology Research Program, Hubei Provincial Department of Education in China (Grant No. D20101203).