Kernel Methods and Hybrid Evolutionary Algorithms in Energy Forecasting [book]

2018
The development of kernel methods and hybrid evolutionary algorithms (HEAs) to support experts in energy forecasting is of great importance to improving the accuracy of the actions derived from an energy decision maker, and it is crucial that they are theoretically sound. In addition, more accurate or more precise energy demand forecasts are required when decisions are made in a competitive environment. Therefore, this is of special relevance in the Big Data era. These forecasts are usually
more » ... d on a complex function combination. These models have resulted in over-reliance on the use of informal judgment and higher expense if lacking the ability to catch the data patterns. The novel applications of kernel methods and hybrid evolutionary algorithms can provide more satisfactory parameters in forecasting models. This book contains articles from the Special Issue titled "Kernel Methods and Hybrid Evolutionary Algorithms in Energy Forecasting", which aimed to attract researchers with an interest in the research areas described above. As Fan et al. [1] indicate, the research direction of energy forecasting in recent years has concentrated on proposing hybrid or combined models: (1) hybridizing or combining these artificial intelligence models with each other; (2) hybridizing or combining with traditional statistical tools; and (3) hybridizing or combining with those superior evolutionary algorithms. Therefore, this Special Issue sought contributions towards the development of HEAs with kernel methods or with other novel methods (e.g., chaotic mapping mechanism, fuzzy theory, and quantum computing mechanism), which, with superior capabilities over the traditional optimization approaches, aim to overcome some embedded drawbacks and then apply these new HEAs to be hybridized with original forecasting models to significantly improve forecasting accuracy. The 10 articles collected in this compendium all display a broad range of cutting-edge topics in the kernel methods and hybrid evolutionary algorithms. The preface author believes that these hybrid approaches will play an important role in energy forecasting accuracy improvements. It is known that the evolutionary algorithms have their theoretical drawbacks, such as a lack of knowledge, memory, or storage functions; they are time consuming in training; and become trapped in local optima. Therefore, the goal of hybridizing optimization methods to adjust their internal parameters (e.g., mutation rate, crossover rate, annealing temperature, etc.) is to overcome these shortcomings. Firstly, for example, in genetic algorithms (GAs), new individuals are generated by the following operators: selection, crossover, and mutation. For all types of objective functions, the generation begins with a binary coding for the parameter set. Based on this special binary coding process, GAs are able to solve some specified problems which are not easily solved by traditional algorithms. GAs can empirically provide a few bestfitted offspring from the whole population, but after several generations, due to low population diversity, it might lead to a premature convergence. Due to the easy implementation process and a special mechanism to escape from local optima, chaos and chaos-based searching algorithms have received intense attention. Applications of chaotic mapping mechanisms to carefully expand variable searching space (i.e., allow variables to travel ergodically over the search space) are increasingly popularly employed in evolutionary computation fields. Secondly, several disadvantages embedded in these evolutionary algorithms need to be improved in order to achieve a more satisfactory performance. For example, based on the operation procedure of simulated annealing algorithm (SA), subtle and skillful adjustment in the annealing schedule is required, such as the size of the temperature steps during annealing. Particularly, the temperature of each state is discrete and unchangeable, which does not meet the requirement of continuous decrease in temperature in actual physical annealing processes. x In addition, SA easily accepts deteriorated solutions with high temperature, and it is difficult to escape from local minimum traps at low temperature. Cloud theory is considered to overcome these drawbacks, as demonstrated in Geng et al. [2]. Cloud theory is a model of the uncertainty transformation between quantitative representation and qualitative concept using language value. Based on the SA operation procedure, subtle and skillful adjustment in the annealing schedule is required (e.g., the size of the temperature steps during annealing, the temperature range, the number of re-starts and re-direction of the search). The annealing process is like a fuzzy system in which the molecules move from large-scale to small-scale randomly as the temperature decreases. In addition, due to its Monte Carlo scheme and lack of knowledge memory functions, its time-consuming nature is another problem. Geng et al. [2] tried to employ a chaotic simulated annealing (CSA) algorithm to overcome these shortcomings. In this, the transiently chaotic dynamics are temporarily generated for foraging and self-organizing. They are then gradually vanished with autonomous decrease of the temperature, and are accompanied by successive bifurcations and converged to a stable equilibrium. Therefore, CSA significantly improves the randomization of the Monte Carlo scheme, and controlled the convergent process by bifurcation structures instead of stochastic "thermal" fluctuations, eventually performing efficient searching including a global optimum state. However, as mentioned above, the temperature of each state is discrete and unchangeable, which does not meet the requirement of continuous decrease in temperature in actual physical annealing processes. Even if some temperature annealing functions are exponential in general, the temperature gradually falls with a fixed value in every annealing step and the changing process of temperature between two neighbor steps is not continuous. This phenomenon also appears when other types of temperature update functions are implemented (e.g., arithmetical, geometrical, or logarithmic). In cloud theory, by introducing the Y condition normal cloud generator to the temperature generation process, it can randomly generate a group of new values that distribute around the given value like a "cloud". The fixed temperature point of each step becomes a changeable temperature zone in which the temperature of each state generation in every annealing step is chosen randomly, the course of temperature change in the whole annealing process is nearly continuous, and fits the physical annealing process better. Therefore, based on chaotic sequence and cloud theory, the chaotic cloud simulated annealing algorithm (CCSA) is employed to replace the stochastic "thermal" fluctuations control from traditional SA to enhance the continuous physical temperature annealing process from CSA. Cloud theory can realize the transformation between a qualitative concept in words and its numerical representation. It can be employed to avoid the problems mentioned above. Thirdly, the concepts of combined or hybrid models also deserve consideration. Note that the term "hybrid" means that some process of the former model is integrated into the process of the later one. For example, hybrid A and B implies some processes of A are controlled by A, and some are controlled by B. On the other hand, for the so-called combined models, the output of the former model becomes the input of the latter one. Therefore, the classification results from combined models will be superior to a single model. Combined models are employed to further capture more data pattern information from the analyzed data series. For example, inspired by the concept of recurrent neural networks (RNNs) where every unit is considered as an output of the network and the provision of adjusted information as input in a training process, the recurrent learning mechanism framework is also combined into the original analyzed model. For a feed-forward neural network, links can be established within layers of a neural network. These types of networks are called recurrent neural networks. RNNs are extensively applied in time series forecasting. Jordan [3] proposes a recurrent neural network model for controlling robots. Elman [4] develops a recurrent neural network model to solve linguistics problems. Williams and Zipser [5] present a recurrent network model to solve nonlinear adaptive filtering and pattern recognition problems. These three models mentioned all consist of a multilayer perceptron (MLP) with a hidden layer. Jordan's networks have a feedback loop from the output xi layer with past values to an additional input, namely a "context layer". Then, output values from the context layer are fed back into the hidden layer. Elman's networks have a feedback loop from the hidden layer to the context layer. In the networks of Williams and Zipser, nodes in the hidden layer are fully connected to each other. Both Jordan's and Elman's networks include an additional information source from the output layer or the hidden layer. Hence, these models use mainly past information to capture detailed information. The networks of Williams and Zipser take much more information from the hidden layer and feed it back into themselves. Therefore, the networks of Williams and Zipser are sensitive when models are implemented. On the other hand, for another combined model, some data series sometimes reveal a seasonal tendency due to cyclic economic activities or seasonal nature hour to hour, day to day, week to week, month to month, and season to season, such as an hourly peak in a working day, a weekly peak in a business week, and a monthly peak in a demand-planned year. In order to excellently deal with cyclic/seasonal trend data series, some useful trial (e.g., seasonal mechanism) is also received some intentions. The preface author proposed a seasonal mechanism [2,6,7] with two steps for convenience in implementation: the first step is calculating the seasonal index (SI) for each cyclic point in a cycle length peak period; the second step is computing the forecasting value by multiplying the seasonal index (SI). This discussion of the work by the author of this preface highlights work in an emerging area of kernel methods and hybrid evolutionary algorithms that has come to the forefront over the past decade. The articles in this collection span many cutting-edge areas that are truly interdisciplinary in nature. Wei-Chiang Hong Guest Editor annealing algorithm in a SVR-based load forecasting model. Neurocomputing 2015, 151, 1362-1373. 3. Jordan, M.I. Attractor dynamics and parallelism in a connectionist sequential machine. Zipser, D. A learning algorithm for continually running fully recurrent neural networks. Neural Comput. 1989, 1, 270-280. 6. Hong, W.C.; Dong, Y.; Zhang, W.Y.; Chen, L.Y.; Panigrahi, B.K. Cyclic electric load forecasting by seasonal SVR with chaotic genetic algorithm. Int. J. Electr. Power Energy Syst. 2013, 44, 604-614. 7. Ju, F.Y.; Hong, W.C. Application of seasonal SVR with chaotic gravitational search algorithm in electricity forecasting. Appl. Math. Modelling 2013, 37, 9643-9651. Abstract: Electric load forecasting is an important issue for a power utility, associated with the management of daily operations such as energy transfer scheduling, unit commitment, and load dispatch. Inspired by strong non-linear learning capability of support vector regression (SVR), this paper presents an SVR model hybridized with the differential empirical mode decomposition (DEMD) method and quantum particle swarm optimization algorithm (QPSO) for electric load forecasting. The DEMD method is employed to decompose the electric load to several detail parts associated with high frequencies (intrinsic mode function-IMF) and an approximate part associated with low frequencies. Hybridized with quantum theory to enhance particle searching performance, the so-called QPSO is used to optimize the parameters of SVR. The electric load data of the New South Wales (Sydney, Australia) market and the New York Independent System Operator (NYISO, New York, USA) are used for comparing the forecasting performances of different forecasting models. The results illustrate the validity of the idea that the proposed model can simultaneously provide forecasting with good accuracy and interpretability. Abstract: Crude oil, as one of the most important energy sources in the world, plays a crucial role in global economic events. An accurate prediction for crude oil price is an interesting and challenging task for enterprises, governments, investors, and researchers. To cope with this issue, in this paper, we proposed a method integrating ensemble empirical mode decomposition (EEMD), adaptive particle swarm optimization (APSO), and relevance vector machine (RVM)-namely, EEMD-APSO-RVM-to predict crude oil price based on the "decomposition and ensemble" framework. Specifically, the raw time series of crude oil price were firstly decomposed into several intrinsic mode functions (IMFs) and one residue by EEMD. Then, RVM with combined kernels was applied to predict target value for the residue and each IMF individually. To improve the prediction performance of each component, an extended particle swarm optimization (PSO) was utilized to simultaneously optimize the weights and parameters of single kernels for the combined kernel of RVM. Finally, simple addition was used to aggregate all the predicted results of components into an ensemble result as the final result. Extensive experiments were conducted on the crude oil spot price of the West Texas Intermediate (WTI) to illustrate and evaluate the proposed method. The experimental results are superior to those by several state-of-the-art benchmark methods in terms of root mean squared error (RMSE), mean absolute percent error (MAPE), and directional statistic (Dstat), showing that the proposed EEMD-APSO-RVM is promising for forecasting crude oil price. Abstract: This paper proposes a new electric load forecasting model by hybridizing the fuzzy time series (FTS) and global harmony search algorithm (GHSA) with least squares support vector machines (LSSVM), namely GHSA-FTS-LSSVM model. Firstly, the fuzzy c-means clustering (FCS) algorithm is used to calculate the clustering center of each cluster. Secondly, the LSSVM is applied to model the resultant series, which is optimized by GHSA. Finally, a real-world example is adopted to test the performance of the proposed model. In this investigation, the proposed model is verified using experimental datasets from the Guangdong Province Industrial Development Database, and results are compared against autoregressive integrated moving average (ARIMA) model and other algorithms hybridized with LSSVM including genetic algorithm (GA), particle swarm optimization (PSO), harmony search, and so on. The forecasting results indicate that the proposed GHSA-FTS-LSSVM model effectively generates more accurate predictive results. Abstract: Accurate short-term electrical load forecasting plays a pivotal role in the national economy and people's livelihood through providing effective future plans and ensuring a reliable supply of sustainable electricity. Although considerable work has been done to select suitable models and optimize the model parameters to forecast the short-term electrical load, few models are built based on the characteristics of time series, which will have a great impact on the forecasting accuracy. For that reason, this paper proposes a hybrid model based on data decomposition considering periodicity, trend and randomness of the original electrical load time series data. Through preprocessing and analyzing the original time series, the generalized regression neural network optimized by genetic algorithm is used to forecast the short-term electrical load. The experimental results demonstrate that the proposed hybrid model can not only achieve a good fitting ability, but it can also approximate the actual values when dealing with non-linear time series data with periodicity, trend and randomness. Abstract: Due to the electricity market deregulation and integration of renewable resources, electrical load forecasting is becoming increasingly important for the Chinese government in recent years. The electric load cannot be exactly predicted only by a single model, because the short-term electric load is disturbed by several external factors, leading to the characteristics of volatility and instability. To end this, this paper proposes a hybrid model based on wavelet transform (WT) and least squares support vector machine (LSSVM), which is optimized by an improved cuckoo search (CS). To improve the accuracy of prediction, the WT is used to eliminate the high frequency components of the previous day's load data. Additional, the Gauss disturbance is applied to the process of establishing new solutions based on CS to improve the convergence speed and search ability. Finally, the parameters of the LSSVM model are optimized by using the improved cuckoo search. According to the research outcome, the result of the implementation demonstrates that the hybrid model can be used in the short-term forecasting of the power system. Abstract: Accurate forecasting of carbon price is important and fundamental for anticipating the changing trends of the energy market, and, thus, to provide a valid reference for establishing power industry policy. However, carbon price forecasting is complicated owing to the nonlinear and non-stationary characteristics of carbon prices. In this paper, a combined forecasting model based on variational mode decomposition (VMD) and spiking neural networks (SNNs) is proposed. An original carbon price series is firstly decomposed into a series of relatively stable components through VMD to simplify the interference and coupling across characteristic information of different scales in the data. Then, a SNN forecasting model is built for each component, and the partial autocorrelation function (PACF) is used to determine the input variables for each SNN model. The final forecasting result for the original carbon price can be obtained by aggregating the forecasting results of all the components. Actual InterContinental Exchange (ICE) carbon price data is used for simulation, and comprehensive evaluation criteria are proposed for quantitative error evaluation. Simulation results and analysis suggest that the proposed VMD-SNN forecasting model outperforms conventional models in terms of forecasting accuracy and reliability. Abstract: In existing forecasting research papers support vector regression with chaotic mapping function and evolutionary algorithms have shown their advantages in terms of forecasting accuracy improvement. However, for classical particle swarm optimization (PSO) algorithms, trapping in local optima results in an earlier standstill of the particles and lost activities, thus, its core drawback is that eventually it produces low forecasting accuracy. To continue exploring possible improvements of the PSO algorithm, such as expanding the search space, this paper applies quantum mechanics to empower each particle to possess quantum behavior, to enlarge its search space, then, to improve the forecasting accuracy. This investigation presents a support vector regression (SVR)-based load forecasting model which hybridizes the chaotic mapping function and quantum particle swarm optimization algorithm with a support vector regression model, namely the SVRCQPSO (support vector regression with chaotic quantum particle swarm optimization) model, to achieve more accurate forecasting performance. Experimental results indicate that the proposed SVRCQPSO model achieves more accurate forecasting results than other alternatives.
doi:10.3390/books978-3-03897-293-8 fatcat:5bss5vi44bfipb4rwcuaq3zjg4