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Abstract
This article presents a hybrid model involving artificial neural networks and biogeography-based optimization for long-term forecasting of India's sector-wise electrical energy demand. It involves socio-economic indicators, such as population and per capita gross domestic product, and uses two artificial neural networks, which are trained through a biogeography-based optimization algorithm with a goal of perfect mapping of the input–output data in the non-linear space through obtaining the global best weight parameters. The biogeography-based optimization based training of the artificial neural network improves the forecasting accuracy and avoids trapping in local optima besides enhancing the convergence to the lowest mean squared error at the minimum number of iterations than existing approaches. The model requires an input and the year of the forecast and predicts the sector-wise energy demand. Forecasts up to the year 2025 are compared with those of the regression model, the artificial neural network model trained by back-propagation, and the artificial neural network model trained by harmony search algorithm to exhibit its effectiveness.
Acknowledgments
The authors gratefully acknowledge the authorities of SCSVMV and Pondicherry Engineering College–Puducherry for their continued support, encouragement, and the facilities provided to carry out this work.
NOMENCLATURE
| ANN | = | artificial neural network |
| ANNBP | = | artificial neural network model trained by back-propagation |
| ANNHSA | = | artificial neural network model trained by harmony search algorithm |
| BBO | = | biogeography-based optimization |
| bh, bo | = | bias for hidden and output layers, respectively |
| Ej | = | electrical energy consumption by j th sector |
| Emax | = | maximum emigration rate |
| f | = | activation function |
| GDP | = | gross domestic product |
| h | = | habitat representing a solution point |
| HSA | = | harmony search algorithm |
| HSI | = | habitat suitability index |
| Imax | = | maximum immigration rate |
| Itermax | = | maximum number of iterations for convergence check |
| LF | = | load forecasting |
| m(s) | = | mutation rate for habitat possessing S species |
| MAPE | = | mean absolute percent error |
| mmax | = | maximum mutation rate |
| MSE | = | mean squared error |
| N | = | number of training data |
| neh | = | number of elite habitats |
| nh | = | number of habitats |
| no | = | number of output neurons |
| Oi(n) | = | output of ith neuron for nth training data |
| PM | = | proposed model |
| Pmax | = | maximum probability |
| = | habitat modification probability | |
| Pop | = | population |
| PPP | = | purchasing power parity |
| = | species count probability | |
| Ps(t) | = | probability that the habitat contains exactly S species at time t |
| PSO | = | particle swarm optimization |
| RA | = | regression analysis |
| RM | = | regression model |
| S | = | number of species in the habitat |
| SIV | = | suitability index variable |
| Smax | = | maximum number of species in the habitat |
| Ti(n) | = | targeted value for ith neuron for nth training data |
| Wih | = | weight matrix in between input and hidden layers |
| Who | = | weight matrix in between hidden and output layers |
| X, T | = | input and target vectors of the training data, respectively |
| Δt | = | small time interval |
| λ, μ | = | immigration and emigration rates, respectively |
| Φi | = | error between actual and forecasted value of ith output |
Additional information
Notes on contributors
Jayaraman Kumaran
Jayaraman Kumaran received his M.Tech from the Department of Computer Science and Engineering, Pondicherry University, India, in 2005. At present, he is an assistant professor in the Computer Science & Engineering Department at Pondicherry Engineering College, Pondicherry, India. He is currently working toward his Ph.D. in computer science and engineering at SCSVM University, Kanchipuram, India. His research is focused on artificial intelligent techniques, forecasting techniques, software engineering, and computer networks.
Govindasamy Ravi
Govindasamy Ravi received his B.E. in electrical and electronics engineering from Mysore University, India, in 1992; his M.E. from Annamalai University, India, in 1994; and his Ph.D. from Jadavpur University, India, in 2005. He is currently a professor of Electrical and Electronics Engineering at Pondicherry Engineering College, Pondicherry, India. His current research includes artificial intelligent techniques, electrical machines, power system operation, planning, and optimization.