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Optimisation, the process of finding either a maximum of a minimum of the problem at hand plays a key role in several disciplines including engineering and science. In this thesis, different Cuckoo Search algorithms are developed for effective optimisation purposes. These algorithms are tested on ten mathematical test functions and then used to optimise a Back-Propagation Neural Network used for short-term electricity load forecasting for South African data, with the focus on the City of Johannesburg. The original Cuckoo Search algorithm is based on random walk step sizes derived from Lévy probability distribution and the switching parameter between local and global random walks is constant. However, other probability distributions like Cauchy, Gaussian and Gamma have also been used and the switching parameter can be changed dynamically.
The first contribution of the thesis is the development a new Cuckoo Search algorithm whose random step sizes are derived from Pareto probability distribution function. This new Pareto-based Cuckoo Search algorithm is tested on ten benchmark test functions together with other Cuckoo Search algorithms using step sizes derived from Gaussian, Cauchy, Gamma and Lévy probability density functions. When using the confidence interval analysis, the Lévy-based Cuckoo Search algorithm outperforms the Pareto based Cuckoo. However, confidence interval results are only superior due to only one test function whereby Lévy-based Cuckoo Search performed well. Moreover, the Pareto-based Cuckoo shows superior performance in comparison to the other algorithms, leading in seven test functions out of ten when tested for convergence.
The second contribution is the implementation of Cuckoo Search algorithms with dynamically increasing switching parameters between local and random walks. The first improvement done on Cuckoo Search algorithm is the implementation of linear increasing switching parameter, the second is the implementation of power increasing switching parameter and the third improvement is the implementation of exponential increasing switching parameter. When tested on benchmark test functions, the exponentially increasing Cuckoo Search algorithm outperforms the other algorithms by obtaining the longest confidence interval of 4.50566 while the next algorithm (original Cuckoo Search) obtains an interval of 3.9699. Moreover, using convergence plots, both exponentially increasing and linear increasing Cuckoo Search algorithms equally perform well with each leading by three on ten benchmark test functions.
The third contribution is the application of Cuckoo Search algorithms to forecast next hour Johannesburg electricity load demand. The neural network training using data from Johannesburg Citypower (hourly electricity data) and South African Weather Services (hourly weather data like temperature, humidity, wind direction and wind speed), the training graphs confirmed that no overfitting occurred. The Cuckoo Search algorithms are further used to forecast hourly electricity demand for the 19th February 2015. The mean absolute percentage errors for different probability based Cuckoo Search algorithms obtained are as follows; 8.4%, 7.2%, 8.3%, 5.6% and 5.8% for the Lévy, Cauchy, Gaussian, Gamma and Pareto, respectively. For the dynamic changing switching parameters, the following mean absolute percentage errors were obtained; 8.4%, 6.2%, 9.7%, 7.1% and 6.7% for the constant, linear decreasing, linear increasing, power increasing and exponential increasing, respectively.