This paper proposes a novel multiple chaos embedded gravitational search algorithm (MCGSA) that simultaneously utilizes multiple different chaotic maps with a manner of local search. The embedded chaotic local search can exploit a small region to refine solutions obtained by the canonical gravitational search algorithm (GSA) due to its inherent local exploitation ability. Meanwhile it also has a chance to explore a huge search space by taking advantages of the ergodicity of chaos. To fully utilize the dynamic properties of chaos, we propose three kinds of embedding strategies. The multiple chaotic maps are randomly, parallelly, or memory-selectively incorporated into GSA, respectively. To evaluate the effectiveness and efficiency of the proposed MCGSA, we compare it with GSA and twelve variants of chaotic GSA which use only a certain chaotic map on a set of 48 benchmark optimization functions. Experimental results show that MCGSA performs better than its competitors in terms of convergence speed and solution accuracy. In addition, statistical analysis based on Friedman test indicates that the parallelly embedding strategy is the most effective for improving the performance of GSA.

With the fast growth of the international tourism industry, it has been a challenge to forecast the tourism demand in the international tourism market. Traditional forecasting methods usually suffer from the prediction accuracy problem due to the high volatility, irregular movements and non-stationarity of the tourist time series. In this study, a novel single dendritic neuron model (SDNM) is proposed to perform the tourism demand forecasting. First, we use a phase space reconstruction to analyze the characteristics of the tourism and reconstruct the time series into proper phase space points. Then, the maximum Lyapunov exponent is employed to identify the chaotic properties of time series which is used to determine the limit of prediction. Finally, we use SDNM to make a short-term prediction. Experimental results of the forecasting of the monthly foreign tourist arrivals to Japan indicate that the proposed SDNM is more efficient and accurate than other neural networks including the multi-layered perceptron, the neuro-fuzzy inference system, the Elman network, and the single multiplicative neuron model.