# Isolated-speciation-based particle swarm optimization (ISPSO)

Since December 18, 2011 by Huidae Cho

The ispso.R file is an R script that implements the ISPSO (Isolated-Speciation-based PSO) algorithm introduced by Cho et al. (2011). The author’s version of Cho et al. (2011) is available here. ISPSO aims to find global and local minima of the objective function. This R script file is distributed under the GNU Public License. If you have questions about this software, leave a comment here.

ISPSO was successfully applied to stochastic rainfall generation (Kim et al. 2013a, Kim et al. 2013b, Kim et al. 2013c, Kim et al. 2016), storm tracking (Cho et al. 2013), uncertainty analysis (Cho and Olivera 2014, Cho et al. 2014), and climate change studies (Heo et al. 2015a, Heo et al. 2015b).

Please cite this software as “Huidae Cho, Dongkyun Kim, Francisco Olivera, Seth D. Guikema, 2011. Enhanced Speciation in Particle Swarm Optimization for Multi-Modal Problems. European Journal of Operational Research 213 (1), 15–23.”

## 1 1-dimensional function

$$F4(x)=1-\exp\left(-2\log(2)\cdot\left(\frac{x-0.08}{0.854}\right)^2\right)\cdot\sin^6\left(5\pi(x^{3/4}-0.05)\right)$$

## 2 Himmelblau function

$$F5(x_1, x_2)=(x_1^2+x_2-11)^2+(x_1+x_2^2-7)^2$$

## 3 Rastrigin function

$$F6(\vec{x})=\sum_{i=1}^D\left[x_i^2-10\cos(2\pi x_i)+10\right]$$

## 4 Griewank function

$$F7(\vec{x})=\frac{1}{4000}\sum_{i=1}^dx_i^2-\prod_{i=1}^d\cos\left(\frac{x_i}{\sqrt{i}}\right)+1$$

## 5 References

Huidae Cho, Dongkyun Kim, Francisco Olivera, Seth D. Guikema, March 2011. Enhanced Speciation in Particle Swarm Optimization for Multi-Modal Problems. European Journal of Operational Research 213 (1), 15–23.

Dongkyun Kim, Francisco Olivera, Huidae Cho, Scott A. Socolofsky, June 2013a. Regionalization of the Modified Bartlett-Lewis Rectangular Pulse Stochastic Rainfall Model. Terrestrial, Atmospheric and Oceanic Sciences 24 (3), 421-436.

Dongkyun Kim, Francisco Olivera, Huidae Cho, October 2013b. Effect of the Inter-Annual Variability of Rainfall Statistics on Stochastically Generated Rainfall Time Series: Part 1. Impact on Peak and Extreme Rainfall Values. Stochastic Environmental Research and Risk Assessment 27 (7), 1601-1610.

Dongkyun Kim, Francisco Olivera, Huidae Cho, Seung Oh Lee, October 2013c. Effect of the Inter-Annual Variability of Rainfall Statistics on Stochastically Generated Rainfall Time Series: Part 2. Impact on Watershed Response Variables. Stochastic Environmental Research and Risk Assessment 27 (7), 1611-1619.

Huidae Cho, Dongkyun Kim, Kanghee Lee, Jinsu Lee, Dongryul Lee, October 2013. Development and Application of a Storm Identification Algorithm that Conceptualizes Storms by Elliptical Shape. Journal of the Korean Society of Hazard Mitigation 13 (5), 325-335.

Huidae Cho, Francisco Olivera, March 2014. Application of Multimodal Optimization for Uncertainty Estimation of Computationally Expensive Hydrologic Models. Journal of Water Resources Planning and Management 140 (3), 313-321.

Huidae Cho, Dongkyun Kim, Kanghee Lee, March 2014. Efficient Uncertainty Analysis of TOPMODEL Using Particle Swarm Optimization. Journal of the Korean Water Resources Association 47 (3), 285-295.

Joonghyeok Heo, Jaehyung Yu, John R. Giardino, Huidae Cho, March 2015a. How Important is Climate Change on the Water Resource in a Humid Subtropical Watershed?: A Case Study from East Texas, USA. Water and Environment Journal 29, 51-60.

Joonghyeok Heo, Jaehyung Yu, John R. Giardino, Huidae Cho, August 2015b. Response of Water Resources to Climate and Land-cover Changes in a Semi-arid Watershed, New Mexico, USA. Terrestrial, Atmospheric and Oceanic Sciences 26 (4), 463-474.

Dongkyun Kim, Huidae Cho, Christian Onof, Minha Choi, March 2016. Let-It-Rain: A Web Application for Stochastic Point Rainfall Generation at Ungaged Basins and Its Applicability in Runoff and Flood Modeling. Stochastic Environmental Research and Risk Assessment.