**1. Introduction**

A new optimization algorithm called Rain optimization Algorithm (ROA) [1] is validated by applying on computationally expensive benchmark problems [2]. ROA mimics the natural behavior of raindrops trickling down a hill (high position) towards a valley (low position) [3].

**2. Inspiration of ROA**

The main inspiration of ROA is from raindrop behavior [4]. Raindrops naturally trickle down along a slope from a peak then form the rivers and always reach to the lowest land points or empty out into the sea which is as represented as the figure below;

**3. Numerical expression of ROA**

RFO starts with an initial population as raindrops [5]. If the population size is Z, the drop number DN is defined as in Equation below;

Where n is the number of optimization variables, V is the variable of optimization problem.

Rain-fall deals with raindrops during an optimization process. It is generated according to uniform random distribution function and subject to all the constraints as mentioned by the below equation,

Where Uni is the uniform distribution function. Ul_{n}, LI_{n }lower and upper limits of n. A point in drops neighborhood, generated randomly during optimization and it is represented as,

Where R is the the real positive vector representing the neighborhood drop NP. is the unit vector of n th dimension. Among all the neighbor points of drop, the dominant neighbor point DNP is a point that satisfies as represented by an equation

FD is the functions for drop. The optimization when there is no dominant neighbor point for a raindrop such that the raindrops status is inactive the explosion process is carried out so the drop gets out from this situation is expressed as,

NP_{(exp)} is the number of neighbor points in normal condition with no explosion. EB is the explosion base and EC is the explosion counter.

The Raindrop’s rank in each iteration of the optimization process, the ranks of all the raindrops are calculated according to Equation as below,

Where OF_{1} and OF_{2} the absolute change in objective functions from the first iteration at iteration n for raindrop FD. φ_{1} and φ_{2} weighting coefficients [6].

**4. Advantages of ROA**

**5. A rainwater control optimization design approach for self-organizing industrials feature map neural network model**

To address the problems of high overflow rate of rainfall efficiency, a rainwater control optimization design approach based on a self-organizing feature map neural network model (SOFM) was addressed [7]. This model can adjust various parameters of the rainwater network and the green infrastructure, and use these parameters as parameters for rainfall runoff simulation [8], it has provided a better decision-making basis for industries for rainwater control design and effectively avoids flooding while overflow of raining [9].

**6. Forecasting rainfall using machine learning strategies based on weather radar data**

Weather forecasting had always been one of the major technologically and scientifically challenging issues around the world [10]. Climate change is one significant and lasting transformation in statistical distributions of the weather patterns. To proceed with all this process, for classifying the predictions and implemented [11]. The implemented is using random forest classifier RFC), XG Boost, and neural networks. The better accuracy will be given by neural networks [12]. The radar data are collected the data. After collecting the data, the model is trained using above approaches, and the model is tested to check the accuracy of the results [13].

**7. Pseudo Code of ROA**

**8. Applications of ROA**

The ROA is applied for solving constrained engineering *optimization* problems [14]. Economic dispatch problem has been solved by ROA [15].

**Reference**

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[2]”The importance of the treatment plant performance during rain to acute water pollution”, Water Science and Technology, vol. 34, no. 3-4, 1996. Available: 10.1016/0273-1223(96)00549-5**.**

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[4]A. Rafieerad et al., “GEP-based method to formulate adhesion strength and hardness of Nb PVD coated on Ti–6Al–7Nb aimed at developing mixed oxide nanotubular arrays”, Journal of the Mechanical Behavior of Biomedical Materials, vol. 61, pp. 182-196, 2016. Available: 10.1016/j.jmbbm.2016.01.028.

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[7]M. Modiri-Delshad, S. Aghay Kaboli, E. Taslimi-Renani and N. Rahim, “Backtracking search algorithm for solving economic dispatch problems with valve-point effects and multiple fuel options”, Energy, vol. 116, pp. 637-649, 2016. Available: 10.1016/j.energy.2016.09.140.

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[9]T. Ngo, A. Sadollah and J. Kim, “A cooperative particle swarm optimizer with stochastic movements for computationally expensive numerical optimization problems”, Journal of Computational Science, vol. 13, pp. 68-82, 2016. Available: 10.1016/j.jocs.2016.01.004.

[10]T. Liao, T. Stützle, M. Montes de Oca and M. Dorigo, “A unified ant colony optimization algorithm for continuous optimization”, European Journal of Operational Research, vol. 234, no. 3, pp. 597-609, 2014. Available: 10.1016/j.ejor.2013.10.024.

[11]M. Singh, B. Panigrahi and A. Abhyankar, “Optimal coordination of electro-mechanical-based overcurrent relays using artificial bee colony algorithm”, International Journal of Bio-Inspired Computation, vol. 5, no. 5, p. 267, 2013. Available: 10.1504/ijbic.2013.057196.

[12]S. He, Q. Wu and J. Saunders, “Group Search Optimizer: An Optimization Algorithm Inspired by Animal Searching Behavior”, IEEE Transactions on Evolutionary Computation, vol. 13, no. 5, pp. 973-990, 2009. Available: 10.1109/tevc.2009.2011992.

[13]S. Kaboli, J. Selvaraj and N. Rahim, “Long-term electric energy consumption forecasting via artificial cooperative search algorithm”, Energy, vol. 115, pp. 857-871, 2016. Available: 10.1016/j.energy.2016.09.015.

[14]S. Kaboli, J. Selvaraj and N. Rahim, “Long-term electric energy consumption forecasting via artificial cooperative search algorithm”, Energy, vol. 115, pp. 857-871, 2016. Available: 10.1016/j.energy.2016.09.015.

[15]A. Gandomi and X. Yang, “Chaotic bat algorithm”, Journal of Computational Science, vol. 5, no. 2, pp. 224-232, 2014. Available: 10.1016/j.jocs.2013.10.002.