RATHA Optimization Algorithm for a Single-Objective Function

sphere function is tested

RATHA (Rainfall-Driven Algorithm for Thermal Optimization) is a nature-inspired optimization algorithm that mimics the process of rainfall and its impact on optimizing thermal systems or related optimization problems. The concept of rainfall is used metaphorically to describe the search for optimal solutions in a dynamic, stochastic, and adaptive environment. It simulates the behavior of rain droplets falling from the clouds and their potential to accumulate or flow into specific areas based on thermal energy gradients.Key Concepts of RATHA:

1. Rainfall Simulation:

• The algorithm models the falling of raindrops, representing a search for solutions. Each raindrop corresponds to a solution, and the location of the rain corresponds to the search space.

1. Thermal Gradient:

• The idea of a thermal gradient is used to represent the change in solution quality. Higher temperatures correspond to better solutions, while cooler temperatures represent suboptimal regions of the solution space.

1. Evaporation and Precipitation:

• Evaporation corresponds to exploration in the search space, where solutions are moved away from the current state to explore new areas.
• Precipitation corresponds to exploitation, where the algorithm focuses on fine-tuning the solutions in areas that show promising results.

1. Rainwater Accumulation:

• The algorithm accumulates rainwater based on solution performance. Solutions in regions with high rainfall (fitness) are considered better, whereas regions with less rainfall are considered worse.

1. Dynamic Adaptation:

• Just as rain patterns and thermal conditions change over time, RATHA adapts its behavior to exploit the best solutions while ensuring diversity through exploration.

Key Steps in the RATHA Algorithm:

1. Initialization:

• A population of solutions (raindrops) is initialized randomly within a search space.

1. Rainfall Dynamics:

• Each raindrop is moved based on its fitness, with the highest "rainfall" being attracted to areas of high solution quality.

1. Evaporation and Precipitation:

• Evaporation and precipitation are controlled to balance exploration and exploitation. Exploration involves moving solutions in random directions, while exploitation focuses on fine-tuning good solutions.

1. Solution Update:

• Raindrops accumulate in the search space, with better solutions being prioritized.

1. Termination:

• The algorithm stops when a predefined stopping criterion (e.g., maximum iterations or a satisfactory fitness level) is reached.