Vimal Optimization Algorithm

sphere function is used

Explanation of the Code

1. Sphere Function: The objective function sphereFunction computes the sum of squares of the elements of x.
2. Initialization: The algorithm generates an initial random population of solutions within the defined bounds.
3. Purity Score: The purity score is calculated as the inverse of the sphere function value. Higher purity scores correspond to better solutions.
4. Purification Process:

• Mutation/Refinement: Small random perturbations are added to the purest solutions to refine them.
• Combination: The purest solutions are blended with their neighbors to create new solutions.

1. Convergence: The algorithm stops when a sufficiently pure (optimal) solution is found or when the maximum number of iterations is reached.
2. Output: The purest solution and its corresponding value of the sphere function are displayed.

Features

• Purification Concept: The algorithm focuses on refining and purifying solutions to reach optimality.
• Combination and Mutation: These mechanisms introduce diversity and ensure the search space is well-explored.

Use Case: Sphere Function Optimization

The sphere function is a standard benchmark for testing optimization algorithms. The Vimal Optimization Algorithm showcases a novel approach inspired by the concept of purity, which can be adapted for more complex problems.