Nithyananda Optimization Algorithm (NOA)

this program implements NOA taking economic dispatch as example by taking the life example of nithyananda swami preaching.

Nithyananda Optimization Algorithm (NOA)

Inspiration:

This algorithm is inspired by the idea of self-realization, transcendence, and energy awakening (as often emphasized in Nithyananda's teachings). The algorithm models the optimization process as a spiritual journey where solutions evolve by awakening their "energy potential" and removing "negative karma" (bad solutions).

Key Concepts in NOA:

1. Self-Realization Points (SRPs) → Potential solutions in the search space.
2. Kundalini Awakening Process (KAP) → Exploration phase where solutions elevate to higher levels.
3. Negative Karma Removal (NKR) → Poor solutions are gradually discarded or transformed.
4. Enlightenment State (ES) → The optimal solution, representing the highest realization.
5. Ashram Effect (AE) → Good solutions attract and enhance nearby solutions (akin to a guru-disciple relationship).
6. Maya Disruption (MD) → Random disturbances to avoid local optima and escape illusions of false solutions.

Mathematical Formulation of NOA:

1. Initialization:

• Generate a random population of SRPs (solutions) within the search space.
• Assign each solution an "Energy Level" based on a fitness function.

1. Kundalini Awakening Process (Exploration Phase):

• Apply a transformation function to update each solution’s energy: Xnew=Xold+α⋅tanh(β⋅R)X_{new} = X_{old} + \alpha \cdot \text{tanh}(\beta \cdot R)Xnew​=Xold​+α⋅tanh(β⋅R)where:
• α\alphaα is the learning rate (energy gain factor).
• β\betaβ controls the influence of spiritual realization.
• RRR is a random perturbation factor.

1. Negative Karma Removal (Exploitation Phase):

• Identify low-energy solutions and either:
• Remove them if they are too weak.
• Mutate them using a Guru Guidance Operator to refine their position.

1. Ashram Effect (Attraction to Stronger Solutions):

• Stronger solutions attract weaker ones based on a gravitational-like influence: Xi=Xi+γ(Xbest−Xi)+δ⋅random perturbationX_i = X_i + \gamma (X_{best} - X_i) + \delta \cdot \text{random perturbation}Xi​=Xi​+γ(Xbest​−Xi​)+δ⋅random perturbationwhere XbestX_{best}Xbest​ is the best-known solution.

1. Maya Disruption (Escaping Local Minima):

• Occasionally introduce random jumps to avoid getting trapped: Xi=Xi+ϵ⋅random noiseX_i = X_i + \epsilon \cdot \text{random noise}Xi​=Xi​+ϵ⋅random noisewhere ϵ\epsilonϵ is a chaos factor ensuring diverse exploration.

1. Convergence to Enlightenment State:

• The process continues until convergence criteria are met, leading to the "final enlightened solution", which represents the optimal answer to the problem.

Applications of NOA:

• Machine Learning Hyperparameter Tuning
• Engineering Design Optimization
• Renewable Energy Resource Allocation
• Financial Portfolio Optimization
• Cryptography and Secure Key Generation

Conclusion:

The Nithyananda Optimization Algorithm (NOA) follows a unique spiritual-based evolutionary strategy to reach the optimal solution. It blends exploration (Kundalini Awakening), exploitation (Ashram Effect), and randomization (Maya Disruption) to navigate the search space effectively.