Gold Rush Optimization for Optimal IDFT Size Selection

Gold Rush Optimization (GRO) for Optimal Selection of IDFT Size

Gold Rush Optimization (GRO) is a population-based optimization technique inspired by the behavior of gold miners searching for rich gold deposits. In this approach, GRO is used to determine the optimal IDFT size that minimizes the Signal-to-Noise Ratio (SNR), thereby improving routing accuracy.

Step 1: Initialization

In the initialization phase, a population of candidate IDFT sizes is randomly generated. Each candidate represents a possible solution.

N_i⁽⁰⁾ = N_min + rand(0,1) × (N_max − N_min)

• N_i – IDFT size of the i^th candidate
• N_min, N_max – minimum and maximum IDFT sizes
• rand(0,1) – uniformly distributed random number

Interpretation: Multiple IDFT sizes are randomly selected to form the initial population.

Step 2: Fitness Function

The objective of the fitness function is to minimize the Signal-to-Noise Ratio (SNR). The SNR is computed as:

SNR = 10 log₁₀ ( P_signal / P_noise )

The optimization objective is:

min   SNR(N_i)

• P_signal – signal power (dB)
• P_noise – noise power (dB)

Interpretation: Each IDFT size produces a different SNR value; the IDFT size with the minimum SNR is considered optimal.

Step 3: Updation

In this phase, the IDFT sizes are updated iteratively based on the Gold Rush Optimization strategy. Candidates move toward the best-performing IDFT size while maintaining random exploration.

N_i^(t+1) = N_i^(t) + α × r + β × ( N_best − N_i^(t) )

• α – exploration coefficient
• β – exploitation coefficient
• r – random number in the range [−1, 1]
• N_best – IDFT size with minimum SNR

Interpretation: Poor solutions change more aggressively, while good solutions converge toward the optimal IDFT size.

Step 4: Termination

The algorithm terminates when the maximum number of iterations is reached or when the improvement in SNR becomes negligible.

| SNR_best^(t) − SNR_best^(t−1) | < ε

The optimal IDFT size is selected as:

N^* = arg min SNR(N)

Summary: Gold Rush Optimization iteratively searches for the optimal IDFT size by evaluating SNR values and guiding candidate solutions toward the best-performing IDFT size while preserving exploration.