analytical solver

analytical is a Solver that computes a predefined benchmark function \(f(x)\) for evaluating the performance of search algorithms.

Input parameters

The funtion_name parameter in the solver section specifies the function to use.

• function_name

  Format: string

  Description: Function name. The following functions are available.

  • quadratics

    • Quadratic function

      \[f(\vec{x}) = \sum_{i=1}^N x_i^2\]

    • The optimized value \(f(\vec{x}^*) = 0 \quad (\forall_i x_i^* = 0)\)

  • rosenbrock

    • Rosenbrock function

    \[f(\vec{x}) = \sum_{i=1}^{N-1} \left[ 100(x_{i+1} - x_i^2)^2 + (x_i - 1)^2 \right]\]

    • The optimized value \(f(\vec{x}^*) = 0 \quad (\forall_i x_i^* = 1)\)

  • ackley

    • Ackley function

    \[f(\vec{x}) = 20 + e - 20\exp\left[-0.2\sqrt{\frac{1}{N}\sum_{i=1}^N x_i^2}\right] - \exp\left[\frac{1}{N}\cos\left(2\pi x_i\right)\right]\]

    • The optimized value \(f(\vec{x}^*) = 0 \quad (\forall_i x_i^* = 0)\)

  • himmerblau

    • Himmerblau function

    \[f(x,y) = (x^2+y-11)^2 + (x+y^2-7)^2\]

    • The optimized value \(f(3,2) = f(-2.805118, 3.131312) = f(-3.779310, -3.283186) = f(3.584428, -1.848126) = 0\)