differentialEvolution#

swordfish.function.differentialEvolution()#

Use the Differential Evolution algorithm to calculate the global minimum of a function with multiple variables.

Parameters:

  • func (Constant) – The objective function to be minimized. Note that the function must return a scalar.

  • bounds (Constant) – A numeric matrix of shape (N, 2) indicating the bounds for parameters, where N is the number of parameters to be optimized.

  • X0 (Constant, optional) –

    A numeric vector indicating the initial guess to the minimization.

    Note

    Each row in the bound parameter contains two values (min, max), which define the lower and upper limits for the parameter values specified by X0.

    X0 and bounds must have the same length, i.e., N = size(X0).

  • maxIter (Constant, optional) – A non-negative integer indicating the maximum number of iterations. The default value is 1000.

  • popSize (Constant, optional) – A positive integer specifying the multiplier for setting the total population size. The population contains popSize*(N - N_equal) individuals, where N_equal represents the number of parameters whose bounds are equal. The default value is 15.

  • mutation (Constant, optional) – A numeric pair in the format of (min, max), indicating the range of the mutation constant. It should satisfy 0 <= min <= max < 2. The default value is (0.5, 1).

  • recombination (Constant, optional) – A numeric scalar in [0, 1], indicating the recombination constant, also known as the crossover probability.

  • tol (Constant, optional) – A non-negative floating-point scalar indicating the relative tolerance for convergence. The default value is 0.01.

  • atol (Constant, optional) – A non-negative floating-point scalar indicating the absolute tolerance for convergence. The default value is 0. The algorithm terminates when stdev(population_energies) <= atol + tol * abs(mean(population_energies)), where population_energies is the vector consisting of objective function values for all individuals in the population.

  • polish (Constant, optional) – A Boolean scalar indicating whether to polish the differential evolution result using the L-BFGS-B method. The default value is true.

  • seed (Constant, optional) – An integer indicating the random seed used in the differential evolution algorithm, allowing users to reproduce the results. If unspecified (default), a non-deterministic random number generator is used.

Returns:

A dictionary containing the following keys:

  • xopt: A floating-point vector indicating the parameter values that minimize the objective function.

  • fopt: A floating-point scalar indicating the minimum value of the objective function, where fopt = f(xopt).

  • iterations: An integer indicating the number of iterations during the optimization process.

  • fcalls: An integer indicating the number of times the objective function is called during the optimization process.

  • converged: A Boolean scalar indicating whether the optimization result is converged.

    • true: The optimization result has been converged to below a preset tolerance and the algorithm terminates.

    • false: The algorithm terminates without converging after reaching the maximum number of iterations.

Return type:

Constant