ampgo

TRXASprefitpack.driver.ampgo(fun: Callable, x0: ndarray, tot_iter: Optional[int] = 20, max_tunnel: Optional[int] = 5, tol_tunnel: Optional[float] = 1e-05, minimizer_kwargs: Optional[dict] = None, eps1: Optional[float] = 0.02, eps2: Optional[float] = 0.1, n_tabu: Optional[int] = 5, strategy: Optional[str] = 'farthest', seed: Optional[Union[int, RandomState]] = None, callback: Optional[Callable] = None, disp: Optional[bool] = False) → OptimizeResult[source]
ampgo: Adaptive Memory Programming for Global Optimization

Based on Tabu Tunneling Method

Parameters

  • fun – Objective function. Objective function should have following form f(x, *args)

  • x0 – initial guess

  • tot_iter – maximum number of global iteration

  • max_tunnel – maximum number of tunneling phase

  • tol_tunnel – Tolerance to determine whether tunneling phase is successful or not. If \(f(x_{best}) \geq 0\) and \(f(x_{tunnel}) < (1+{tol})f(x_{best})+{tol}\) or \(f(x_{best}) < 0\) and \(f(x_{tunnel}) < (1-{tol})f(x_{best})+{tol}\) then such tunneling phase is regarded as successful phase.

  • minimizer_kwargs –

    Extra keyword arguments to be passed to the local minimizer scipy.optimize.minimize. Some important options could be:

    • method (str): The minimization Method (default: L-BFGS-B)

    • args (tuple): The extra arguments passed to the objective function (fun) and its derivatives (jac, hess)

    • jac: jacobian of objective function (see scipy.optimize.minimize)

    • hess: hessian of objective function (see scipy.optimize.minimize)

    • bounds (Sequence of Tuple): Boundary of variable (see scipy.optimize.minimize)

  • eps1 – Constant used to define aspiration value

  • eps2 – Perturbation factor used to move away from the latest local minimum

  • n_tabu – size of tabulist

  • strategy ({'farthest', 'oldest'}) –

    The strategy to delete element of tabulist when the size of tabulist exceeds n_tabu.

    • farthest: Delete farthest point from the latest local minimum point

    • oldest: Delete oldest point

  • seed – seed used for random perturbation of local minimum. This argument is useful when someone wants to reproduce optimization results.

  • callback – callback function to monitor each global iteration and tunneling phase. function signature should be callback(x, f_val)

  • disp – display level, If zero or None, then no output is printed on screen. If postive number then status messages are printed.

Returns

The optimization results represented as a scipy.OptimizeResult object. The important attributes are

  • x: The solution of the optimization

  • fun: values of objective fuction.

  • success: Whether or not the optimizer exited successfuly

  • message: Description of the cause of the termination

Note

The implementation of ampgo method is based on L. Lasdon et al. Computers & Operations Research 37 (2010) 1500–1509. and Andrea Gavana’s Python Implementation.