Represents test indicating whether optimization result should be accepted

Basinhopping algorithm outcomes

• niter_completed: Maximum number of local optimisatiosn reached
• early_stop: Callback function requested an early stop to the algorithm
• success_condition: Same minimum found more than specified number of times

struct BasinhoppingParams{T<:StepTaker,U<:AcceptanceTest,C<:Function}

Optional parameters to Basinhopping algorithm

Fields

• niter::Int64: Total number of local optimisations performed.
• step_taker::T: Total number of local optimizations performed.
• test::U: Test determining whether local optimization is accepted.
• callback::C: Function to be called after each local optimization. Signature: (x, minimum, parameters_after_local_opt, minimum_after_local_opt, test_result) -> bool. If this returns true the algorithm is stopped.
• niter_success::Int64: Stop if the global minimum candidate remains the same for this number of iterations.

function BasinhoppingParams(;<keyword arguments>)

Keyword arguments

• niter: Default: 20.
• step_taker: Default RandomDisplacement(0.5, Random.GLOBAL_RNG, 50, 0.5, 0.9).
• test: Default: MetropolisTest(1.0, Random.GLOBAL_RNG).
• callback::Int64: Default: (...) -> false.
• niter_success::Int64: Default: 2

Basinhopping algorithm result

Fields

• minimization_result: local optimization result identified as global minimum
• total_iterations::Int64: total number of local optimizations performed
• f_calls::Int64: total number of function evaluations
• g_calls::Int64: total number of gradient calls
• h_calls::Int64: total number of Hessian evaluations
• exit_code::BasinhoppingOutcome: Result of algorithm (see BasinhoppingOutcome documentation)

Group multiple tests together

Metropolis acceptance test parameters

function MetropolisTest(T[, rng])

Create Metropolis acceptance test with temperature T = 1/beta.

Random displacement of parameters.

Fields

• stepsize::Float64: Size of random displacement.
• rng::RNG: Source of pseudorandomness.
• interval::Int64: total number of function evaluations.
• target_accept_rate::Float64: Ratio between local minima being accepted and all local optimizations.
• factor::Float64: Factor by which to adjust step size when updating.

Represents perturbation of parameters between local optimizations.

Result of applying acceptance test

• accept: Test passed, local minimum accepted
• reject: Test failed, local minimum rejected
• force: Forced acceptance of local minimum

Returns global minimum found by basinhopping

Show global minimum found

function apply_test(test,
                    minimum_after_local_opt,
                    x_after_local_opt,
                    minimum,
                    x)

Apply acceptance test.

Arguments

• optimizer: an optimization routine; must be a callable accepting a single argument, the initial parameters for a local optimization
• x0: initial parameters for first local optimization
• parameters: optional parameters; see BasinhoppingParams

function apply_test(test::CompositeTest,
                    minimum_after_local_opt,
                    x_after_local_opt,
                    minimum,
                    x)

Evaluates composite acceptace test; test is accepted either if all tests are accepted or if one test forces the acceptance by returning force.

function apply_test(test::MetropolisTest,
                    minimum_after_local_opt,
                    x_after_local_opt,
                    minimum,
                    x)

Evaluates Metropolis acceptace test.

See also metropolis_criterion

function basinhopping(optimizer, x0[, parameters])

Basinhopping optimization algorithm.

Arguments

• optimizer: an optimization routine; must be a callable accepting a single argument, the initial parameters for a local optimization
• x0: initial parameters for first local optimization
• parameters: optional parameters; see BasinhoppingParams

Evaluates Metropolis criterion.

Reports on exit code of basinhopping

take_step!(d::RandomDisplacement, x)

Random perturbation in every coordinate of x.

take_step!(d::StepTaker, x)

Perturbs parameters x as specified by a step taker d

update!(d::RandomDisplacement, nstep, naccept)

update!(d::StepTaker, nstep, naccept)

Updates step taking routine.

Arguments

• d::StepTaker:
• nstep::Int: Number of local optimizations performed so far.
• naccept::Int: Number of local minima accepted so far.

Returns total number of function evaluations

Returns total number of gradient evaluations

Returns total number of Hessian evaluations

Returns parameters at which global minimum was found