simulated_annealing_module Module

number of variables in the function to be optimized.

denotes whether the function should be maximized or minimized. a true value denotes maximization while a false value denotes minimization. intermediate output (see iprint) takes this into account.

error tolerance for termination. if the final function values from the last neps temperatures differ from the corresponding value at the current temperature by less than eps and the final function value at the current temperature differs from the current optimal function value by less than eps, execution terminates and ier = 0 is returned.

number of cycles. after ns function evaluations, each element of vm is adjusted according to the input step_mode the suggested value is 20.

number of iterations before temperature reduction. after ntns function evaluations, temperature (t) is changed by the factor rt. value suggested by corana et al. is max(100, 5n). see goffe et al. for further advice.

number of final function values used to decide upon termination. see eps. suggested value is 4.

the maximum number of function evaluations. if it is exceeded, ier = 1.

if false, the initial guess is ignored and a random point in the bounds is used for the first function evaluation

number of times to run the main loop (must be >=1)

the lower bound for the allowable solution variables.

the upper bound for the allowable solution variables. if the algorithm chooses x(i) < lb(i) or x(i) > ub(i), i = 1, n, a point is from inside is randomly selected. this this focuses the algorithm on the region inside ub and lb. unless the user wishes to concentrate the search to a particular region, ub and lb should be set to very large positive and negative values, respectively. note that the starting vector x should be inside this region. also note that lb and ub are fixed in position, while vm is centered on the last accepted trial set of variables that optimizes the function.

vector that controls the step length adjustment. the suggested value for all elements is 2.0.

controls printing inside sa:

the first seed for the random number generator.

the second seed for the random number generator. different values for iseed1 and iseed2 will lead to an entirely different sequence of trial points and decisions on downhill moves (when maximizing). see goffe et al. on how this can be used to test the results of sa.

how to vary vm after ns cycles.

for step_mode=3, the factor to adjust vm

unit number for prints.

temperature reduction schedule:

parameter for cooling schedules 3 and 5. suggested value: 1.0

if the optional f value is known, it can be specified by optimal_f.

if optimal_f_specified=True the solver will stop if this value is achieved.

absolute tolerance for the optimal_f check

distribution to use for perturbations for each variable:

standard deviation for normal/truncated_normal

scale parameter for cauchy/bipareto distributions

shape parameter for bipareto distribution

the user's function

how often to report intermediate results to the user via report function:

if associated, this function is called to report intermediate results to the user.

if true, the user wants to evaluate multiple points in parallel (e.g. on a GPU or with OpenMP). if false, the user will evaluate one point at a time. if true, the user must provide all of n_inputs_to_send, fcn_parallel_input and fcn_parallel_output.

if the user wants to evaluate multiple points in parallel, this function should return the number of input points that will be sent for evaluation at a time.

this function receives the input points for evaluation

this function receives the output points from the parallel evaluation. The x here will be one of the ones sent via sa_func_parallel_inputs_func, The algorithm will only process one at the time.

minimum allowable step size. if all vm values fall below this, terminate with ier=6

this is public so we can use it in the tests

variable index

variable value to perturb

perturbation distribution mode (see distribution_mode for details)

lower bound

upper bound

lower bound

upper bound

mean of the distribution

standard deviation

location parameter (median)

scale parameter

mean of the underlying normal distribution

standard deviation

lower bound

upper bound

mode of the distribution (should be in [0,1])

center location of the distribution

scale parameter for the Pareto distribution

shape parameter (smaller values = heavier tails)

lower bound

upper bound

temperature reduction schedule (1-5)

parameter for cooling schedules 3 and 5

if the optional f value is known, it can be specified by optimal_f. [Default is False]

if optimal_f_specified=True the solver will stop if this value is achieved.

absolute tolerance for the optimal_f check

distribution for perturbations (per variable):

std dev for normal/truncated_normal (per variable or scalar)

scale for cauchy/pareto (per variable or scalar)

shape for pareto (per variable or scalar)

the user's function for scalar evaluation. if not present, the user must provide all of n_inputs_to_send, fcn_parallel_input and fcn_parallel_output for parallel evaluation.

if the user wants to evaluate multiple points in parallel, this function should return the number of input points that will be sent for evaluation at a time.

this function receives the input points for evaluation

this function receives the output points from the parallel evaluation. The x here will be one of the ones sent via sa_func_parallel_inputs_func, The algorithm will only process one at the time.

how often to report intermediate results to the user via report function:

if associated, this function is called to report intermediate results to the user.

on input: the starting values for the variables of the function to be optimized. [Will be replaced by final point]

the temperature reduction factor. the value suggested by corana et al. is .85. see goffe et al. for more advice.

on input, the initial temperature. see goffe et al. for advice. on output, the final temperature. Note that if t=0, then all downhill steps will be rejected

the step length vector. on input it should encompass the region of interest given the starting value x. for point x(i), the next trial point is selected is from x(i) - vm(i) to x(i) + vm(i). since vm is adjusted so that about half of all points are accepted, the input value is not very important (i.e. if the value is off, sa adjusts vm to the correct value). note: if vm=0.0, then it is set to abs(xu-xl)`.

the variables that optimize the function.

the optimal value of the function.

the number of accepted function evaluations.

the total number of function evaluations. in a minor point, note that the first evaluation is not used in the core of the algorithm; it simply initializes the algorithm.

the error return number:

input optimization variable vector to perturb

step length vector

the perturbed x value

the value of the user function at xp

total number of function evaluations

status output code

to use the input x the first time

the first seed for the random number generator.

the second seed for the random number generator.