Optimal Computer Budget Allocation (OCBA)
References
Chun-Hung Chen and Loo Hay Lee:
Stochastic Simulation Optimization: An Optimal Computer Budget Allocation,
pp. 49 and pp. 215
C.S.M Currie and T. Monks:
How to choose the best setup for a system. A tutorial for the Simulation Workshop 2021,
see:
https://colab.research.google.com/github/TomMonks/sim-tools/blob/master/examples/sw21_tutorial.ipynb
and
https://github.com/TomMonks/sim-tools
Examples:
From the Chen et al. book (p. 49):
mean_y = np.array([1,2,3,4,5])
var_y = np.array([1,1,9,9,4])
get_ocba(mean_y, var_y, 50)
[11 9 19 9 2]
Args:
means (numpy.array):
means
vars (numpy.array):
variances
delta (int):
incremental budget
Returns:
(numpy.array):
budget recommendations. (n,) numpy.array
Source code in spotPython/budget/ocba.py
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79 | def get_ocba(means, vars, delta):
"""
Optimal Computer Budget Allocation (OCBA)
References:
Chun-Hung Chen and Loo Hay Lee:
Stochastic Simulation Optimization: An Optimal Computer Budget Allocation,
pp. 49 and pp. 215
C.S.M Currie and T. Monks:
How to choose the best setup for a system. A tutorial for the Simulation Workshop 2021,
see:
https://colab.research.google.com/github/TomMonks/sim-tools/blob/master/examples/sw21_tutorial.ipynb
and
https://github.com/TomMonks/sim-tools
Examples:
From the Chen et al. book (p. 49):
mean_y = np.array([1,2,3,4,5])
var_y = np.array([1,1,9,9,4])
get_ocba(mean_y, var_y, 50)
[11 9 19 9 2]
Args:
means (numpy.array):
means
vars (numpy.array):
variances
delta (int):
incremental budget
Returns:
(numpy.array):
budget recommendations. `(n,)` numpy.array
"""
n_designs = means.shape[0]
allocations = zeros(n_designs, int32)
ratios = zeros(n_designs, float64)
budget = delta
ranks = get_ranks(means)
best, second_best = argpartition(ranks, 2)[:2]
ratios[second_best] = 1.0
select = [i for i in range(n_designs) if i not in [best, second_best]]
temp = (means[best] - means[second_best]) / (means[best] - means[select])
ratios[select] = square(temp) * (vars[select] / vars[second_best])
select = [i for i in range(n_designs) if i not in [best]]
temp = (square(ratios[select]) / vars[select]).sum()
ratios[best] = sqrt(vars[best] * temp)
more_runs = full(n_designs, True, dtype=bool)
add_budget = zeros(n_designs, dtype=float)
more_alloc = True
while more_alloc:
more_alloc = False
ratio_s = (more_runs * ratios).sum()
add_budget[more_runs] = (budget / ratio_s) * ratios[more_runs]
add_budget = around(add_budget).astype(int)
mask = add_budget < allocations
add_budget[mask] = allocations[mask]
more_runs[mask] = 0
if mask.sum() > 0:
more_alloc = True
if more_alloc:
budget = allocations.sum() + delta
budget -= (add_budget * ~more_runs).sum()
t_budget = add_budget.sum()
add_budget[best] += allocations.sum() + delta - t_budget
return add_budget - allocations
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