forked from reinhardfechter/Opt_of_Exp_Design
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sensitivity_analysis.py
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sensitivity_analysis.py
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# ## Optimisation of the Experimental Design for the Flexible PVC Modelling Experiments
# Allocation of Degree and Student for each experiment
from milp import solve_milp
from numpy import linspace
from matplotlib.pyplot import plot, xlim, ylim, legend, figure, show, xlabel, ylabel
#get_ipython().magic(u'pylab inline')
# ####Define Constants
p = [45*8, 45*8, 80, 80] #Time limit for each student
#p = [i*0.7 for i in p] #Scale factor for time (safety factor) might not be necessary
# Use working day calculator (south-africa.workingdays.org)
# to calculate number of hours available for p[0] which is R Fechter
# from 1 Feb to 6 April
mm_lambda_1 = 1.0 #Minimax constraint minimum degree value
mm_lambda_2 = 2.0 #Minimax constraint minimum no. experiments per student
# Experimental time requirements
exp_time_data = {'Antistat': {'exp_time': 5.0,
'sample_prep_time': 25.0,
'no_exp_p_day': None,
'no_exp_p_run': 1.0},
'Rheometer':{'exp_time': 210.0,
'sample_prep_time': None,
'no_exp_p_day': None,
'no_exp_p_run': 1.0},
'Metrastat':{'exp_time': 180.0,
'sample_prep_time': 25.0,
'no_exp_p_day': None,
'no_exp_p_run': 3.0},
'Ransomat': {'exp_time': 300.0,
'sample_prep_time': 20.0,
'no_exp_p_day': None,
'no_exp_p_run': 8.0},
'Vicat': {'exp_time': 20.0, #Need more info
'sample_prep_time': None,
'no_exp_p_day': None,
'no_exp_p_run': 5.0},
'TMA': {'exp_time': 30,
'sample_prep_time': None,
'no_exp_p_day': None,
'no_exp_p_run': 1.0},
'Tensile': {'exp_time': 15.0, #Need more info
'sample_prep_time': 25.0,
'no_exp_p_day': None,
'no_exp_p_run': 1.0},
'Impact': {'exp_time': 15.0, #Need more info
'sample_prep_time': 25.0,
'no_exp_p_day': None,
'no_exp_p_run': 1.0},
'Cone_Cal': {'exp_time': None,
'sample_prep_time': 25.0,
'no_exp_p_day': 14,
'no_exp_p_run': 1.0},
'Micro_Cone':{'exp_time': None, #Need more info
'sample_prep_time': None, # Ask Monique
'no_exp_p_day': 12,
'no_exp_p_run': 1.0},
'UL94': {'exp_time': 10.0, #Need more info
'sample_prep_time': 10.0,
'no_exp_p_day': None,
'no_exp_p_run': 1.0},
'LOI': {'exp_time': None, #Need more info
'sample_prep_time': None,# Ask Monique
'no_exp_p_day': 12,
'no_exp_p_run': 1.0}}
experiments = ['Antistat',
'Rheometer',
'Metrastat',
'Ransomat',
'Vicat',
'TMA',
'Tensile',
'Impact',
'Cone_Cal',
'Micro_Cone',
'UL94',
'LOI']
experiments.sort() #experiment list must be alphabetical for output to make sense
# ####Sensitivity Analysis
# Varying experiment time requirements
data_types = ['exp_time', 'sample_prep_time', 'no_exp_p_day']
all_obj_val_per_data_type = []
all_adj_val_per_data_type = []
for data_type in data_types[:1]:
new_data_type = 1
if data_type == 'no_exp_p_day':
start = 1
interval = 1
end_1 = 25
else:
start = 0
interval = 5
end_1 = 100
end_2 = 600
all_obj_val_per_exp = []
all_adj_val_per_exp = []
for n, experiment in enumerate(experiments):
if n == 0 and data_type == 'exp_time':
new_data_type = 0
elif new_data_type == 1:
exp_time_data[prev_exp][prev_data_type] = prev_val
else:
exp_time_data[prev_exp][data_type] = prev_val
val = exp_time_data[experiment][data_type]
if val != None:
new_data_type = 0
if val <= 30:
all_adjusted_val = range(start, end_1, interval)#int(val)*2 + 1, interval)
else:
all_adjusted_val = range(start, end_2, 10)#int(val)*2 + 1, 10)
all_obj_val = []
for i in all_adjusted_val:
exp_time_data[experiment][data_type] = i
print '***********************************'
print 'Experiment %s, Data Type %s, Value %s'%(experiment, data_type, i)
[obj_val, status] = solve_milp(p, mm_lambda_1, mm_lambda_2, exp_time_data, experiments)
if status == 1:
all_obj_val.append(obj_val)
else:
all_obj_val.append(0.0)
all_obj_val_per_exp.append(all_obj_val)
all_adj_val_per_exp.append(all_adjusted_val)
prev_exp = experiment
prev_val = val
else:
all_obj_val_per_exp.append(None)
all_adj_val_per_exp.append(None)
all_obj_val_per_data_type.append(all_obj_val_per_exp)
all_adj_val_per_data_type.append(all_adj_val_per_exp)
prev_data_type = data_type
exp_time_data[prev_exp][data_type] = prev_val
print '*******************'
# Plotting sensitivity
colors = ['b', 'g', 'r', 'c', 'm', 'y', 'k']
col_cntr = 0
for n, (obj_val_per_data_type, adj_val_per_data_type) in enumerate(zip(all_obj_val_per_data_type, all_adj_val_per_data_type)):
fig = figure()
fig.suptitle(data_types[n])
for m, (all_obj_val_per_exp, all_adj_val_per_exp) in enumerate(zip(obj_val_per_data_type, adj_val_per_data_type)):
if all_obj_val_per_exp != None:# and m in [2, 9, 10]:
plot(all_adj_val_per_exp, all_obj_val_per_exp, colors[col_cntr], label=experiments[m])
ori_val = exp_time_data[experiments[m]][data_types[n]]
index = all_adj_val_per_exp.index(ori_val)
plot(all_adj_val_per_exp[index], all_obj_val_per_exp[index], 'o' + colors[col_cntr])
if col_cntr != 6:
col_cntr += 1
else:
col_cntr = 0
legend()
if n == 2:
xlabel('No. of Exp. per Day')
legend(loc='lower right')
ylim([26, 37])
else:
xlabel('Time (min)')
ylim([32, 35.5])
xlim([0, 100])
ylabel('Optimum Objective Function')
# Varying the amount of time available per student
# increase = 50 #Amount of increase in hrs
# all_p_adjust_per_stu = []
# all_obj_val_per_stu = []
# for student in range(4):
# p_current = p[student]
# all_p_adjusted = range(0, p_current + increase, 10)
# all_p_adjust_per_stu.append(all_p_adjusted)
# all_obj_val = []
# for n, i in enumerate(all_p_adjusted):
# p[student] = i
# print '***********************************'
# print 'Student %s Time Limit %s'%(student + 1, i)
# [obj_val, status] = solve_milp(p, mm_lambda_1, mm_lambda_2, exp_time_data, experiments)
# if status == 1:
# all_obj_val.append(obj_val)
# else:
# all_obj_val.append(0.0)
# all_obj_val_per_stu.append(all_obj_val)
# p[student] = p_current
# Plot sensitivity
# fig = figure()
# fig.suptitle('Student Time Limit Adjust')
# col_cntr = 0
# for student in range(4):
# plot(all_p_adjust_per_stu[student], all_obj_val_per_stu[student], colors[col_cntr], label='Student %s'%(student + 1))
# index = all_p_adjust_per_stu[student].index(p[student])
# plot(all_p_adjust_per_stu[student][index], all_obj_val_per_stu[student][index], colors[col_cntr] + 'o')
# if col_cntr != 6:
# col_cntr += 1
# else:
# col_cntr = 0
# legend(loc='lower right')
# xlim([0, 400])
# ylim([20, 37])
# xlabel('Time (h)')
# ylabel('Optimum Objective Function')
show()