def run_opt_sim(args, inputfile, usernamespace):
"""Run a simulation using Taguchi's optmisation process.
Args:
args (dict): Namespace with command line arguments
inputfile (object): File object for the input file.
usernamespace (dict): Namespace that can be accessed by user
in any Python code blocks in input file.
"""
tsimstart = perf_counter()
if args.n > 1:
raise CmdInputError(
'When a Taguchi optimisation is being carried out the number of model runs argument is not required'
)
inputfileparts = os.path.splitext(inputfile.name)
# Default maximum number of iterations of optimisation to perform (used
# if the stopping criterion is not achieved)
maxiterations = 20
# Process Taguchi code blocks in the input file; pass in ordered
# dictionary to hold parameters to optimise
tmp = usernamespace.copy()
tmp.update({'optparams': OrderedDict()})
taguchinamespace = taguchi_code_blocks(inputfile, tmp)
# Extract dictionaries and variables containing initialisation parameters
optparams = taguchinamespace['optparams']
fitness = taguchinamespace['fitness']
if 'maxiterations' in taguchinamespace:
maxiterations = taguchinamespace['maxiterations']
# Store initial parameter ranges
optparamsinit = list(optparams.items())
# Dictionary to hold history of optmised values of parameters
optparamshist = OrderedDict((key, list()) for key in optparams)
# Import specified fitness function
fitness_metric = getattr(
import_module('user_libs.optimisation_taguchi.fitness_functions'),
fitness['name'])
# Select OA
OA, N, cols, k, s, t = construct_OA(optparams)
taguchistr = '\n--- Taguchi optimisation'
print('{} {}\n'.format(taguchistr,
'-' * (get_terminal_width() - 1 - len(taguchistr))))
print(
'Orthogonal array: {:g} experiments per iteration, {:g} parameters ({:g} will be used), {:g} levels, and strength {:g}'
.format(N, cols, k, s, t))
tmp = [(k, v) for k, v in optparams.items()]
print('Parameters to optimise with ranges: {}'.format(
str(tmp).strip('[]')))
print('Output name(s) from model: {}'.format(fitness['args']['outputs']))
print('Fitness function "{}" with stopping criterion {:g}'.format(
fitness['name'], fitness['stop']))
print('Maximum iterations: {:g}'.format(maxiterations))
# Initialise arrays and lists to store parameters required throughout optimisation
# Lower, central, and upper values for each parameter
levels = np.zeros((s, k), dtype=floattype)
# Optimal lower, central, or upper value for each parameter
levelsopt = np.zeros(k, dtype=np.uint8)
# Difference used to set values for levels
levelsdiff = np.zeros(k, dtype=floattype)
# History of fitness values from each confirmation experiment
fitnessvalueshist = []
iteration = 0
while iteration < maxiterations:
# Reset number of model runs to number of experiments
args.n = N
usernamespace['number_model_runs'] = N
# Fitness values for each experiment
fitnessvalues = []
# Set parameter ranges and define experiments
optparams, levels, levelsdiff = calculate_ranges_experiments(
optparams, optparamsinit, levels, levelsopt, levelsdiff, OA, N, k,
s, iteration)
# Run model for each experiment
# Mixed mode MPI with OpenMP or CUDA - MPI task farm for models with
# each model parallelised with OpenMP (CPU) or CUDA (GPU)
if args.mpi:
run_mpi_sim(args, inputfile, usernamespace, optparams)
# Standard behaviour - models run serially with each model parallelised
# with OpenMP (CPU) or CUDA (GPU)
else:
run_std_sim(args, inputfile, usernamespace, optparams)
# Calculate fitness value for each experiment
for experiment in range(1, N + 1):
outputfile = inputfileparts[0] + str(experiment) + '.out'
fitnessvalues.append(fitness_metric(outputfile, fitness['args']))
os.remove(outputfile)
taguchistr = '\n--- Taguchi optimisation, iteration {}: {} initial experiments with fitness values {}.'.format(
iteration + 1, N, fitnessvalues)
print('{} {}\n'.format(
taguchistr, '-' * (get_terminal_width() - 1 - len(taguchistr))))
# Calculate optimal levels from fitness values by building a response
# table; update dictionary of parameters with optimal values
optparams, levelsopt = calculate_optimal_levels(
optparams, levels, levelsopt, fitnessvalues, OA, N, k)
# Update dictionary with history of parameters with optimal values
for key, value in optparams.items():
optparamshist[key].append(value[0])
# Run a confirmation experiment with optimal values
args.n = 1
usernamespace['number_model_runs'] = 1
# Mixed mode MPI with OpenMP or CUDA - MPI task farm for models with
# each model parallelised with OpenMP (CPU) or CUDA (GPU)
if args.mpi:
run_mpi_sim(args, inputfile, usernamespace, optparams)
# Standard behaviour - models run serially with each model parallelised
# with OpenMP (CPU) or CUDA (GPU)
else:
run_std_sim(args, inputfile, usernamespace, optparams)
# Calculate fitness value for confirmation experiment
outputfile = inputfileparts[0] + '.out'
fitnessvalueshist.append(fitness_metric(outputfile, fitness['args']))
# Rename confirmation experiment output file so that it is retained for each iteraction
os.rename(
outputfile,
os.path.splitext(outputfile)[0] + '_final' + str(iteration + 1) +
'.out')
taguchistr = '\n--- Taguchi optimisation, iteration {} completed. History of optimal parameter values {} and of fitness values {}'.format(
iteration + 1, dict(optparamshist), fitnessvalueshist)
print('{} {}\n'.format(
taguchistr, '-' * (get_terminal_width() - 1 - len(taguchistr))))
iteration += 1
# Stop optimisation if stopping criterion has been reached
if fitnessvalueshist[iteration - 1] > fitness['stop']:
taguchistr = '\n--- Taguchi optimisation stopped as fitness criteria reached: {:g} > {:g}'.format(
fitnessvalueshist[iteration - 1], fitness['stop'])
print('{} {}\n'.format(
taguchistr,
'-' * (get_terminal_width() - 1 - len(taguchistr))))
break
# Stop optimisation if successive fitness values are within a percentage threshold
fitnessvaluesthres = 0.1
if iteration > 2:
fitnessvaluesclose = (np.abs(fitnessvalueshist[iteration - 2] -
fitnessvalueshist[iteration - 1]) /
fitnessvalueshist[iteration - 1]) * 100
if fitnessvaluesclose < fitnessvaluesthres:
taguchistr = '\n--- Taguchi optimisation stopped as successive fitness values within {}%'.format(
fitnessvaluesthres)
print('{} {}\n'.format(
taguchistr,
'-' * (get_terminal_width() - 1 - len(taguchistr))))
break
tsimend = perf_counter()
# Save optimisation parameters history and fitness values history to file
opthistfile = inputfileparts[0] + '_hist.pickle'
with open(opthistfile, 'wb') as f:
pickle.dump(optparamshist, f)
pickle.dump(fitnessvalueshist, f)
pickle.dump(optparamsinit, f)
taguchistr = '\n=== Taguchi optimisation completed in [HH:MM:SS]: {} after {} iteration(s)'.format(
datetime.timedelta(seconds=int(tsimend - tsimstart)), iteration)
print('{} {}\n'.format(taguchistr,
'=' * (get_terminal_width() - 1 - len(taguchistr))))
print('History of optimal parameter values {} and of fitness values {}\n'.
format(dict(optparamshist), fitnessvalueshist))
def run_opt_sim(args, numbermodelruns, inputfile, usernamespace):
"""Run a simulation using Taguchi's optmisation process.
Args:
args (dict): Namespace with command line arguments
numbermodelruns (int): Total number of model runs.
inputfile (str): Name of the input file to open.
usernamespace (dict): Namespace that can be accessed by user in any Python code blocks in input file.
"""
if numbermodelruns > 1:
raise CmdInputError('When a Taguchi optimisation is being carried out the number of model runs argument is not required')
inputfileparts = os.path.splitext(inputfile)
# Default maximum number of iterations of optimisation to perform (used if the stopping criterion is not achieved)
maxiterations = 20
# Process Taguchi code blocks in the input file; pass in ordered dictionary to hold parameters to optimise
tmp = usernamespace.copy()
tmp.update({'optparams': OrderedDict()})
taguchinamespace = taguchi_code_blocks(inputfile, tmp)
# Extract dictionaries and variables containing initialisation parameters
optparams = taguchinamespace['optparams']
fitness = taguchinamespace['fitness']
if 'maxiterations' in taguchinamespace:
maxiterations = taguchinamespace['maxiterations']
# Store initial parameter ranges
optparamsinit = list(optparams.items())
# Dictionary to hold history of optmised values of parameters
optparamshist = OrderedDict((key, list()) for key in optparams)
# Import specified fitness function
fitness_metric = getattr(importlib.import_module('user_libs.optimisation_taguchi_fitness'), fitness['name'])
# Select OA
OA, N, cols, k, s, t = construct_OA(optparams)
print('\n{}\n\nTaguchi optimisation: orthogonal array with {} experiments, {} parameters ({} used), {} levels, and strength {} will be used.'.format(68*'*', N, cols, k, s, t))
# Initialise arrays and lists to store parameters required throughout optimisation
# Lower, central, and upper values for each parameter
levels = np.zeros((s, k), dtype=floattype)
# Optimal lower, central, or upper value for each parameter
levelsopt = np.zeros(k, dtype=floattype)
# Difference used to set values for levels
levelsdiff = np.zeros(k, dtype=floattype)
# History of fitness values from each confirmation experiment
fitnessvalueshist = []
iteration = 0
while iteration < maxiterations:
# Reset number of model runs to number of experiments
numbermodelruns = N
usernamespace['number_model_runs'] = numbermodelruns
# Fitness values for each experiment
fitnessvalues = []
# Set parameter ranges and define experiments
optparams, levels, levelsdiff = calculate_ranges_experiments(optparams, optparamsinit, levels, levelsopt, levelsdiff, OA, N, k, s, iteration)
# Run model for each experiment
if args.mpi: # Mixed mode MPI/OpenMP - MPI task farm for models with each model parallelised with OpenMP
run_mpi_sim(args, numbermodelruns, inputfile, usernamespace, optparams)
else: # Standard behaviour - models run serially with each model parallelised with OpenMP
run_std_sim(args, numbermodelruns, inputfile, usernamespace, optparams)
# Calculate fitness value for each experiment
for experiment in range(1, numbermodelruns + 1):
outputfile = inputfileparts[0] + str(experiment) + '.out'
fitnessvalues.append(fitness_metric(outputfile, fitness['args']))
os.remove(outputfile)
print('\nTaguchi optimisation, iteration {}: {} initial experiments with fitness values {}.'.format(iteration + 1, numbermodelruns, fitnessvalues))
# Calculate optimal levels from fitness values by building a response table; update dictionary of parameters with optimal values
optparams, levelsopt = calculate_optimal_levels(optparams, levels, levelsopt, fitnessvalues, OA, N, k)
# Run a confirmation experiment with optimal values
numbermodelruns = 1
usernamespace['number_model_runs'] = numbermodelruns
run_std_sim(args, numbermodelruns, inputfile, usernamespace, optparams)
# Calculate fitness value for confirmation experiment
outputfile = inputfileparts[0] + '.out'
fitnessvalueshist.append(fitness_metric(outputfile, fitness['args']))
# Rename confirmation experiment output file so that it is retained for each iteraction
os.rename(outputfile, os.path.splitext(outputfile)[0] + '_final' + str(iteration + 1) + '.out')
print('\nTaguchi optimisation, iteration {} completed. History of optimal parameter values {} and of fitness values {}'.format(iteration + 1, dict(optparamshist), fitnessvalueshist, 68*'*'))
iteration += 1
# Stop optimisation if stopping criterion has been reached
if fitnessvalueshist[iteration - 1] > fitness['stop']:
print('\nTaguchi optimisation stopped as fitness criteria reached')
break
# Stop optimisation if successive fitness values are within a percentage threshold
if iteration > 2:
fitnessvaluesclose = (np.abs(fitnessvalueshist[iteration - 2] - fitnessvalueshist[iteration - 1]) / fitnessvalueshist[iteration - 1]) * 100
fitnessvaluesthres = 0.1
if fitnessvaluesclose < fitnessvaluesthres:
print('\nTaguchi optimisation stopped as successive fitness values within {}%'.format(fitnessvaluesthres))
break
# Save optimisation parameters history and fitness values history to file
opthistfile = inputfileparts[0] + '_hist'
np.savez(opthistfile, dict(optparamshist), fitnessvalueshist)
print('\n{}\nTaguchi optimisation completed after {} iteration(s).\nHistory of optimal parameter values {} and of fitness values {}\n{}\n'.format(68*'*', iteration, dict(optparamshist), fitnessvalueshist, 68*'*'))
# Plot the history of fitness values and each optimised parameter values for the optimisation
plot_optimisation_history(fitnessvalueshist, optparamshist, optparamsinit)
def run_opt_sim(args, numbermodelruns, inputfile, usernamespace):
"""Run a simulation using Taguchi's optmisation process.
Args:
args (dict): Namespace with command line arguments
numbermodelruns (int): Total number of model runs.
inputfile (str): Name of the input file to open.
usernamespace (dict): Namespace that can be accessed by user in any Python code blocks in input file.
"""
tsimstart = perf_counter()
if numbermodelruns > 1:
raise CmdInputError('When a Taguchi optimisation is being carried out the number of model runs argument is not required')
inputfileparts = os.path.splitext(inputfile)
# Default maximum number of iterations of optimisation to perform (used if the stopping criterion is not achieved)
maxiterations = 20
# Process Taguchi code blocks in the input file; pass in ordered dictionary to hold parameters to optimise
tmp = usernamespace.copy()
tmp.update({'optparams': OrderedDict()})
taguchinamespace = taguchi_code_blocks(inputfile, tmp)
# Extract dictionaries and variables containing initialisation parameters
optparams = taguchinamespace['optparams']
fitness = taguchinamespace['fitness']
if 'maxiterations' in taguchinamespace:
maxiterations = taguchinamespace['maxiterations']
# Store initial parameter ranges
optparamsinit = list(optparams.items())
# Dictionary to hold history of optmised values of parameters
optparamshist = OrderedDict((key, list()) for key in optparams)
# Import specified fitness function
fitness_metric = getattr(import_module('user_libs.optimisation_taguchi.fitness_functions'), fitness['name'])
# Select OA
OA, N, cols, k, s, t = construct_OA(optparams)
taguchistr = '\n--- Taguchi optimisation'
print('{} {}\n'.format(taguchistr, '-' * (get_terminal_width() - 1 - len(taguchistr))))
print('Orthogonal array: {:g} experiments per iteration, {:g} parameters ({:g} will be used), {:g} levels, and strength {:g}'.format(N, cols, k, s, t))
tmp = [(k, v) for k, v in optparams.items()]
print('Parameters to optimise with ranges: {}'.format(str(tmp).strip('[]')))
print('Output name(s) from model: {}'.format(fitness['args']['outputs']))
print('Fitness function "{}" with stopping criterion {:g}'.format(fitness['name'], fitness['stop']))
print('Maximum iterations: {:g}'.format(maxiterations))
# Initialise arrays and lists to store parameters required throughout optimisation
# Lower, central, and upper values for each parameter
levels = np.zeros((s, k), dtype=floattype)
# Optimal lower, central, or upper value for each parameter
levelsopt = np.zeros(k, dtype=np.uint8)
# Difference used to set values for levels
levelsdiff = np.zeros(k, dtype=floattype)
# History of fitness values from each confirmation experiment
fitnessvalueshist = []
iteration = 0
while iteration < maxiterations:
# Reset number of model runs to number of experiments
numbermodelruns = N
usernamespace['number_model_runs'] = numbermodelruns
# Fitness values for each experiment
fitnessvalues = []
# Set parameter ranges and define experiments
optparams, levels, levelsdiff = calculate_ranges_experiments(optparams, optparamsinit, levels, levelsopt, levelsdiff, OA, N, k, s, iteration)
# Run model for each experiment
if args.mpi: # Mixed mode MPI/OpenMP - MPI task farm for models with each model parallelised with OpenMP
run_mpi_sim(args, numbermodelruns, inputfile, usernamespace, optparams)
else: # Standard behaviour - models run serially with each model parallelised with OpenMP
run_std_sim(args, numbermodelruns, inputfile, usernamespace, optparams)
# Calculate fitness value for each experiment
for experiment in range(1, numbermodelruns + 1):
outputfile = inputfileparts[0] + str(experiment) + '.out'
fitnessvalues.append(fitness_metric(outputfile, fitness['args']))
os.remove(outputfile)
taguchistr = '\n--- Taguchi optimisation, iteration {}: {} initial experiments with fitness values {}.'.format(iteration + 1, numbermodelruns, fitnessvalues)
print('{} {}\n'.format(taguchistr, '-' * (get_terminal_width() - 1 - len(taguchistr))))
# Calculate optimal levels from fitness values by building a response table; update dictionary of parameters with optimal values
optparams, levelsopt = calculate_optimal_levels(optparams, levels, levelsopt, fitnessvalues, OA, N, k)
# Update dictionary with history of parameters with optimal values
for key, value in optparams.items():
optparamshist[key].append(value[0])
# Run a confirmation experiment with optimal values
numbermodelruns = 1
usernamespace['number_model_runs'] = numbermodelruns
run_std_sim(args, numbermodelruns, inputfile, usernamespace, optparams)
# Calculate fitness value for confirmation experiment
outputfile = inputfileparts[0] + '.out'
fitnessvalueshist.append(fitness_metric(outputfile, fitness['args']))
# Rename confirmation experiment output file so that it is retained for each iteraction
os.rename(outputfile, os.path.splitext(outputfile)[0] + '_final' + str(iteration + 1) + '.out')
taguchistr = '\n--- Taguchi optimisation, iteration {} completed. History of optimal parameter values {} and of fitness values {}'.format(iteration + 1, dict(optparamshist), fitnessvalueshist)
print('{} {}\n'.format(taguchistr, '-' * (get_terminal_width() - 1 - len(taguchistr))))
iteration += 1
# Stop optimisation if stopping criterion has been reached
if fitnessvalueshist[iteration - 1] > fitness['stop']:
taguchistr = '\n--- Taguchi optimisation stopped as fitness criteria reached: {:g} > {:g}'.format(fitnessvalueshist[iteration - 1], fitness['stop'])
print('{} {}\n'.format(taguchistr, '-' * (get_terminal_width() - 1 - len(taguchistr))))
break
# Stop optimisation if successive fitness values are within a percentage threshold
if iteration > 2:
fitnessvaluesclose = (np.abs(fitnessvalueshist[iteration - 2] - fitnessvalueshist[iteration - 1]) / fitnessvalueshist[iteration - 1]) * 100
fitnessvaluesthres = 0.1
if fitnessvaluesclose < fitnessvaluesthres:
taguchistr = '\n--- Taguchi optimisation stopped as successive fitness values within {}%'.format(fitnessvaluesthres)
print('{} {}\n'.format(taguchistr, '-' * (get_terminal_width() - 1 - len(taguchistr))))
break
tsimend = perf_counter()
# Save optimisation parameters history and fitness values history to file
opthistfile = inputfileparts[0] + '_hist.pickle'
with open(opthistfile, 'wb') as f:
pickle.dump(optparamshist, f)
pickle.dump(fitnessvalueshist, f)
pickle.dump(optparamsinit, f)
taguchistr = '\n=== Taguchi optimisation completed in [HH:MM:SS]: {} after {} iteration(s)'.format(datetime.timedelta(seconds=int(tsimend - tsimstart)), iteration)
print('{} {}\n'.format(taguchistr, '=' * (get_terminal_width() - 1 - len(taguchistr))))
print('History of optimal parameter values {} and of fitness values {}\n'.format(dict(optparamshist), fitnessvalueshist))
def run_opt_sim(args, numbermodelruns, inputfile, usernamespace):
"""Run a simulation using Taguchi's optmisation process.
Args:
args (dict): Namespace with command line arguments
numbermodelruns (int): Total number of model runs.
inputfile (str): Name of the input file to open.
usernamespace (dict): Namespace that can be accessed by user in any Python code blocks in input file.
"""
if numbermodelruns > 1:
raise CmdInputError(
'When a Taguchi optimisation is being carried out the number of model runs argument is not required'
)
inputfileparts = os.path.splitext(inputfile)
# Default maximum number of iterations of optimisation to perform (used if the stopping criterion is not achieved)
maxiterations = 20
# Process Taguchi code blocks in the input file; pass in ordered dictionary to hold parameters to optimise
tmp = usernamespace.copy()
tmp.update({'optparams': OrderedDict()})
taguchinamespace = taguchi_code_blocks(inputfile, tmp)
# Extract dictionaries and variables containing initialisation parameters
optparams = taguchinamespace['optparams']
fitness = taguchinamespace['fitness']
if 'maxiterations' in taguchinamespace:
maxiterations = taguchinamespace['maxiterations']
# Store initial parameter ranges
optparamsinit = list(optparams.items())
# Dictionary to hold history of optmised values of parameters
optparamshist = OrderedDict((key, list()) for key in optparams)
# Import specified fitness function
fitness_metric = getattr(
importlib.import_module('user_libs.optimisation_taguchi_fitness'),
fitness['name'])
# Select OA
OA, N, cols, k, s, t = construct_OA(optparams)
print(
'\n{}\n\nTaguchi optimisation: orthogonal array with {} experiments, {} parameters ({} used), {} levels, and strength {} will be used.'
.format(68 * '*', N, cols, k, s, t))
# Initialise arrays and lists to store parameters required throughout optimisation
# Lower, central, and upper values for each parameter
levels = np.zeros((s, k), dtype=floattype)
# Optimal lower, central, or upper value for each parameter
levelsopt = np.zeros(k, dtype=floattype)
# Difference used to set values for levels
levelsdiff = np.zeros(k, dtype=floattype)
# History of fitness values from each confirmation experiment
fitnessvalueshist = []
iteration = 0
while iteration < maxiterations:
# Reset number of model runs to number of experiments
numbermodelruns = N
usernamespace['number_model_runs'] = numbermodelruns
# Fitness values for each experiment
fitnessvalues = []
# Set parameter ranges and define experiments
optparams, levels, levelsdiff = calculate_ranges_experiments(
optparams, optparamsinit, levels, levelsopt, levelsdiff, OA, N, k,
s, iteration)
# Run model for each experiment
if args.mpi: # Mixed mode MPI/OpenMP - MPI task farm for models with each model parallelised with OpenMP
run_mpi_sim(args, numbermodelruns, inputfile, usernamespace,
optparams)
else: # Standard behaviour - models run serially with each model parallelised with OpenMP
run_std_sim(args, numbermodelruns, inputfile, usernamespace,
optparams)
# Calculate fitness value for each experiment
for experiment in range(1, numbermodelruns + 1):
outputfile = inputfileparts[0] + str(experiment) + '.out'
fitnessvalues.append(fitness_metric(outputfile, fitness['args']))
os.remove(outputfile)
print(
'\nTaguchi optimisation, iteration {}: {} initial experiments with fitness values {}.'
.format(iteration + 1, numbermodelruns, fitnessvalues))
# Calculate optimal levels from fitness values by building a response table; update dictionary of parameters with optimal values
optparams, levelsopt = calculate_optimal_levels(
optparams, levels, levelsopt, fitnessvalues, OA, N, k)
# Run a confirmation experiment with optimal values
numbermodelruns = 1
usernamespace['number_model_runs'] = numbermodelruns
run_std_sim(args, numbermodelruns, inputfile, usernamespace, optparams)
# Calculate fitness value for confirmation experiment
outputfile = inputfileparts[0] + '.out'
fitnessvalueshist.append(fitness_metric(outputfile, fitness['args']))
# Rename confirmation experiment output file so that it is retained for each iteraction
os.rename(
outputfile,
os.path.splitext(outputfile)[0] + '_final' + str(iteration + 1) +
'.out')
print(
'\nTaguchi optimisation, iteration {} completed. History of optimal parameter values {} and of fitness values {}'
.format(iteration + 1, dict(optparamshist), fitnessvalueshist,
68 * '*'))
iteration += 1
# Stop optimisation if stopping criterion has been reached
if fitnessvalueshist[iteration - 1] > fitness['stop']:
print('\nTaguchi optimisation stopped as fitness criteria reached')
break
# Stop optimisation if successive fitness values are within a percentage threshold
if iteration > 2:
fitnessvaluesclose = (np.abs(fitnessvalueshist[iteration - 2] -
fitnessvalueshist[iteration - 1]) /
fitnessvalueshist[iteration - 1]) * 100
fitnessvaluesthres = 0.1
if fitnessvaluesclose < fitnessvaluesthres:
print(
'\nTaguchi optimisation stopped as successive fitness values within {}%'
.format(fitnessvaluesthres))
break
# Save optimisation parameters history and fitness values history to file
opthistfile = inputfileparts[0] + '_hist'
np.savez(opthistfile, dict(optparamshist), fitnessvalueshist)
print(
'\n{}\nTaguchi optimisation completed after {} iteration(s).\nHistory of optimal parameter values {} and of fitness values {}\n{}\n'
.format(68 * '*', iteration, dict(optparamshist), fitnessvalueshist,
68 * '*'))
# Plot the history of fitness values and each optimised parameter values for the optimisation
plot_optimisation_history(fitnessvalueshist, optparamshist, optparamsinit)