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lab_mc.py
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lab_mc.py
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#!/usr/bin/env python
from copy import deepcopy
from math import ceil
from collections import Counter
from itertools import zip_longest
from random import randint, choice, random
from math import exp
from lab_defs import Experiment, teaching_length
num_pairs = 40
num_theory = 5
pairs_per_cohort = ceil(num_pairs / 4)
tutorials = {"NA": Experiment(201, "Numerical Analysis", "NA", count=75,
writeup=False, fixed=True),
"LVT": Experiment(298, "LabVIEW Tutorial", "LVT", count=75,
writeup=False, fixed=True)}
experiments = {"CDP": Experiment(204, "Chaotic Double Pendulum", "CDP",
writeup=False, undesirable=True),
"ESR": Experiment(221, "Electron Spin Resonance", "ESR"),
"BG": Experiment(222,
'<font face="AvenirNext">α</font>, '
'<font face="AvenirNext">β</font>, and '
'<font face="AvenirNext">γ</font>-radiation',
"BG"),
"FHz": Experiment(223, "Franck Hertz", "FHz"),
"RS": Experiment(224, "Rutherford Scattering", "RS"),
"HL": Experiment(238, "Hubble's Law", "HL", writeup=False,
undesirable=True),
"BS": Experiment(241, "Balmer Series of the Hydrogen Atom",
"BS"),
"VIS": Experiment(242, "Measurement of Viscosity", "VIS"),
"POL": Experiment(244, "Polarimeter", "POL"),
"MSD": Experiment(246, "Multiple Slit Diffraction", "MSD"),
"EB": Experiment(247, "Edser Butler Method", "EB"),
"BH": Experiment(261, "B/H Curve", "BH"),
"LV": Experiment(299, "LabVIEW: Calibrating a Thermistor", "LV",
count=12, writeup=False, undesirable=True)}
experiment_list = list(experiments.values())
reserve_experiments = {"DoS": Experiment(202, "Density of States", "DoS",
writeup=False, undesirable=True),
"SE": Experiment(248, "Diffraction at a Straight Edge",
"SE", 4, True, True),
"EM": Experiment(204, "e/m", "EM", 2, True, True),
"GYR": Experiment(252, "Gyroscope", "GYR", 4, True,
True),
"MSA": Experiment(271, "More Spectroscopic Analysis",
"MSA", 50, False, True),
"SA": Experiment(270, "Spectroscopic Analysis", "SA",
writeup=False, undesirable=True)}
GP = ([Experiment("", "Group Project – Week {}".format(i+1), "", count=20,
fixed=True) for i in range(4)]
+ [Experiment("", "Group Project – Presentations /100", "", count=40,
fixed=True)])
writeup1 = Experiment("", "Report write-up time", "", count=75, fixed=True)
writeup2 = Experiment(" ", "Report write-up time", "", count=75, fixed=True)
null_experiment = Experiment("", "", "", count=1000)
bad_null = Experiment("", "", "—", count=0)
all_experiments = {**experiments, **reserve_experiments, **tutorials}
def cohort(pair_number):
'''Identify which cohort a pair is in. Must be edited to match this year's
pair count.'''
if 0 <= pair_number <= 9:
return 0
elif 10 <= pair_number <= 19:
return 1
elif 20 <= pair_number <= 29:
return 2
elif 30 <= pair_number <= 39:
return 3
else:
raise ValueError("Pair is not in a cohort")
def null_start():
'''Start with an empty timetable.'''
pairs = [[tutorials["NA"]] + [bad_null] * 10 for _ in range(num_pairs)]
for pair_idx, pair in enumerate(pairs):
if pair_idx not in (list(range(num_theory))):
pair.extend([tutorials["LVT"]] + [bad_null] * 10)
gp_semester = cohort(pair_idx) // 2
semester_cohort = cohort(pair_idx) % 2
base = 1 + teaching_length * gp_semester + semester_cohort * 5
pair[base:base+5] = GP
if semester_cohort == 0:
pair[teaching_length - 1] = writeup1
pair[-1] = writeup2
else:
if gp_semester == 0:
pair[teaching_length // 2] = writeup1
pair[-1] = writeup2
else:
pair[teaching_length - 1] = writeup1
pair[teaching_length + teaching_length // 2] = writeup2
return pairs
def cold_start():
'''Start with a prepopulated timetable based on cycling through a list.
Unfortunately doesn't tend to give a perfect timetable straight off
because of group projects skewing things. If it did then the Monte Carlo
would have been somewhat superfluous'''
canonical_ordering = ["POL", "EB", "MSD", "RS", "BH", "CDP",
"HL", "VIS", "BG", "LV", "BS", "ESR", "FHz"]
assert len(canonical_ordering) == len(set(canonical_ordering))
pairs = null_start()
num_experiments = len(canonical_ordering)
for pair_index, pair in enumerate(pairs):
# The pre-this-code timetable made pairs run in quadruplets to
# simplify scheduling. This initial condition replicates that.
quad_offset = pair_index // 4
pair_experiments = (
canonical_ordering[num_experiments - quad_offset:]
+ canonical_ordering[:num_experiments - quad_offset]
)
if cohort(pair_index) <= 1:
lv_offset = 4
else:
lv_offset = 10
lv_index = pair_experiments.index("LV")
if lv_index < lv_offset:
pair_experiments.pop(lv_index)
if cohort(pair_index) == 0:
lv_index += 9
elif cohort(pair_index) == 1:
lv_index += 4
elif lv_index < 5:
lv_index += 9
else:
lv_index += 4
pair_experiments.insert(lv_index, "LV")
for experiment_index, experiment in enumerate(pair):
if experiment == bad_null:
pair[experiment_index] = experiments[pair_experiments.pop(0)]
tableform(pairs)
return pairs
def badness(pairs):
'''Badness: The distance we are from a timetable that could in principle
operate (with no regard to student complaints). I.e. meets the criteria:
* No pair does any experiment more than once
* No week has more pairs doing an experiment than there is kit available
* All students doing PH-211 have LabView scheduled in TB2.
* No student has LabView scheduled in TB1.
Three separate distances are returned, for the first, second, and
(third+fourth) constraints.'''
duplicate_badness = 0
resource_badness = 0
labview_badness = 0
experiments_by_week = list(zip_longest(*pairs, fillvalue=null_experiment))
for pair_index, pair in enumerate(pairs):
duplicate_badness += 5 * (1 - len(set(pair)) / len(pair))
if len(pair) > teaching_length and experiments["LV"] not in pair:
labview_badness += 1
elif (experiments["LV"] in pair
and pair.index(experiments["LV"]) < teaching_length):
labview_badness += 3
# Previously there was an option to have two slightly different
# versions of the Polarimeter experiment. Yes, this was hard-coded. Sorry.
# if experiments["POL"] in pair and experiments["POL*"] in pair:
# duplicate_badness += 1
for week in experiments_by_week:
counter = Counter(week)
for required_count, experiment in zip(counter.values(),
counter.keys()):
if required_count > experiment.count:
resource_badness += 1
return duplicate_badness, resource_badness, labview_badness
def unpleasantness(pairs):
'''Unpleasantness: The degree to which a timetable will inflict pain on
students. The main pain point is not having enough experiments to write up
in the semester with group projects. Only 4 experiment slots are available,
and in PH-211 one of those is LabView which can't be written up. As such
we try to make the scheduler avoid putting CDP or HL in the same block.
There is also an IOP constraint that every student must do Edser Butler.
This was added at the last minute so has been hacked into this function.
In principle it should be added to badness, but that would require
defining a new class of badness and a targeted update for it.
Would benefit from refactoring.'''
undesirable_count = sum(1
for pair in pairs
for experiment in pair
if experiment.undesirable)
very_undesirable_count = 0
for pair_index, pair in enumerate(pairs):
local_count = max(sum(1 for experiment in pair[1:11]
if experiment.undesirable
or not experiment.writeup
or "Group Project" in experiment.title
or experiment.title == "LabVIEW") - 5,
0)
if local_count > 0:
very_undesirable_count += local_count ** 3
if len(pair) > 11:
local_count = max(sum(1 for experiment in pair[12:]
if experiment.undesirable
or not experiment.writeup
or "Group Project" in experiment.title
or experiment.title == "LabVIEW") - 5,
0)
if local_count > 0:
very_undesirable_count += local_count ** 3
# IOP constraint
if experiments["EB"] not in pair:
very_undesirable_count += 1000
return undesirable_count + very_undesirable_count
def unpleasant_badness(pairs):
# Add a weighting to the unpleasantness relative to badness for the update
return sum(badness(pairs)) + 0.2 * unpleasantness(pairs)
def randomupdate(pairs, beta):
'''Try placing a random experiment into a random slot, with constraints.
Do a Metropolis-style accept/reject test.'''
while True:
pair = randint(0, num_pairs - 1)
week = randint(0, 2 * teaching_length)
if week >= len(pairs[pair]):
continue
if pairs[pair][week].fixed:
continue
old_expt = pairs[pair][week]
old_badness = unpleasant_badness(pairs)
pairs[pair][week] = choice(experiment_list)
new_badness = unpleasant_badness(pairs)
if new_badness < old_badness:
return 1, new_badness
elif random() < exp(beta * (old_badness - new_badness)):
return 1, new_badness
else:
pairs[pair][week] = old_expt
return 0, old_badness
def pleasantupdate(pairs, beta):
'''Target unpleasant experiments, replace them with pleasant ones.
This would be better if it tried swapping them for pleasant ones in the
opposing semester.'''
unpleasant_experiments = [(pair_index, experiment_index)
for pair_index, pair in enumerate(pairs)
for experiment_index, experiment
in enumerate(pair)
if experiment.undesirable]
if unpleasant_experiments == []:
tableform(pairs)
raise ValueError("No unpleasant experiments??")
pair, week = choice(unpleasant_experiments)
old_expt = pairs[pair][week]
old_badness = unpleasant_badness(pairs)
pairs[pair][week] = choice(experiment_list)
new_badness = unpleasant_badness(pairs)
if new_badness < old_badness:
return 1, new_badness
elif random() < exp(beta * (old_badness - new_badness)):
return 1, new_badness
else:
pairs[pair][week] = old_expt
return 0, old_badness
def target_duplicates(pairs, beta):
'''Try to fix pairs doing the same experiment twice.'''
for pair_index, pair in enumerate(pairs):
if len(set(pair)) < len(pair):
old_badness = unpleasant_badness(pairs)
counter = Counter(pair)
experiment_to_replace, n = counter.most_common(1)[0]
index_to_replace = randint(0, n)
indices = [i for i, j in enumerate(pair)
if j == experiment_to_replace]
index_to_replace = choice(indices)
pair[index_to_replace] = choice(experiment_list)
new_badness = unpleasant_badness(pairs)
if new_badness <= old_badness:
return 1, new_badness
elif random() < exp(beta * (old_badness - new_badness)):
return 1, new_badness
else:
pair[index_to_replace] = experiment_to_replace
return 0, old_badness
# With two different polarimeter scripts/types, it would have been
# necessary to handle this by hand.
# if experiments["POL"] in pair and experiments["POL*"] in pair:
# old_badness = unpleasant_badness(pairs)
# indices = [i for i, j in enumerate(pair)
# if j in polarimeters]
# index_to_replace = choice(indices)
# experiment_to_replace = pair[index_to_replace]
# pair[index_to_replace] = choice(experiment_list)
# new_badness = unpleasant_badness(pairs)
#
# if new_badness <= old_badness:
# return 1, new_badness
# elif random() < exp(beta * (old_badness - new_badness)):
# return 1, new_badness
# else:
# pair[index_to_replace] = experiment_to_replace
# return 0, old_badness
raise ValueError("targeting duplicates but look OK")
def target_resources(pairs, beta):
'''Try and fix not having enough copies of an experiment to run in a
given week.'''
experiments_by_week = list(zip_longest(*pairs, fillvalue=null_experiment))
for week_index, week in enumerate(experiments_by_week):
counter = Counter(week)
for required_count, experiment in zip(counter.values(), counter.keys()):
if required_count > experiment.count:
old_badness = unpleasant_badness(pairs)
indices = [i for i, j in enumerate(week)
if j == experiment]
index_to_replace = choice(indices)
pairs[index_to_replace][week_index] = choice(experiment_list)
new_badness = unpleasant_badness(pairs)
if new_badness <= old_badness:
return 1, new_badness
elif random() < exp(beta * (old_badness - new_badness)):
return 1, new_badness
else:
pairs[index_to_replace][week_index] = experiment
return 0, old_badness
raise ValueError("targeting resources but look OK")
def target_labview(pairs, beta):
'''Try and fix problems with LabView'''
dbg_indices = []
for pair_index, pair in enumerate(pairs):
if pair_index >= num_theory and experiments["LV"] not in pair:
old_badness = unpleasant_badness(pairs)
while True:
index_to_replace = randint(teaching_length + 1,
teaching_length * 2 - 1)
old_expt = pair[index_to_replace]
if not old_expt.fixed:
break
pair[index_to_replace] = experiments["LV"]
new_badness = unpleasant_badness(pairs)
if new_badness <= old_badness:
return 1, new_badness
elif random() < exp(beta * (old_badness - new_badness)):
return 1, new_badness
else:
pair[index_to_replace] = old_expt
return 0, old_badness
indices = [i for i, j in enumerate(pair)
if j == experiments["LV"]]
if len(indices) == 0:
continue
if len(indices) > 1 or indices[0] < teaching_length:
old_badness = unpleasant_badness(pairs)
index_to_replace = choice(indices)
pair[index_to_replace] = choice(experiment_list)
new_badness = unpleasant_badness(pairs)
if new_badness <= old_badness:
return 1, new_badness
elif random() < exp(beta * (old_badness - new_badness)):
return 1, new_badness
else:
pair[index_to_replace] = experiments["LV"]
return 0, old_badness
dbg_indices.append(indices)
tableform(pairs)
print(dbg_indices)
raise ValueError("targeting labview but looks OK")
# def shuffle_polarimeter(pairs):
# experiments_by_week = list(zip_longest(*pairs,
# fillvalue=null_experiment))
#
# for week_index, week in enumerate(experiments_by_week):
# counter = Counter(week)
# num_to_replace = (experiments["POL*"].count -
# counter[experiments["POL*"]])
# if num_to_replace > 0 and counter[experiments["POL"]] > 0:
# pair_indices = [i for i, j in enumerate(week)
# if j == experiments["POL"]]
# shuffle(pair_indices)
# for _ in range(num_to_replace):
# pairs[pair_indices.pop()][week_index] = experiments["POL*"]
def targetedupdate(pairs, beta):
'''Work out where the badness problem is, and run the appropriate
targeted update.'''
duplicate_badness, resource_badness, labview_badness = badness(pairs)
if duplicate_badness > 0:
return target_duplicates(pairs, beta)
elif resource_badness > 0:
return target_resources(pairs, beta)
elif labview_badness > 0:
try:
return target_labview(pairs, beta)
except ValueError as ex:
print(duplicate_badness, resource_badness, labview_badness)
raise ex
else:
raise ValueError("Nothing to do!")
def tableform(pairs):
'''Format a list of pairs (in turn a list of experiments) into a neat
table that just fits in a wide terminal window.'''
for pair_index, pair in enumerate(pairs):
print("{}\t{}".format(pair_index + 1,
"\t".join([ex.acronym for ex in pair])))
def schedule(start):
'''Try to organise a schedule for a given starting condition.
Uses a simulated annealing-style process to allow large changes
initially so as not to get stuck in a metastability but gradually try
to head towards a minimum.'''
pairs = start()
current_badness = sum(badness(pairs))
iterations = 0
beta = 1
accept = 0
update = targetedupdate
try:
while True:
iterations += 1
if iterations % 1000 == 0:
if iterations % 10000 == 0:
print('Slow going, may have insufficient resources, or '
'just an unlucky starting choice.\n'
'Current badness: {:.04}, acceptance {}%.\n'
'Ctrl+C stops and outputs current progress.'.format(
current_badness, accept / 10
))
# if accept < 750:
# update = targetedupdate
# else:
# update = randomupdate
accept = 0
beta *= 1.05
step_accept, current_badness = update(pairs, beta)
current_badness = sum(badness(pairs))
accept += step_accept
if current_badness == 0:
break
except KeyboardInterrupt:
print("Interrupted, returning current state")
# tableform(pairs)
return pairs, False
iterations = 0
acc = 0
terminating = False
min_unpleasantness = unpleasantness(pairs)
minimally_unpleasant_state = deepcopy(pairs)
while ((iterations < 1000000 and
unpleasantness(pairs) > 0 and
not terminating)
or sum(badness(pairs)) > 0):
try:
if iterations % 1000 == 0:
print(
"Unpleasantness: {}\tCurrent acceptance: {}\t"
"Lowest unpleasantness seen: {}\tCurrent beta: {}".format(
unpleasantness(pairs), acc/1000,
min_unpleasantness, beta
)
)
acc = 0
iterations += 1
beta *= 1.0001
if sum(badness(pairs)) > 0:
acc += targetedupdate(pairs, beta)[0]
else:
acc += pleasantupdate(pairs, beta)[0]
current_unpleasantness = unpleasantness(pairs)
if (current_unpleasantness < min_unpleasantness
and sum(badness(pairs)) == 0):
min_unpleasantness = current_unpleasantness
minimally_unpleasant_state = deepcopy(pairs)
except KeyboardInterrupt as ki:
if terminating:
tableform(pairs)
raise ki
else:
terminating = True
print("OK, will get badness to zero and give a result")
# shuffle_polarimeter(pairs)
print(badness(pairs))
print(unpleasantness(pairs))
return minimally_unpleasant_state, True
if __name__ == "__main__":
# Just a way to test by eye that the initial condition generator works
pairs = schedule(null_start)
tableform(pairs)