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master > master: code py - verbesserte Darstellung + »korrekte« Behandlung von Reihenfolgen

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- im Kurs wird die Permutation nur für Greedy-Berechnungen angewandt
- die Reihenfolge der Items in der Hauptberechnung bei B&B bleibt wie bei Angaben
This commit is contained in:
RD
2022-06-14 14:40:02 +02:00
parent e3c3bbec37
commit 3b8f80cff9
12 changed files with 169 additions and 147 deletions
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122
code/python/src/algorithms/rucksack/algorithms.py
View File

@@ -28,8 +28,8 @@ __all__ = [
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
def rucksack_greedy_algorithm(
capacity: float,
weights: np.ndarray,
max_cost: float,
costs: np.ndarray,
values: np.ndarray,
items: np.ndarray,
fractional: bool,
@@ -43,12 +43,11 @@ def rucksack_greedy_algorithm(
eine obere Schranke des maximalen Wertes beim Originalproblem.
'''
# sortiere daten:
order = resort_by_value_per_weight(weights=weights, values=values, items=items);
uorder = iperm(order);
order = get_sort_order(costs=costs, values=values);
# verbose output hier behandeln (irrelevant für Algorithmus):
if verbose:
repr = display_order(order=order, weights=weights[uorder], values=values[uorder], items=items[uorder], one_based=True);
repr = display_order(order=order, costs=costs, values=values, items=items, one_based=True);
print('');
print('\x1b[1mRucksack Problem - Greedy\x1b[0m');
print('');
@@ -56,46 +55,39 @@ def rucksack_greedy_algorithm(
print('');
# führe greedy aus:
n = len(weights);
weight_total = 0;
n = len(costs);
cost_total = 0;
vector = [ 0 for _ in range(n) ];
for i in range(n):
for i in order:
# füge Item i hinzu, solange das Gesamtgewicht noch <= Schranke
if weight_total + weights[i] <= capacity:
weight_total += weights[i];
if cost_total + costs[i] <= max_cost:
cost_total += costs[i];
vector[i] = 1;
# sonst abbrechen. Falls Bruchteile erlaubt, füge einen Bruchteil des i. Items hinzu
else:
if fractional:
vector[i] = (capacity - weight_total)/weights[i];
# falls Bruchteile erlaubt sind, füge einen Bruchteil des i. Items hinzu und abbrechen
elif fractional:
vector[i] = (max_cost - cost_total)/costs[i];
break;
# ansonsten weiter machen:
else:
continue;
# Aspekte der Lösung speichern:
rucksack = [i for i, v in enumerate(vector) if v > 0]; # Indexes von Items im Rucksack
soln = Solution(
vector = vector,
items = items[rucksack].tolist(),
weights = weights[rucksack].tolist(),
costs = costs[rucksack].tolist(),
values = values[rucksack].tolist(),
);
# verbose output hier behandeln (irrelevant für Algorithmus):
if verbose:
# Umsortierung rückgängig machen:
vector = [ soln.vector[i] for i in order ];
rucksack = sorted([ uorder[r] for r in rucksack ]);
permute_data(weights=weights, values=values, items=items, perm=uorder);
# Ausdrücke bestimmen:
expr_value = display_sum(vector=vector, values=values);
expr_weight = display_sum(vector=vector, values=weights);
repr_rucksack = display_rucksack(items=items[rucksack], costs=costs[rucksack], values=values[rucksack]);
print('\x1b[1mEingeschätzte Lösung\x1b[0m');
print('');
if fractional:
print(f'Mask: {soln.vector}');
print(f' ---> {vector} (unter urspr. Sortierung)');
print(f'Rucksack: {", ".join(items[rucksack])}.');
print(f'max. Value ≈ {expr_value}');
print(f'∑ Weights = {expr_weight}');
print(f'Mask: {soln.vector}');
print('Rucksack:')
print(repr_rucksack);
print('');
# Lösung ausgeben
@@ -106,8 +98,8 @@ def rucksack_greedy_algorithm(
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
def rucksack_branch_and_bound_algorithm(
capacity: float,
weights: np.ndarray,
max_cost: float,
costs: np.ndarray,
values: np.ndarray,
items: np.ndarray,
verbose: bool,
@@ -117,12 +109,11 @@ def rucksack_branch_and_bound_algorithm(
unter Rücksicht der Kapizitätsschranke exakt und effizienter bestimmt.
'''
order = resort_by_value_per_weight(weights=weights, values=values, items=items);
uorder = iperm(order);
order = get_sort_order(costs=costs, values=values);
# verbose output hier behandeln (irrelevant für Algorithmus):
if verbose:
repr = display_order(order=order, weights=weights[uorder], values=values[uorder], items=items[uorder], one_based=True);
repr = display_order(order=order, costs=costs, values=values, items=items, one_based=True);
print('');
print('\x1b[1mRucksack Problem - Branch & Bound\x1b[0m');
print('');
@@ -130,12 +121,12 @@ def rucksack_branch_and_bound_algorithm(
print('');
logged_steps = [];
vector = empty_mask(n=len(weights));
vector = empty_mask(n=len(costs));
lb_estimate = np.inf;
S = Stack();
S.push(vector);
while not S.empty():
lb, u, can_add_all, can_add_none = estimate_lower_bound(mask=S.top(), capacity=capacity, weights=weights, values=values, items=items);
lb, u, can_add_all, can_add_none = estimate_lower_bound(mask=S.top(), max_cost=max_cost, costs=costs, values=values, items=items);
if verbose:
logged_steps.append((lb_estimate, lb, str(S), u, can_add_all, can_add_none));
# Update nur nötig, wenn die (eingeschätzte) untere Schranke von A das bisherige Minimum verbessert:
@@ -155,7 +146,7 @@ def rucksack_branch_and_bound_algorithm(
B, C = A.split();
S.push(B);
# Nur dann C auf Stack legen, wenn mind. eine Möglichkeit in C die Kapazitätsschranke erfüllt:
if sum(weights[C.indexes_one]) <= capacity:
if sum(costs[C.indexes_one]) <= max_cost:
S.push(C);
# Aspekte der Lösung speichern
@@ -164,29 +155,20 @@ def rucksack_branch_and_bound_algorithm(
vector = vector.decision,
items = items[rucksack].tolist(),
values = values[rucksack].tolist(),
weights = weights[rucksack].tolist(),
costs = costs[rucksack].tolist(),
);
# verbose output hier behandeln (irrelevant für Algorithmus):
if verbose:
# NOTE: Information in Tabelle gemäß permutierten Daten:
repr = display_branch_and_bound(values=values, steps=logged_steps);
# Umsortierung rückgängig machen:
vector = [ soln.vector[i] for i in order ];
rucksack = sorted([ uorder[r] for r in rucksack ]);
permute_data(weights=weights, values=values, items=items, perm=uorder);
# Ausdrücke bestimmen:
expr_value = display_sum(vector=vector, values=values);
expr_weight = display_sum(vector=vector, values=weights);
repr = display_branch_and_bound(values=values, steps=logged_steps, order=order);
repr_rucksack = display_rucksack(items=items[rucksack], costs=costs[rucksack], values=values[rucksack]);
print('\x1b[1mLösung\x1b[0m');
print('');
print(repr);
print('');
print(f'Mask: {soln.vector}');
print(f' ---> {vector} (unter urspr. Sortierung)');
print(f'Rucksack: {", ".join(items[rucksack])}.');
print(f'max. Value ≈ {expr_value}');
print(f'∑ Weights = {expr_weight}');
print('Rucksack:');
print(repr_rucksack);
print('');
# Lösung ausgeben
@@ -196,35 +178,19 @@ def rucksack_branch_and_bound_algorithm(
# AUXILIARY METHOD resort
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
def resort_by_value_per_weight(
weights: np.ndarray,
values: np.ndarray,
items: np.ndarray,
) -> List[int]:
def get_sort_order(costs: np.ndarray, values: np.ndarray) -> List[int]:
'''
Sortiert Daten absteigend nach values/weights.
Sortiert Daten absteigend nach values/costs.
'''
n = len(weights);
n = len(costs);
indexes = list(range(n));
order = sorted(indexes, key=lambda i: -values[i]/weights[i]);
permute_data(weights=weights, values=values, items=items, perm=order);
order = sorted(indexes, key=lambda i: -values[i]/costs[i]);
return order;
def permute_data(
weights: np.ndarray,
values: np.ndarray,
items: np.ndarray,
perm: List[int],
):
weights[:] = weights[perm];
values[:] = values[perm];
items[:] = items[perm];
return;
def estimate_lower_bound(
mask: Mask,
capacity: float,
weights: np.ndarray,
max_cost: float,
costs: np.ndarray,
values: np.ndarray,
items: np.ndarray,
) -> Tuple[float, List[float], bool]:
@@ -243,19 +209,19 @@ def estimate_lower_bound(
# Berechnungen bei Items mit bekanntem Status in Rucksack:
value_rucksack = sum(values[indexes_one]);
weight_rucksack = sum(weights[indexes_one]);
cost_rucksack = sum(costs[indexes_one]);
vector[indexes_one] = 1;
# Für Rest des Rucksacks (Items mit unbekanntem Status):
weight_rest = capacity - weight_rucksack;
cost_rest = max_cost - cost_rucksack;
can_add_all = False;
can_add_none = False;
# Prüfe, ob man als Lösung alles/nichts hinzufügen kann:
if len(indexes_unset) > 0 and sum(weights[indexes_unset]) <= weight_rest:
if len(indexes_unset) > 0 and sum(costs[indexes_unset]) <= cost_rest:
can_add_all = True;
vector[indexes_unset] = 1;
value_rest = sum(values[indexes_unset]);
elif len(indexes_unset) > 0 and min(weights[indexes_unset]) > weight_rest:
elif len(indexes_unset) > 0 and min(costs[indexes_unset]) > cost_rest:
can_add_none = True;
vector[indexes_unset] = 0;
value_rest = 0;
@@ -263,8 +229,8 @@ def estimate_lower_bound(
# NOTE: Lösung ist eine Überschätzung des max-Wertes.
else:
soln_rest = rucksack_greedy_algorithm(
capacity = weight_rest, # <- Kapazität = Restgewicht
weights = weights[indexes_unset],
max_cost = cost_rest, # <- Kapazität = Restgewicht
costs = costs[indexes_unset],
values = values[indexes_unset],
items = items[indexes_unset],
fractional = True,

117
code/python/src/algorithms/rucksack/display.py
View File

@@ -17,8 +17,9 @@ from src.models.stacks import *;
__all__ = [
'display_order',
'display_sum',
'display_rucksack',
'display_branch_and_bound',
'display_sum',
];
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
@@ -27,31 +28,88 @@ __all__ = [
def display_order(
order: List[int],
weights: np.ndarray,
costs: np.ndarray,
values: np.ndarray,
items: np.ndarray,
one_based: bool = False,
) -> str:
table = pd.DataFrame({
'items': items,
'order': order,
'values': values,
'weights': weights,
'u': (values/weights),
'items': items,
'order': order,
'values': values,
'costs': costs,
'u': (values/costs),
}) \
.reset_index(drop=True);
if one_based:
table['order'] += 1;
# benutze pandas-Dataframe + tabulate, um schöner darzustellen:
repr = tabulate(
pd.DataFrame(table),
headers=['item', 'greedy order', 'value', 'weight', 'value/weight'],
table,
headers=['item', 'greedy order', 'value', 'cost', 'value/cost'],
showindex=False,
colalign=('left', 'center', 'center', 'center', 'right'),
tablefmt='rst'
);
return repr;
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# METHOD display rucksack
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
def display_rucksack(
items: np.ndarray,
costs: np.ndarray,
values: np.ndarray,
) -> str:
table = pd.DataFrame({
'items': items.tolist() + ['----', '∑'],
'costs': costs.tolist() + ['', f'\x1b[92;1m{sum(costs)}\x1b[0m'],
'values': values.tolist() + ['', f'\x1b[92;1m{sum(values)}\x1b[0m'],
});
repr = tabulate(
table,
headers=['item', 'cost', 'value'],
showindex=False,
colalign=('left', 'center', 'center'),
tablefmt='rst'
);
return repr;
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# METHOD display result of branch and bound
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
def display_branch_and_bound(
values: np.ndarray,
steps: List[Tuple[float, float, Stack, List[float], bool, bool]],
order: Optional[List[int]] = None,
) -> str:
# füge Summen-Ausdrücke für Greedy-Alg hinzu:
rows = [];
used_vectors = [];
for lb_estimate, lb, S, u, can_add_all, can_add_none in steps:
pad = '1' if can_add_all else ('0' if can_add_none else '');
if u in used_vectors:
expr = f'{lb:g}';
else:
used_vectors.append(u)
expr = display_sum(vector=u, values=values, as_maximum=False, order=order);
rows.append((f'{lb_estimate:g}', expr, pad, S));
table = pd.DataFrame(rows) \
.rename(columns={0: 'b', 1: 'g(TOP(S))', 2: 'pad?', 3: 'S'}) \
.reset_index(drop=True);
# benutze pandas-Dataframe + tabulate, um schöner darzustellen:
repr = tabulate(
table,
headers=['b', 'g(TOP(S))', 'pad?', 'S'],
showindex=False,
colalign=('left', 'left', 'center', 'right'),
tablefmt='rst'
);
return repr;
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# METHOD display sum
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
@@ -59,47 +117,18 @@ def display_order(
def display_sum(
vector: List[float],
values: np.ndarray,
order: Optional[List[int]] = None,
as_maximum: bool = True,
) -> str:
value = sum([ u*x for u, x in zip(vector,values)]);
parts = [ (u, x) for u, x in zip(vector, values)];
if not (order is None):
parts = [ parts[j] for j in order ];
value = sum([ u*x for u, x in parts]);
expr = '+'.join([
f'{x:g}' if u == 1 else f'{Fraction(str(u))}·{x:g}'
for u, x in zip(vector,values) if u > 0
for u, x in parts if u > 0
]);
if as_maximum:
return f'{value:g} = {expr}';
else:
return f'-{value:g} = -({expr})';
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# METHOD display result of branch and bound
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
def display_branch_and_bound(
values: np.ndarray,
steps: List[Tuple[float, float, Stack, List[float], bool, bool]]
) -> str:
# füge Summen-Ausdrücke für Greedy-Alg hinzu:
rows = [];
used_vectors = [];
for lb_estimate, lb, S, u, can_add_all, can_add_none in steps:
pad = '1' if can_add_all else ('0' if can_add_none else '');
if u in used_vectors:
expr = f'{lb:g}';
else:
used_vectors.append(u)
expr = display_sum(vector=u, values=values, as_maximum=False);
rows.append((f'{lb_estimate:g}', expr, pad, S));
table = pd.DataFrame(rows) \
.rename(columns={0: 'b', 1: 'g(TOP(S))', 2: 'pad?', 3: 'S'}) \
.reset_index(drop=True);
# benutze pandas-Dataframe + tabulate, um schöner darzustellen:
repr = tabulate(
pd.DataFrame(table),
headers=['b', 'g(TOP(S))', 'pad?', 'S'],
showindex=False,
colalign=('left', 'left', 'center', 'right'),
tablefmt='rst'
);
return repr;