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master > master: code py - algorithmus angepasst:

- korrekte behandlung von Permutationen
- hervorhebung von Summanden
- Spalte mit Infos über Moves
- optionen, um alle Gewichte zu zeigen / alle Summen zu zeigen
master
RD 2 months ago
parent
commit
77b2f40215
  1. 56
      code/python/src/algorithms/rucksack/algorithms.py
  2. 96
      code/python/src/algorithms/rucksack/display.py
  3. 3
      code/python/src/models/rucksack/__init__.py
  4. 47
      code/python/src/models/rucksack/logging.py

56
code/python/src/algorithms/rucksack/algorithms.py

@ -57,25 +57,25 @@ def rucksack_greedy_algorithm(
# führe greedy aus:
n = len(costs);
cost_total = 0;
vector = [ Fraction(0) for _ in range(n) ];
choice = [ Fraction(0) for _ in range(n) ];
for i in order:
# füge Item i hinzu, solange das Gesamtgewicht noch <= Schranke
if cost_total + costs[i] <= max_cost:
cost_total += costs[i];
vector[i] = Fraction(1);
choice[i] = Fraction(1);
# falls Bruchteile erlaubt sind, füge einen Bruchteil des i. Items hinzu und abbrechen
elif fractional:
vector[i] = Fraction(Fraction(max_cost - cost_total)/Fraction(costs[i]), _normalize=False);
choice[i] = Fraction(Fraction(max_cost - cost_total)/Fraction(costs[i]), _normalize=False);
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
rucksack = [i for i, v in enumerate(choice) if v > 0]; # Indexes von Items im Rucksack
soln = Solution(
order = order,
choice = vector,
choice = choice,
items = items[rucksack].tolist(),
costs = costs[rucksack].tolist(),
values = values[rucksack].tolist(),
@ -83,7 +83,7 @@ def rucksack_greedy_algorithm(
# verbose output hier behandeln (irrelevant für Algorithmus):
if verbose:
repr_rucksack = display_rucksack(items=items[rucksack], costs=costs[rucksack], values=values[rucksack]);
repr_rucksack = display_rucksack(items=items, costs=costs, values=values, choice=choice);
print('\x1b[1mEingeschätzte Lösung\x1b[0m');
print('');
print(f'Mask: [{", ".join(map(str, soln.choice))}]');
@ -122,24 +122,31 @@ def rucksack_branch_and_bound_algorithm(
print('');
logged_steps = [];
vector = empty_mask(n=len(costs));
lb_estimate = np.inf;
step: Step;
mask = empty_mask(n=len(costs));
bound = np.inf;
S = Stack();
S.push(vector);
S.push(mask);
while not S.empty():
lb, choice, order_, pad = estimate_lower_bound(mask=S.top(), max_cost=max_cost, costs=costs, values=values, items=items);
# top-Element auslesen und Bound berechnen:
A: Mask = S.top();
bound_subtree, choice, order_, pad = estimate_lower_bound(mask=A, max_cost=max_cost, costs=costs, values=values, items=items);
# für logging:
if verbose:
logged_steps.append((lb_estimate, lb, str(S), choice, order_, pad));
step = Step(bound=bound, bound_subtree=bound_subtree, stack_str=str(S), choice=choice, order=order_, indexes=A.indexes_unset, pad=pad);
S.pop();
# Update nur nötig, wenn die (eingeschätzte) untere Schranke von A das bisherige Minimum verbessert:
A: Mask = S.pop();
if lb < lb_estimate:
# Bound, wenn sich A nicht weiter aufteilen lässt od. man A wie eine einelementige Option behandeln kann:
if bound_subtree < bound:
# Bound aktualisieren, wenn sich A nicht weiter aufteilen od. wenn sich A wie eine einelementige Option behandeln läst:
if not A.splittable() or pad != MaskValue.UNSET:
lb_estimate = lb;
bound = bound_subtree;
# falls A als einelementige Menge betrachtet werden kann, ersetze unbekannte Werte:
if pad != MaskValue.UNSET:
A = A.pad(pad);
vector = A;
mask = A;
# für logging:
if verbose:
step.move = EnumBranchAndBoundMove.BOUND;
# Branch sonst
else:
B, C = A.split();
@ -147,12 +154,17 @@ def rucksack_branch_and_bound_algorithm(
# Nur dann C auf Stack legen, wenn mind. eine Möglichkeit in C die Kapazitätsschranke erfüllt:
if sum(costs[C.indexes_one]) <= max_cost:
S.push(C);
# für logging:
if verbose:
step.move = EnumBranchAndBoundMove.BRANCH;
if verbose:
logged_steps.append(step);
# Aspekte der Lösung speichern
rucksack = vector.indexes_one; # Indexes von Items im Rucksack
rucksack = mask.indexes_one; # Indexes von Items im Rucksack
soln = Solution(
order = order,
choice = vector.choice,
choice = mask.choice,
items = items[rucksack].tolist(),
values = values[rucksack].tolist(),
costs = costs[rucksack].tolist(),
@ -161,11 +173,11 @@ def rucksack_branch_and_bound_algorithm(
# verbose output hier behandeln (irrelevant für Algorithmus):
if verbose:
repr = display_branch_and_bound(values=values, steps=logged_steps);
repr_rucksack = display_rucksack(items=items[rucksack], costs=costs[rucksack], values=values[rucksack]);
print('\x1b[1mLösung\x1b[0m');
print('');
repr_rucksack = display_rucksack(items=items, costs=costs, values=values, choice=mask.choice);
print(repr);
print('');
print('\x1b[1mLösung\x1b[0m');
print('');
print(f'Mask: [{", ".join(map(str, soln.choice))}]');
print('Rucksack:');
print(repr_rucksack);
@ -201,7 +213,7 @@ def estimate_lower_bound(
mit Greedy-Algorithmus »lösen«,
um schnell eine gute Einschätzung zu bestimmen.
NOTE: Diese Funktion wird `g(vector)` im Skript bezeichnet.
NOTE: Diese Funktion wird `g(mask)` im Skript bezeichnet.
'''
indexes_one = mask.indexes_one;
indexes_unset = mask.indexes_unset;

96
code/python/src/algorithms/rucksack/display.py

@ -9,6 +9,8 @@ from src.thirdparty.code import *;
from src.thirdparty.maths import *;
from src.thirdparty.types import *;
from src.setup import config;
from models.generated.config import *;
from src.models.stacks import *;
from src.models.rucksack import *;
@ -62,18 +64,31 @@ def display_rucksack(
items: np.ndarray,
costs: np.ndarray,
values: np.ndarray,
choice: List[Fraction],
) -> str:
show_options = config.OPTIONS.rucksack.show;
render = lambda r: f'{r:g}';
choice = np.asarray(choice);
rucksack = np.where(choice > 0);
if not(EnumRucksackShow.all_weights in show_options):
items = items[rucksack];
costs = costs[rucksack];
values = values[rucksack];
choice = choice[rucksack];
table = pd.DataFrame({
'items': items.tolist() + ['----', ''],
'costs': list(map(render, costs)) + ['', f'\x1b[92;1m{sum(costs):g}\x1b[0m'],
'values': list(map(render, values)) + ['', f'\x1b[92;1m{sum(values):g}\x1b[0m'],
'nr': list(map(str, choice))
+ ['----', f'\x1b[92;1m{float(sum(choice)):g}\x1b[0m'],
'costs': list(map(render, costs))
+ ['----', f'\x1b[92;1m{sum(choice*costs):g}\x1b[0m'],
'values': list(map(render, values))
+ ['----', f'\x1b[92;1m{sum(choice*values):g}\x1b[0m'],
});
repr = tabulate(
table,
headers=['item', 'cost', 'value'],
headers=['item', 'nr', 'cost', 'value'],
showindex=False,
colalign=('left', 'center', 'center'),
colalign=('left', 'center', 'center', 'center'),
tablefmt='rst'
);
return repr;
@ -82,30 +97,39 @@ def display_rucksack(
# METHOD display result of branch and bound
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
def display_branch_and_bound(
values: np.ndarray,
steps: List[Tuple[float, float, Stack, List[Fraction], List[int], MaskValue]],
) -> str:
# füge Summen-Ausdrücke für Greedy-Alg hinzu:
def display_branch_and_bound(values: np.ndarray, steps: List[Step]) -> str:
show_options = config.OPTIONS.rucksack.show;
show_all_sums = (EnumRucksackShow.all_sums in show_options);
rows = [];
used_choices = [];
for lb_estimate, lb, S, choice, order, pad in steps:
if choice in used_choices:
expr = f'{lb:g}';
index_soln = max([-1] + [ i for i, step in enumerate(steps) if step.move == EnumBranchAndBoundMove.BOUND ]);
for i, step in enumerate(steps):
if show_all_sums or step.choice not in used_choices:
# Füge Summen-Ausdrücke für Greedy-Alg hinzu:
used_choices.append(step.choice);
expr = display_sum(choice=step.choice, values=values, as_maximum=False, order=step.order, indexes=step.indexes);
else:
used_choices.append(choice);
expr = display_sum(choice=choice, values=values, as_maximum=False, order=order);
rows.append((f'{lb_estimate:g}', expr, ('' if pad == MaskValue.UNSET else pad.value), S));
expr = f'{step.bound_subtree:g}';
pad_str = ('' if step.pad == MaskValue.UNSET else step.pad.value);
move_str = ('' if step.move == EnumBranchAndBoundMove.NONE else step.move.value);
if i == index_soln:
move_str = f'{move_str} *';
rows.append({
'bound': f'{step.bound:+g}',
'bound_subtree': expr,
'stack': step.stack_str,
'pad': f'\x1b[2m{pad_str}\x1b[0m',
'move': f'\x1b[2m{move_str}\x1b[0m',
});
table = pd.DataFrame(rows) \
.rename(columns={0: 'b', 1: 'g(TOP(S))', 2: 'pad?', 3: 'S'}) \
.reset_index(drop=True);
table = pd.DataFrame(rows).reset_index(drop=True);
# benutze pandas-Dataframe + tabulate, um schöner darzustellen:
repr = tabulate(
table,
headers=['b', 'g(TOP(S))', 'pad?', 'S'],
headers=['bound', 'g(TOP(S))', 'S — stack', '\x1b[2mpad?\x1b[0m', '\x1b[2mmove\x1b[0m'],
showindex=False,
colalign=('left', 'left', 'center', 'right'),
colalign=('left', 'left', 'right', 'center', 'left'),
tablefmt='rst'
);
return repr;
@ -118,17 +142,31 @@ def display_sum(
choice: List[Fraction],
values: np.ndarray,
order: Optional[List[int]] = None,
indexes: List[int] = [],
as_maximum: bool = True,
) -> str:
parts = [ (u, x) for u, x in zip(choice, values)];
show_options = config.OPTIONS.rucksack.show;
show_all_weights = (EnumRucksackShow.all_weights in show_options);
def render(x: Tuple[bool, Fraction, float]):
b, u, value = x;
if u == 0:
expr = f'\x1b[94;2m{value:g}\x1b[0m' if b else f'\x1b[2m{value:g}\x1b[0m';
else:
expr = f'\x1b[94m{value:g}\x1b[0m' if b else f'\x1b[0m{value:g}\x1b[0m';
if not show_all_weights and u == 1:
return expr;
return f'\x1b[2;4m{u}\x1b[0m\x1b[2m·\x1b[0m{expr}';
parts = [ (i in indexes, u, x) for i, (u, x) in enumerate(zip(choice, 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'{u}·{x:g}'
for u, x in parts if u > 0
]);
if not show_all_weights:
parts = list(filter(lambda x: x[1] > 0, parts));
value = sum([ u*x for _, u, x in parts ]);
expr = '\x1b[2m+\x1b[0m'.join(map(render, parts));
if as_maximum:
return f'{value:g} = {expr}';
else:
return f'-{value:g} = -({expr})';
return f'{value:g} \x1b[2m=\x1b[0m {expr}';
return f'-{value:g} \x1b[2m= -(\x1b[0m{expr}\x1b[2m)\x1b[0m';

3
code/python/src/models/rucksack/__init__.py

@ -7,6 +7,7 @@
from src.models.rucksack.mask import *;
from src.models.rucksack.solution import *;
from src.models.rucksack.logging import *;
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# EXPORTS
@ -17,4 +18,6 @@ __all__ = [
'MaskValue',
'Mask',
'Solution',
'EnumBranchAndBoundMove',
'Step',
];

47
code/python/src/models/rucksack/logging.py

@ -0,0 +1,47 @@
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# IMPORTS
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
from __future__ import annotations;
from src.thirdparty.maths import *;
from src.thirdparty.types import *;
from src.models.rucksack.mask import *;
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# EXPORTS
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
__all__ = [
'EnumBranchAndBoundMove',
'Step',
];
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# CLASS Move
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
class EnumBranchAndBoundMove(Enum):
NONE = -1;
BOUND = 'bound';
BRANCH = 'branch';
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# CLASS Step
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
@dataclass
class Step():
bound: float = field();
bound_subtree: float = field();
stack_str: str = field();
choice: List[Fraction] = field();
order: List[int] = field();
# the indexes upon which the greedy algorithm is carried out:
indexes: List[int] = field();
pad: MaskValue = field();
move: EnumBranchAndBoundMove = field(default=EnumBranchAndBoundMove.NONE);
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