I have spent a week working on this branch and bound code for the knapsack problem, and I have looked at numerous articles and books on the subject. However, when I am running my code I don't get the result I expect. Input is received from a text file, such as this:
12
4 1
1 1
3 2
2 3
where the first line is the capacity, and each subsequent line are value/weight pairs. The result I get from using this file is '8' instead of '10' (unless I am mistaken and all the items won't fit in the knapsack). Here is my code:
#!/usr/bin/python
# -*- coding: utf-8 -*-
import Queue
from collections import namedtuple
Item = namedtuple("Item", ['index', 'value', 'weight', 'level', 'bound', 'contains'])
class Node:
def __init__(self, level, value, weight, bound, contains):
self.level = level
self.value = value
self.weight = weight
self.bound = bound
self.contains = contains
def upper_bound(u, k, n, v, w):
if u.weight > k:
return 0
else:
bound = u.value
wt = u.weight
j = u.level + 1
while j < n and wt + w[j] <= k:
bound += v[j]
wt += w[j]
j += 1
# fill knapsack with fraction of a remaining item
if j < n:
bound += (k - wt) * (v[j] / w[j])
return bound
def knapsack(items, capacity):
item_count = len(items)
v = [0]*item_count
w = [0]*item_count
# sort items by value to weight ratio
items = sorted(items, key=lambda k: k.value/k.weight, reverse = True)
for i,item in enumerate(items, 0):
v[i] = int(item.value)
w[i] = int(item.weight)
q = Queue.Queue()
root = Node(0, 0, 0, 0.0, [])
root.bound = upper_bound(root, capacity, item_count, v, w)
q.put(root)
value = 0
taken = [0]*item_count
best = set()
while not q.empty():
c = q.get()
if c.bound > value:
level = c.level+1
# check 'left' node (if item is added to knapsack)
left = Node(c.value + v[level], c.weight + w[level], level, 0.0, c.contains[:])
left.contains.append(level)
if left.weight <= capacity and left.value > value:
value = left.value
best |= set(left.contains)
left.bound = upper_bound(left, capacity, item_count, v, w)
if left.bound > value:
q.put(left)
# check 'right' node (if items is not added to knapsack)
right = Node(c.value, c.weight, level, 0.0, c.contains[:])
right.contains.append(level)
right.bound = upper_bound(right, capacity, item_count, v, w)
if right.bound > value:
q.put(right)
for b in best:
taken[b] = 1
value = sum([i*j for (i,j) in zip(v,taken)])
return str(value)
Are my indices off? Am I not traversing the tree or calculating the bounds correctly?
def upper_bound(u, k, n, v, w):
if u.weight > k:
return 0
else:
bound = u.value
wt = u.weight
j = u.level
while j < n and wt + w[j] <= k:
bound += v[j]
wt += w[j]
j += 1
# fill knapsack with fraction of a remaining item
if j < n:
bound += (k - wt) * float(v[j])/ w[j]
return bound
def knapsack(items, capacity):
item_count = len(items)
v = [0]*item_count
w = [0]*item_count
# sort items by value to weight ratio
items = sorted(items, key=lambda k: float(k.value)/k.weight, reverse = True)
for i,item in enumerate(items, 0):
v[i] = int(item.value)
w[i] = int(item.weight)
q = Queue.Queue()
root = Node(0, 0, 0, 0.0,[])
root.bound = upper_bound(root, capacity, item_count, v, w)
q.put(root)
value = 0
taken = [0]*item_count
best = set()
while not q.empty():
c = q.get()
if c.bound > value:
level = c.level+1
# check 'left' node (if item is added to knapsack)
left = Node(level,c.value + v[level-1], c.weight + w[level-1], 0.0, c.contains[:])
left.bound = upper_bound(left, capacity, item_count, v, w)
left.contains.append(level)
if left.weight <= capacity:
if left.value > value:
value = left.value
best = set(left.contains)
if left.bound > value:
q.put(left)
# check 'right' node (if items is not added to knapsack)
right = Node(level,c.value, c.weight, 0.0, c.contains[:])
right.bound = upper_bound(right, capacity, item_count, v, w)
if right.weight <= capacity:
if right.value > value:
value = right.value
best = set(right.contains)
if right.bound > value:
q.put(right)
for b in best:
taken[b-1] = 1
value = sum([i*j for (i,j) in zip(v,taken)])
return str(value)