Fast Polynomial Time Approximate Solution for 0-1 Knapsack Problem

Algorithm 2

Approximate Algorithm for (KP).

	Step 1 Input the capacity c, size n, weights and profits of items.
	Step 2 Obtain the critical item by (10).
	Step 3 Let .
	Step 4 Obtain the upper bound and its solution by (8).
	Step 5 If , then . Otherwise, .
	Step 6 If , then exit.
	Step 7 Obtain the initial solution by (18).
	Step 8 Obtain the best solution in the neighborhood and its objective value by Algorithm 1.
	Step 9 If , then .
	Step 10 If , then , get and its solution by (8); else, , get and its solution by (8). Go to Step 5.