Problem: Given, number of items each with a weight and value. The aim is to find each item to be put in a knapsack so that the total weight of included items is less than or equal to the capacity of the knapsack simultaneous total value of the included items should be maximum. It’s a problem that belongs to the NP class of problems. The decision problem form of the knapsack problem is NP-complete whereas optimization problem is NP-hard..

1. Presented By
Sunawar Khan
Mehwish Shabbir
Presented To:
Dr. Ayaz Hussain
1

2.  Paper Title
GENETIC ALGORITHM BASED APPROACH TO SOLVE NON-
FRACTIONAL (0/1) KNAPSACK OPTIMIZATION PROBLEM.
 Author Name
Vikas Thada, Shivali Dhaka, Amity University, Gurgaon, India
 YEAR OF PUBLISH
2014.
 JOURNAL
International Journal of Computer Applications (0975 – 8887) -
Volume 100 – No.15, August 2014.
2

3.  Solve the non-fractional knapsack problem also known as 0-1
knapsack using genetic algorithm.
 Keywords: Genetic algorithm, Knapsack, Optimization.
 The other approaches for solving are greedy method and
dynamic programming. The greedy approach does not always
results in an optimal solution and dynamic programming method
having time complexity of O(nW) where n is number of items and
W is the capacity of the knapsack..
3

4. Problem: Given, number of items each with a weight and value. The aim is to
find each item to be put in a knapsack so that the total weight of included items is
less than or equal to the capacity of the knapsack simultaneous total value of the
included items should be maximum. It’s a problem that belongs to the NP class of
problems. The decision problem form of the knapsack problem is NP-complete
whereas optimization problem is NP-hard..
 Hypothesis: The GA based methods takes very less time and returns results
in an efficient manner as compare to Greedy and DP methods.
4

5. GENETIC ALGORITHM
Fitness Evaluation
Selection
Crossover
Mutation
5

6. Knapsack problem with knapsack and four
items
15-6

7. Item (xi) Profit (pi) Weight (wi)
1 25 3
2 20 2
3 15 1
4 40 4
5 50 5
15-7
Total possible solutions 25
=32

8. 15-8

9.  MATLAB IMPLEMENTATION of 0-1 Knapsack Problem by GA.

Fitness Function
Constraint Function
Creation Function
9

10.  Conclusion:
GA method is more efficient and less time consuming than Greedy and DP
methods even with large dataset.
10

11.  Remainder Selection Operator
 Uniform Selection Operator
 Roulette Selection Operator
 Stochastic Selection Operator
 Results: The GA based methods takes very less time and
returns results in an efficient manner as compare to Greedy and
DP methods.
15-11

12. 12