Genetic Algorithm based Approach to solve Non-Fractional (0/1) Knapsack Optimization Problem

Presented By Sunawar Khan

Mehwish Shabbir

Presented To:Dr. Ayaz Hussain

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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.

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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..

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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.

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GENETIC ALGORITHMFitness EvaluationSelectionCrossoverMutation

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Knapsack problem with knapsack and four items

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Item (xi) Profit (pi) Weight (wi)1 25 32 20 23 15 14 40 45 50 5

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Total possible solutions 25=32

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MATLAB IMPLEMENTATION of 0-1 Knapsack Problem by GA.

Fitness FunctionConstraint FunctionCreation Function

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

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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.

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