A Evolutionary Multiobjective Genetic Algorithm to Solve 0/1 Knapsack Problem
Subhra Swetanisha
1
, Prof. Bhabani Sankar Prasad Mishra
2
1
Lect. Comp.Sc Dept , Trident Academy Of Technology, Bhubaneswar
2
KIIT University, Bhubaneswar
+
Corresponding author. E-mail address: swetanisha.subhra@gmail.com
Abstract. The 0/1 Knapsack Problem is very well known and it appears in many real life
world with different application. The solution to the multi objective 0/1 Knapsack problem can
be viewed as the result of a sequence of decisions. The problem is NP - complete and it also
generalization of the 0/1 Knapsack problem in which many Knapsack are considered. A
evolutionary algorithm for solving multi objective 0/1 Knapsack Problem is introduced in this
paper. This algorithm used a genetic algorithm for direct comparison of two solutions. Our
motivation for developing a genetic algorithm in this paper in a multi objective optimization
framework was that ( a) GA is robust search method. ( b) GA performs the global search. ( c )
GA already work with a population of candidate solutions, which makes them naturally
suitable for multi objective problem solving, where this algorithm is used to consider a set of
optimal solutions at each iteration. Few numerical experiments are realized using the best and
recent algorithm in this paper. Experimental outcome show that the new proposed algorithm
performs better.
Keywords: 0/1 Knapsack Problem, Evolutionary multi objective optimization. Genetic
algorithm, NP completeness.
1. Introduction
Due to practical importance the 0/1 Knapsack Problem is widely used. In last few years the generalization of
this problem has been studied and many algorithms have been proposed. Evolutionary approach for solving the
multi-objective 0/1 Knapsack Problem is one of them, many real worked papers founded in the literature about
multi-objective Knapsack Problem and about the algorithms introduced for solving them. ([6], [7], [8], [9]).
In this paper we introduced a new evolutionary approach for multi objective 0/1 Knapsack Problem. We use
the genetic algorithm in order to determine the solution quality.
2. Problem Description
The knapsack problem [8] [9] is a problem in combinatorial optimization. Given a set of items, each with a
cost and a value, determine the number of each item to include in a collection so that the total cost is least than a
given limit and the total value is as large as possible.
We have n kind of items. 1 through n, each item i has a value Pi and a weight Wi. The maximum weight that we
can carry the knapsack is C.
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2009 International Conference on Computer Engineering and Applications
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