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A Novel Method for Solving Unbounded Knapsack Problem

Chen Rung

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Abstract

Knapsack problem is one kind of NP-Complete problem. Unbounded knapsack problems are more complex and harder than general knapsack problem. In this paper,we apply QGAs (Quantum Genetic Algorithms) to solve unbounded knapsack problem and then follow other procedures. First,present the problem into the mode of QGAs and figure out the corresponding genes types and their fitness functions. Then,find the perfect combination of limitation and largest benefit. Finally,the best solution will be found. Primary experiment indicates that our method has well results.

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What this paper is about

Knapsack problem is one kind of NP-Complete problem. Unbounded knapsack problems are more complex and harder than general knapsack problem. In this paper,we apply QGAs (Quantum Genetic Algorithms) to solve unbounded knapsack problem and then follow other procedures. First,present the problem into the mode of QGAs and figure out the corresponding genes types and their fitness functions. Then,find the perfect combination of limitation and largest benefit. Finally,the best solution will be found. Primary experiment indicates that our method has well results.

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Available abstract

Knapsack problem is one kind of NP-Complete problem. Unbounded knapsack problems are more complex and harder than general knapsack problem. In this paper,we apply QGAs (Quantum Genetic Algorithms) to solve unbounded knapsack problem and then follow other procedures. First,present the problem into the mode of QGAs and figure out the corresponding genes types and their fitness functions. Then,find the perfect combination of limitation and largest benefit. Finally,the best solution will be found. Primary experiment indicates that our method has well results.

Key concepts: Knapsack problem, Continuous knapsack problem, Change-making problem, Mathematics, Polynomial-time approximation scheme, Cutting stock problem, Mathematical optimization, Genetic algorithm

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