In this paper a new evolutionary algorithm is presented for the unbounded knapsack problem, which is a famous NP-complete combinatorial optimization problem. The proposed genetic algorithm is based on two techniques. One is a heuristic operator, which utilizes problem-specific knowledge, and the other is a preprocessing technique. Computational results show that the proposed algorithm is capable of obtaining high-quality solutions for problems of standard randomly generated knapsack instances, while requiring only a modest amount of computational effort.
", as we proved in . The KP has very important applications in the financial and industry domains, such as resource distribution, investment decision-making, items shipment, budget controlling . "
[Show abstract][Hide abstract] ABSTRACT: Knapsack Problem (KP) is a most popular subset selection problem. The aim is to assign an optimal subset among all original items to a knapsack, such that the overall profit of the selected items be maximized, while the total weight of them does not exceed the capacity of the knapsack. Artificial Bee Colony (ABC) algorithm is a new metaheuristic with a stochastic search strategy. In ABC, the neighborhood of the best found food sources is searched in order to achieve better food sources. This paper presents a binary version of ABC algorithm for the KP. In this approach a hybrid probabilistic mutation scheme is performed for searching the neighborhood of food sources. The proposed algorithm can guide the search space quickly and improve the local search ability. Experimental results demonstrate that the presented approach has improved the quality and efficiency greatly.
Innovations in Intelligent Systems and Applications (INISTA), 2012 International Symposium on; 01/2012
"Among those heuristic algorithms for knapsack problem, Genetic Algorithm is found to be an effective method to solve the knapsack instances approximately. Ken-li Li  presented a problem-specific genetic algorithm for solving the UKP. They have solved the UKP by transforming it into 0- 1 knapsack problem. "
[Show abstract][Hide abstract] ABSTRACT: In this paper a new Genetic Algorithm based on a heuristic operator and Centre of Mass selection operator (CMGA) is designed for the unbounded knapsack problem(UKP), which is NP-Hard combinatorial optimization problem. The proposed genetic algorithm is based on a heuristic operator, which utilizes problem specific knowledge. This center of mass operator when combined with other Genetic Operators forms a competitive algorithm to the existing ones. Computational results show that the proposed algorithm is capable of obtaining high quality solutions for problems of standard randomly generated knapsack instances. Comparative study of CMGA with simple GA in terms of results for unbounded knapsack instances of size up to 200 show the superiority of CMGA. Thus CMGA is an efficient tool of solving UKP and this algorithm is competitive with other Genetic Algorithms also.
"Genetic algorithms, originally proposed by Holland, have been applied to many different areas. Li used genetic algorithms to solve the unbounded knapsack problem, using problem-specific knowledge and incorporating a preprocessing procedure, but it was affected by knowledge. "
[Show abstract][Hide abstract] ABSTRACT: The Knapsack problem is an NP-Complete problem. Unbounded Knapsack problems are more complex and harder to solve than the
general Knapsack problem. In this paper, we apply the genetic algorithm to solve the unbounded Knapsack problem. We use an
elitism strategy to overcome the defect of the slow convergence rate of the general genetic algorithm. The elitism strategy
retains good chromosomes and ensures that they are not eliminated through the mechanism of crossover and mutation, while ensuring
that the features of the offspring chromosomes are at least as good as their parents. The system automatically adapts the
number of the initial population of chromosomes and the number of runs of the genetic algorithm. In addition, we use the strategy
of greedy method to auto adaptive the sequence of chromosomes to enhance the effect of executing. Experimental results showed
that our method could fast find the best solution of the problem.
Frontiers of High Performance Computing and Networking ISPA 2007 Workshops, ISPA 2007 International Workshops SSDSN, UPWN, WISH, SGC, ParDMCom, HiPCoMB, and IST-AWSN Niagara Falls, Canada, August 28 - September 1, 2007, Proceedings; 01/2007
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