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A new hybrid combinatorial genetic algorithm for multidimensional knapsack problems

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Abstract

Multidimensional knapsack problem (MKP) is known to be a NP-hard problem, more specifically a NP-complete problem, which cannot be resolved in polynomial time up to now. MKP can be applicable in many management, industry and engineering fields, such as cargo loading, capital budgeting and resource allocation, etc. In this article, using a combinational permutation constructed by the convex combinatorial value \(M_j=(1-\lambda ) u_j+ \lambda x^\mathrm{LP}_j\) of both the pseudo-utility ratios of MKP and the optimal solution \(x^\mathrm{LP}\) of relaxed LP, we present a new hybrid combinatorial genetic algorithm (HCGA) to address multidimensional knapsack problems. Comparing to Chu’s GA (J Heuristics 4:63–86, 1998), empirical results show that our new heuristic algorithm HCGA obtains better solutions over 270 standard test problem instances.

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Acknowledgments

This work is partially supported by the Project of Department of Education of Guangdong Province (No. 2013KJCX0128), the Nature Science Foundation of Guangdong Province (No. 10152104101000004 and No. S2013010013101), and the Foundation of Hanshan Normal University (Grant No. QD20131101). The authors would like to thank the anonymous referees for valuable comments and suggestions, which helped a lot in improving the quality of this paper.

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Authors and Affiliations

  1. Computer Engineering Technical College, Guangdong Institute of Science and Technology, Zhuhai,  519090, China

    Guoming Lai

  2. Department of Mathematics, Hanshan Normal University, Chaozhou , 521041, Guangdong, China

    Dehui Yuan

  3. Department of Computer Science and Engineering, Hanshan Normal University, Chaozhou,  521041, China

    Shenyun Yang

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  1. Guoming Lai
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  2. Dehui Yuan
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Correspondence to Shenyun Yang.

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Lai, G., Yuan, D. & Yang, S. A new hybrid combinatorial genetic algorithm for multidimensional knapsack problems. J Supercomput 70, 930–945 (2014). https://doi.org/10.1007/s11227-014-1268-9

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