Intelligent water drops algorithm
A new optimization method for solving
the multiple knapsack problem
Electrical and Computer Engineering Department,
Shahid Beheshti University, Tehran, Iran
Purpose – The purpose of this paper is to test the capability of a new population-based optimization
algorithm for solving an NP-hard problem, called “Multiple Knapsack Problem”, or MKP.
Design/methodology/approach – Here, the intelligent water drops (IWD) algorithm, which is a
population-based optimization algorithm, is modiﬁed to include a suitable local heuristic for the MKP.
Then, the proposed algorithm is used to solve the MKP.
Findings – The proposed IWD algorithm for the MKP is tested by standard problems and the results
demonstrate that the proposed IWD-MKP algorithm is trustable and promising in ﬁnding the optimal
or near-optimal solutions. It is proved that the IWD algorithm has the property of the convergence in
Originality/value – This paper introduces the new optimization algorithm, IWD, to be used for the
ﬁrst time for the MKP and shows that the IWD is applicable for this NP-hard problem. This research
paves the way to modify the IWD for other optimization problems. Moreover, it opens the way to get
possibly better results by modifying the proposed IWD-MKP algorithm.
Keywords Programming and algorithm theory, Optimization techniques, Systems and control theory
Paper type Research paper
The multiple knapsack problem (MKP), is an NP-hard combinatorial optimization
problem with applications such as cutting stock problems (Gilmore and Gomory, 1966),
processor allocation in distributed systems (Gavish and Pirkul, 1982), cargo loading
(Shih, 1979), capital budgeting (Weingartner, 1966), and economics (Martello and Toth,
Two general approaches exist for solving the MKP: the exact algorithms and the
approximate algorithms. The exact algorithms are used for solving small- to
moderate-size instances of the MKP such as those based on dynamic programming
employed by Gilmore and Gomory (1966) and Weingartner and Ness (1967) and those
based on the branch-and-bound approach suggested by Shih (1979) and Gavish and
Pirkul (1985). A recent review of the MKP is given by Freville (2004).
The approximate algorithms may use metaheuristic approaches to approximately
solve difﬁcult optimization problems. The term “metaheuristic” was introduced by
Glover and it refers to general purpose algorithms which can be applied to different
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The author would like to express his gratitude to grateful to the anonymous referees for their
valuable comments and suggestions, which led to the better presentation of this paper in IJICC.
Received 12 December 2007
Revised 25 February 2008
Accepted 4 March 2008
International Journal of Intelligent
Computing and Cybernetics
Vol. 1 No. 2, 2008
q Emerald Group Publishing Limited