Applied Soft Computing 13 (2013) 1774–1780 Contents lists available at SciVerse ScienceDirect Applied Soft Computing j ourna l ho me p age: www.elsevier.com/l ocate/asoc Chemical reaction optimization with greedy strategy for the 0–1 knapsack problem Tung Khac Truong a,b , Kenli Li a,∗ , Yuming Xu a a College of Information Science and Engineering, Hunan University, National Supercomputing Center in Changsha, 410082, China b Faculty of Information Technology, Industrial university of Hochiminh city, Hochiminh, Vietnam a r t i c l e i n f o Article history: Received 28 March 2012 Received in revised form 27 November 2012 Accepted 29 November 2012 Available online 11 January 2013 Keywords: Chemical reaction optimization Greedy 0–1 Knapsack problem a b s t r a c t The 0–1 knapsack problem (KP01) is a well-known combinatorial optimization problem. It is an NP-hard problem which plays important roles in computing theory and in many real life applications. Chemi- cal reaction optimization (CRO) is a new optimization framework, inspired by the nature of chemical reactions. CRO has demonstrated excellent performance in solving many engineering problems such as the quadratic assignment problem, neural network training, multimodal continuous problems, etc. This paper proposes a new chemical reaction optimization with greedy strategy algorithm (CROG) to solve KP01. The paper also explains the operator design and parameter turning methods for CROG. A new repair function integrating a greedy strategy and random selection is used to repair the infeasible solutions. The experimental results have proven the superior performance of CROG compared to genetic algorithm (GA), ant colony optimization (ACO) and quantum-inspired evolutionary algorithm (QEA). © 2013 Published by Elsevier B.V. 1. Introduction The 0–1 knapsack problem (KP01) is known to be a combina- torial optimization problem. The knapsack problem has a variety of practical applications such as cutting stock problems, portfolio optimization, scheduling problems [20] and cryptography [1,9,3]. The knapsack appears as a sub-problem in many complex mathe- matical models of real world problems. In a given set of n items, each of them has a weight q i and a profit p i . The problem is to select a subset from the set of n items such that the overall profit is maxi- mized without exceeding a given weight capacity C. It is an NP-Hard problem and hence it does not have a polynomial time algorithm unless P = NP [2]. The problem may be mathematically modelled as follows: Maximize n  i=1 x i p i (1) Subject to n  i=1 x i q i ≤ C, x i ∈ {0, 1}, ∀i ∈ {1, 2, . . . , n} where x i takes values either 1 or 0 which represents the selection or rejection of the ith item. ∗ Corresponding author. E-mail address: LKL510@263.net (K. Li). Over the last four decades, researchers have proposed many approaches to solve KP01. We can classify the methods for this problem into two classes namely, exact algorithms and approxi- mate algorithms. Exact approaches include dynamic programming proposed by Bellman [20] and Branch and Bound proposed by Kolesar [8]. Recently, researchers, such as Kellerer et al. [7] have worked on ways to exactly solve ever larger instances of the knapsack prob- lem. Many of these involve solving some “core” of the problem and then building this partial solution to a full solution. A parallel algo- rithm based on an EREW-SIMD machine with shared memory was proposed by Li et al. [16]. Among the early heuristic approaches, a “polynomial approx- imation schemes” was first developed for the knapsack problem by Sahni [22]. Such schemes may be thought of as solution meth- ods in which one may specify a desired guarantee for the quality of solution in advance of solving. As to be expected, the work to solve increases quickly with the quality required. Immediately afterwards, this was improved by Ibarra and Kim [6] to a fully poly- nomial approximation scheme which makes the trade-off between quality of solution and effort slightly more favorable. Specialized solution techniques to solve the knapsack problem and its variants were provided by Martello and Toth [20]. In recent years, many heuristic algorithms have been employed to solve KP01 problems: Chou-Yuan [15] proposed an ant colony optimization (ACO) for KP01; Shi [24] modified the parameters of the ant colony optimization model to adapt itself to KP01 prob- lems; Li [17] proposed a binary particle swarm optimization based 1568-4946/$ – see front matter © 2013 Published by Elsevier B.V. http://dx.doi.org/10.1016/j.asoc.2012.11.048