Abstract
In this paper, we propose the binary version of the Social Group Optimization (BSGO) algorithm for solving the 0-1 knapsack problem. The standard Social Group Optimization (SGO) is used for continuous optimization problems. So a transformation function is used to convert the continuous values generated from SGO into binary ones. The experiments are carried out using both low-dimensional and high-dimensional knapsack problems. The results obtained by the BSGO algorithm are compared with other binary optimization algorithms. Experimental results reveal the superiority of the BSGO algorithm in achieving a high quality of solutions over different algorithms and prove that it is one of the best finding algorithms especially in high-dimensional cases.
Highlights
The 0-1 knapsack problem (KP) may be defined mathematically as, min āNi 1 pixi (1) subject toāNi 1 wixi ā¤ C, xi ā {0, 1} (2)where N is the set of items are contained by KP, each item has a weight w and a profit p
We propose the binary version of the Social Group Optimization (BSGO) algorithm for solving the 0-1 knapsack problem
Chemical reaction optimization based on a greedy strategy (CROG) (Truong et al, 2015) is proposed to solve 0-1 KP
Summary
The 0-1 knapsack problem (KP) may be defined mathematically as, min āNi 1 pixi (1) subject toāNi 1 wixi ā¤ C , xi ā {0, 1} (2)where N is the set of items are contained by KP, each item has a weight w and a profit p. There are several methods to solve the knapsack problems and are categorized into exact algorithms and meta-heuristic algorithms. Exact algorithms such as dynamic programming and branch-and-bound can give accurate solutions. A novel quantum-inspired cuckoo search (Layeb, 2011), discrete binary version of the cuckoo search algorithm (Gherboudj, Layeb & Chikhi, 2012) and, an improved hybrid encoding cuckoo search algorithm (Feng, Jia & He, 2014) are proposed to solve 0-1 knapsack problems. Chemical reaction optimization based on a greedy strategy (CROG) (Truong et al, 2015) is proposed to solve 0-1 KP. A hybrid algorithm based on tabu search and chemical reaction optimization is proposed to solve 0-1 KP (Yan et al, 2015). In respect of the importance of knapsack problem in practical applications, developing new algorithms to solve large-scale types of knapsack problem applications undoubtedly becomes a true challenge
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