Noising methods with hybrid greedy repair operator for 0-1 knapsack problem

Noising methods (NMs) include a set of local search methods and can be considered as simulated annealing algorithm or threshold accepting (TA) method when its components are properly chosen. This paper studies how to utilize NMs for solving the 0-1 knapsack problem (0-1 KP). Two noising strategies, noising variation of objective function and noising data, are used to help NMs escape from local optima. When noising variation of objective function is used, probabilistic acceptance or deterministic acceptance is used to decide whether to accept neighbor solutions. Two decreasing strategies, arithmetical decreasing and geometrical decreasing, are used to control the change of parameter noise-rate. In total, six variants of NMs including two TAs are designed to solve the 0-1 KP. In those variants, a hybrid greedy repair operator, which combines density-based and value-based greedy drop and add operators, is designed to get better balance between intensification and diversification. Extensive experiments were performed to compare the performances of the six variants of NMs. The performances of the six variants of NMs were also compared with some state-of-the-art metaheuristics on a wide range of small size, medium size, and large size 0-1 KP instances. Simulation results show that NMs are better than or competitive with other state-of-the-art metaheuristics.