A large-scale Discount {0-1} Knapsack Problem (D{0-1} KP) is difficult to solve with the deterministic algorithms, thus a differential crow search algorithm based on Lévy flight named LDECSA was proposed. Firstly, the coding problem about the second mathematical model of D{0-1} KP was solved by using mixed coding. Secondly, a New greedy Repair and Optimization Algorithm (NROA) was used to deal with the infeasible solution. Thirdly, in order to avoid the problems of local optimum and slow convergence, Lévy flight and differential strategy were introduced. Finally, the reasonable value of awareness probability and flight length were determined through experiments, the differential strategy was also chosen. The experimental results on four types of large-scale D{0-1} KP show that LDECSA is very suitable for solving large-scale D{0-1} KP with very satisfactory approximate solution.

In Discount {0-1} Knapsack Problem (D{0-1}KP), the weight coefficients and the value coefficients in a large range, are difficult to solve by deterministic algorithms. To solve this problem, a Chaotic Crow Search Algorithm based on Differential Evolution strategy (DECCSA) was proposed. Firstly, the initial crow population was generated by chaotic mapping. Secondly, mixed coding and Greedy Repair and Optimization Strategy (GROS) were used to solve the coding problem of D{0-1}KP. Finally, Difference Evolution (DE) strategy was introduced to improve the convergence rate of the algorithm. The experimental results on four large-scale D{0-1}KP instances show that DECCSA is better than Genetic Algorithm (GA), bacterial foraging optimization algorithm, and mutated bat algorithm, and it can get the optimal solution or approximate optimal solution. It's very suitable for solving D{0-1}KP.