In order to solve the Knapsack Problem with a single Continuous variable (KPC) efficiently, a novel S-shape transfer function based on Gauss error function was proposed, and a new approach of transforming a real vector into a 0-1 vector by using the proposed transfer function was given, thereby a New Binary Particle Swarm Optimization algorithm (NBPSO) was proposed. Then, based on the second mathematical model of KPC and the combination of NBPSO and the effective algorithm to deal with the infeasible solutions of KPC, a new approach to solve KPC was proposed. For validating the performance of NBPSO in solving KPS, NBPSO was utilized to solve four kinds of large-scale KPC instances, and the obtained calculation results were compared with those of Binary Particle Swarm Optimization algorithms (BPSOs) based on other S and V-shape transfer functions, Single-population Binary Differential Evolution with Hybrid encoding (S-HBDE), Bi-population Binary Differential Evolution with Hybrid encoding (B-HBDE) and Binary Particle Swarm Optimization algorithm (BPSO). The comparison results show that NBPSO is superior to the comparison algorithms in average calculation result and stability, illustrating that NBPSO has the performance better than other algorithms.

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.

Since the deterministic algorithms are difficult to solve the Discounted {0-1} Knapsack Problem (D{0-1}KP) with large-scale and wide data range, a Mutated Double codes Binary Bat Algorithm (MDBBA) was proposed. Firstly, the coding problem of D{0-1} KP was solved by double coding. Secondly, the Greedy Repair and Optimization Algorithm (GROA) was applied to the individual fitness calculation of bats, and the algorithm was quickly and effectively solved. Then, the mutation strategy in Differential Evolution (DE) was selected to improve the global optimization ability. Finally, Lévy flight was carried out by the bat individual according to certain probability to enhance the ability of the algorithm to explore and jump out of local extrema. Simulation was tested on four large-scale instances. The result shows that MDBBA is very suitable for solving large-scale D {0-1} KP, which has better optimal value and mean value than FirEGA (First Genetic Algorithm) algorithm and Double Binary Bat Algorithm (DBBA), and MDBBA converges significantly faster than DBBA.

In order to solve the problem that large amounts of supervised information was needed to achieve satisfactory performance, owing to the implementation of the semi-supervised community detection methods based on Non-negative Matrix Factorization (NMF) which selected prior information randomly, an Active Link Selection algorithm for semi-supervised community detection based on Graph regularization NMF (ALS_GNMF) was proposed. Firstly, in the iteration framework, the most uncertain and informative links were selected actively as prior information links. Secondly, the must-link constraints of these links, which generated the prior matrix, were added to enhance the connections in a certain community. At the same time, the cannot-link constraints were added, which modified the adjacency matrix, to weaken the connections between communities. Finally, the prior matrix was used as a graph regularization term to incorporate into the optimization objective function of NMF. And combining with network topology information, higher community discovery accuracy and robustness were achieved with less prior information. At the same prior ratio on both synthetic and real networks, experimental results demonstrate that the ALS_GNMF algorithm significantly outperformes the existing semi-supervised NMF algorithms in terms of efficiency, and it is stable especially on networks with unclear structure.

The Firefly Algorithm (FA) has a few disadvantages in the global searching, including slow convergence speed, low solving precision and high possibility of being trapped in local optimum. A FA based on chaotic dynamic population was proposed. Firstly, chaotic sequence generated by cube map was used to initiate individual position, which strengthened the diversity of global searching; secondly, through dynamic monitoring of population, whenever the algorithm meets the preset condition, the new population individuals were generated using chaotic sequences, thus effectively improving convergence speed; thirdly, a Gaussian disturbance would be given on the global optimum of each generation, thus the algorithm could effectively jump out of local minima. Based on six complex test functions, the test results show that chaos-based dynamic population FA improves the capacity of global searching optimal solution, convergence speed and computational precision of solution.