The flexible job shop scheduling problem (FJSP) is an extension of the classical job shop scheduling problem and one of the more well-known NP-hard problems. To get better global optima of the FJSP, a novel hybrid whale optimization algorithm (HWOA) is proposed for solving FJSP, in which minimizing the makespan is considered as the objective. Firstly, the uniformity and extensiveness of the initial population distribution are increased with a good point set (GPS). Secondly, a new nonlinear convergence factor (NCF) is proposed for coordinating the weight of global and local search. Then, a new multi-neighborhood structure (MNS) is proposed, within which a total of three new neighborhoods are used to search for the optimal solution from different directions. Finally, a population diversity reception mechanism (DRM), which ensures to some extent that the population diversity is preserved with iteration, is presented. Seven international benchmark functions are used to test the performance of HWOA, and the results show that HWOA is more efficient. Finally, the HWOA is applied to 73 FJSP and four Ra international instances of different scales and flexibility, and the results further verify the effectiveness and superiority of the HWOA.
Due to the frequent opening and shutting of turbine valves in the power system, valve point effect (VPE) that makes the economic dispatching (ED) problem non-linear, non-smooth and non-convex may be generated. Moreover, various constraints appear in the operation process, such as network transmission loss, and power balance during unit operation, which make it more difficult to find the global optimum through traditional mathematical methods. Nowadays, intelligent algorithms have successfully become a useful optimization tool to deal with nonlinear problems. In this paper, an improved bat algorithm (IBA), into which random black hole strategy and Gaussian mutation are introduced, is proposed to solve the ED problem. Furthermore, the random black hole strategy can enhance the diversity of the population and improve the convergence speed of IBA. Gaussian mutation is adopted to help jumping out of the local optimum. IBA is tested in 50 and 100 dimensions on 10 sets of well-known benchmark functions respectively, and compared with the methods in literature to verify its feasibility. Then, three different scales economic dispatching problems (3 units, 13 units, 40 units) are solved by this method, which further proves its effectiveness. The results show that IBA has obvious advantages and practical application value compared with other optimization methods.
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