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Bike-sharing systems, which are used in many cities worldwide, need to maintain a balance between the availability of bicycles and the availability of unoccupied bicycle slots. This paper presents an investigation of the net flow of each bike-sharing station in Jersey City. The data was recorded at 1-minute intervals. The sum of the initial bicycle number and the minimum net flow value was determined to be the demand for static rebalancing, and this led to the proposal of a bike-sharing demand prediction method based on autoregressive integrated moving average models. Considering that the existence of bicycles in a state of disrepair may adversely affect demand prediction and routine planning, we present an integer linear programming formulation to model bike-sharing static rebalancing. The proposed formulation takes into account the problem introduced by the need to collect bicycles in need of repair. A hybrid Discrete Particle Swarm Optimization (DPSO) algorithm was proposed to solve the model, which incorporates a reduced variable neighborhood search (RVNS) functionality together with DPSO to improve the global optimization performance. The effectiveness of the algorithms was verified by a detailed numerical example.

As wavelet basis in wavelet analysis is neither arbitrary nor unique, the same signal dealing with different wavelet bases will generate different results. Therefore, how to construct a wavelet basis suitable for the characteristics of the analyzed signal and solve its algorithm and realization is a fundamental problem which perplexed many researchers. To solve these problems, in accordance with the basic features of the measured millisecond blast vibration signal, a new wavelet basis construction method based on the separation blast vibration signal is proposed, and the feasibility of this method is verified by comparing the practical effect of the newly constructed wavelet with other known wavelets in signal processing.

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