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Stochastic Expected Value Model for Multiple Bus Headways Optimization

XU Wang-tu1,2,HE Shi-wei1,2,SONG Rui1,2,ZHAO Li1,2,HE Bi-sheng1,2(1.School of Traffic and Transportation,Beijing Jiaotong University,Beijing 100044,China; 2.MOE Key Laboratory for Urban Transportation Complex Systems Theory and Technology, Beijing Jiaotong University,Beijing 100044,China)  
To investigate the headways determining methods for single bus line during different operating time periods under stochastic event conditions,assumptions on stochastic events are made and according to which an expected value model for multiple bus headways optimization aiming at maximal social welfare is formulated.The objective function of the proposed model is discontinuous,its point discontinuities happen at the moment when operation time period changes.A hybrid intelligent algorithm is employed to solve the model,in which stochastic simulation,neutral network,genetic algorithm are embedded.A numerical example is tested to discuss the feasibility of the headways determination model as well as the efficiency of its solution algorithm.This hybrid intelligent algorithm runs at high efficiency when solving the stochastic expected value model,while it is easy to fall into the trap of local optimization.
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