| Summary: | As a typical scheduling problem, the vehicle scheduling problem (VSP) plays a significant role in public transportation systems. VSP is difficult to solve, since it is classified as a high-dimensional combination optimization problem, which is well known as an NP-hard problem. Although the existing studies on VSP usually assume that all factors in the problem are deterministic and known in advance, various uncertain factors are always present in practical applications, in particular uncertain processing time. In this paper, we consider the problem of VSP with an uncertain processing time. In order to solve this problem, a hybrid cooperative co-evolution algorithm (hccEA) is proposed. First, we design two-phase encoding and decoding mechanisms with the aim to search a larger solution space and filter infeasible solutions for the genetic algorithm (GA) and particle swarm optimization (PSO). Second, to overcome performance degradation due to high-dimensional variables, a modified PSO is embedded into the cooperative co-evolution framework, which is called ccPSO. Third, a self-adaptive mechanism for parameters of PSO is proposed to balance the uncertain factors. Then, the GA and the ccPSO work alternately in an iterative way. Finally, numerical experiments under an uncertain environment verify the superiority of the proposed hccEA based on comparisons with state-of-the-art algorithms.
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