Designing the master schedule for demand-adaptive transit systems

Demand-Adaptive Systems (DAS) display features of both traditional fixed-line bus services and purely on-demand systems such as dial-a-ride, that is they offer demand-responsive services within the framework of traditional scheduled bus transportation. A DAS bus line serves, on one hand, a given a set of compulsory stops according to a predefined schedule specifying the time windows associated to each, providing the traditional use of the transit line, without requiring any reservation. On the other hand, passengers may also issue requests for transportation between two desired, optional, stops, which induces detours in the vehicle routes. The design of a DAS line is a complex planning operation that requires to determine not only its design in terms of selecting the compulsory stops, but also its master schedule in terms of the time windows associated to the compulsory stops. Designing a DAS thus combines elements of strategic and tactical planning. In this paper we focus on determining a master-schedule for a single DAS line. We propose a mathematical description and a solution framework based on the estimation of a number of statistical parameters of the demand and the DAS line service. Results of numerical experiments are also given and analyzed. Cooperation as problem-solving and algorithm-design strategy is widely used to build methods addressing complex discrete optimization problems. In most cooperative-search algorithms, the explicit cooperation scheme yields a dynamic process not deliberately controlled by the algorithm design but inflecting the global behaviour of the cooperative solution strategy. The paper presents an overview of explicit cooperation mechanisms and describes issues related to the associated dynamic processes and the emergent computation they often generate. It also identifies a number of research directions into cooperation mechanisms, strategies for dynamic learning, automatic guidance, and selfadjustment, and the associated emergent computation processes.