Abstract
The timetabling problem (TTP) and vehicle scheduling problem (VSP) are two indispensable problems in public transit planning process. They used to be solved in sequence; hence, optimality of resulting solutions is compromised. To get better results, some integrated approaches emerge to solve the TTP and VSP as an integrated problem. In the existing integrated approaches, the passenger comfort on bus and the uncertainty in the real world are rarely considered. To provide better service for passengers and enhance the robustness of the schedule to be compiled, we study the integrated optimization of TTP and VSP with uncertainty. In this paper, a novel multiobjective optimization approach with the objectives of minimizing the passenger travel cost, the vehicle scheduling cost, and the incompatible trip-link cost is proposed. Meanwhile, a multiobjective hybrid algorithm, which is a combination of the self-adjust genetic algorithm (SGA), large neighborhood search (LNS) algorithm, and Pareto separation operator (PSO), is applied to solve the integrated optimization problem. The experimental results show that the approach outperforms existing approaches in terms of service level and robustness.
Highlights
To enhance the passenger satisfaction and the robustness of the vehicle schedule generated, we proposed a multiobjective model of the integrated timetabling problem (TTP) and vehicle scheduling problem (VSP) with stochastic passenger flow and trip times
Due to the NP-hard nature of the multiobjective optimization problem, the exact approach is difficult to solve the problem. erefore, we develop a multiobjective hybrid algorithm to optimize the multiobjective integrated optimization problem. e algorithm is a combination of a selfadjust genetic algorithm (SGA), large neighborhood search (LNS) algorithm, and Pareto separation operator (PSO). e self-adjust genetic algorithm (SGA) is applied to construct a new headway, the LNS is employed to find the optimal trip-link chain under the headway, and the PSO is used to select the multiobjective optimal solution. e solution obtained by the hybrid algorithm is the scheduling scheme that consists of the headway and trip-link chain
In our self-adjust genetic algorithm G (s), a chromosome represents a headway vector Tg. e new headway vector Tg at each iteration g is acquired from a pair of parent chromosomes, which are selected by the roulette wheel
Summary
E integrated problem of timetabling and vehicle scheduling is concerned with the generation of a timetable and a vehicle schedule. Considering the departure intervals are different in different time periods, the whole day trips should be divided into different periods. A timetable contains a set of headways within each time period. E departure time of each trip could be calculated based on the set of headways in A timetable contains a set of headways within each time period. e departure time of each trip could be calculated based on the set of headways in
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