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The introduction of customized bus (CB) service intends to expand and elevate existing transit service, which offers an efficient and sustainable alternative to serve commuters. A probabilistic model is proposed to optimize CB service with mixed vehicle sizes in an urban setting considering stochastic bus arrival time and spatiotemporal demand, which minimizes total cost subject to bus capacity and time window constraints. The studied optimization problem is combinatorial with many decision variables including vehicle assignment, bus routes, timetables, and fleet size. A heuristic algorithm is developed, which integrates a hybrid genetic algorithm (HGA) and adaptive destroy-and-repair (ADAR) method. The efficiency of HGA-ADAR is demonstrated through numerical comparisons to the solutions obtained by LINGO and HGA. Numerical instances are carried out, and the results suggested that the probabilistic model considering stochastic bus arrival time is valuable and can dramatically reduce the total cost and early and late arrival penalties. A case study is conducted in which the proposed model is applied to optimize a real-world CB service in Xi'an, China. The relationship between decision variables and model parameters is explored. The impacts of time window and variance of bus arrival time, which significantly affect service reliability, are analysed. [ABSTRACT FROM AUTHOR]

• Vehicle route, speed and departure time are optimized for shared autonomous electric vehicles (SAEVs) service. • A mixed-integer linear model is formulated for a time-dependent vehicle routing problem for SAEVs service. • Realistic energy consumption and congestion is considered in route optimization. • Adaptive large neighborhood search algorithm (ALNS) is proposed, and is embedded with departure time and speed optimization. Shared autonomous electric vehicles (SAEVs) are expected to become a popular choice for urban transportation in the future. A solution to a vehicle routing problem that considers congestion and energy consumption of SAEVs is proposed to assist green transportation under poor traffic conditions. In addition to routing the fleet of SAEVs to serve customers, the proposed method also determines the vehicle speed in each arc and the departure time at each node by minimizing the cost considering the travel distance, energy consumption, and travel time. In the time-dependent vehicle routing problem with departure time and speed optimization for SAEV service (SAEV-TD-VRP-DSO), the electric vehicles (EVs) exchange batteries at battery swapping stations (BSSs), and the corresponding vehicle routing method also includes recharge scheduling. We develop a mixed-integer linear model (MILP) to formulate the SAEV-TD-VRP-DSO and show that the state-of-the-art commercial optimization solver (CPLEX) can only solve a few instances (no more than 8 requests). Thus, an adaptive large neighborhood search (ALNS) algorithm is proposed to find near-optimal solutions for larger-size instances. The removal and insertion operators of ALNS help optimize the node sequences. A departure time and speed optimization procedure (DSOP) is employed to optimize the speed and departure time in each arc. The good performance of the proposed algorithm is demonstrated using instance sets. The optimization results of a case study in the Yanta Administrative District in Xi'an, China, show that speed and departure time optimization result in 24.99% cost savings. The sensitivity analysis results provide the SAEV operators with alternative cost-saving solutions. Empty vehicles traveling at a slower speed can reduce energy cost. The total cost of operating vehicles with passengers can be reduced by avoiding congestion and utilizing larger capacity batteries (32 kWh or more) and a lower minimum battery level (0.2-0.3). [ABSTRACT FROM AUTHOR]