This paper introduces an Adaptive Large Neighborhood Search algorithm that uses an epsilon-greedy movement selection strategy to solve a pickup and delivery problem for Smile Pickup, a real-life business. The algorithm also takes into account multiple time windows, heterogeneous fleets, and multiple depots as additional constraints. The algorithm utilises two diversification processes: a simulated annealing technique to update the current solution, and an epsilon-greedy strategy to balance between exploration and exploitation for the selection of neighbourhoods. We evaluated the algorithm’s performance using our own benchmark PickOptBench and Li & Lim benchmarks, and found that it shows great promise in solving Smile Pickup’s problem. Moreover, combining both the epsilon-greedy and simulated annealing restart strategies resulted in a 1% improvement in ALNS performance on both benchmarks. We also discovered that the algorithm found more than 70% of the best-known solutions for 4 out of the 6 classes of instances in the Li & Lim benchmark.