###### Abstract
MATSim (Multi-Agent Transport Simulation), Albatross and ADAPTS (Agent-based Dynamic Activity Planning and Travel Scheduling) are typical examples of these simulation tools [17; 18; 19]. Most traffic simulation tools that are concerned with resident trips use activity-based models to identify optimal combinations of activities in time and space [20]. However, it is also necessary to carry out commuting-based traffic simulations, especially for public transit. The key element of the simulation tools mentioned above is the replanning module, which employs the scores and plans of the agents and determines whether these travel plans must be modified. Most optimization algorithms for travel planning focus on four dimensions, specifically the departure time, travel route, travel mode and the combinations of activities represented by the activity chain [21]. The optimization of the departure time contains two steps. The first of these steps involves setting a range of time adjustments based on the current departure time. The second step involves drawing an adjustment value at random from within the range and adding this adjustment to the previous departure time ([PERSON] et al., 2005; [PERSON], 2013) [2; 22]. The optimization of the travel route is based on static traffic assignment using the user equilibrium (UE) or the stochastic user equilibrium (SUE) models ([PERSON] et al., 2003) [23]. The multinomial logit model and the probit model are often used to optimize the mode of travel, and the optimization of the combinations of activities represented by the activity chain is based on heuristic solution algorithms, such as hill-climbing algorithms or the tabu search algorithm ([PERSON] and [PERSON], 2009; [PERSON] and [PERSON], 2016) [20; 21; 24; 25]. Of the four types of optimization algorithms, research on the optimization of departure time is still insufficient. The challenges involved in such studies are as follows. First, it is difficult to define the direction of adjustment of the departure time, i.e., whether the optimal departure time is earlier or later than the current departure time. Second, it is also difficult to know when the iteration can be stopped. In this study, iteration refers to the replanning process in our simulation tool. Person agents must replan their travel strategies--i.e., perform departure time adjustment--to avoid late arrival or missing their desired metro trips. If there are no person agents who are late when going to work or who become caught in congestion at metro stops when getting off work, the iteration will end. In view of the two challenges identified above, this paper aims to explore a strategy for adjusting departure times to obtain relatively optimal travel utility values, using metro travel as an example. To address the first problem, the two concepts of \"obligatory arrival times\" and \"empirical travel times\" are introduced to determine the direction of departure time adjustment. For the second problem, an explicit condition is proposed for the termination of iteration. With these adjustments, shorter travel times can be achieved. Moreover, we find the latest average departure time with no risk of being late when going to work and the earliest average departure time with no risk of missing metro trips when getting off work. This research on the optimization of departure times will broaden the horizons in this field and can be used to provide the public with suggestions regarding their travel plans.