Baoding: A Case Study for Testing a New Household Utility Function in MATSim

Baoding is a medium-sized city in Hebei Province, China. The Baoding case study—testing a new household utility function—proposed two scenarios to compare the performance of two utility functions: the household and individual utility functions. In Scenario 1, it was assumed that each household sought to maximize their overall household utilities when they scheduled; thus, family members’ communication and coordination was communal in each household. In Scenario 2, the individual utility function—the default utility function in MATSim—was utilized to score plans; here, each agent tried only to maximize his own utilities without communicating with other family members. Overall, Scenario 1 di ered from Scenario 2 only in the utility function; other input data and parameters in these two scenarios were kept the same. The scenarios simulated only urban residents’ travel behavior. In 2007, the study area population was 1 060 783, in 299 850 households, encompassing 355 465 privately owned cars.

Travel Demand Generation For initial demand generation, a GA (Genetic Algorithm), adopting utility maximization theory, was implemented. For Scenario 1, this GA used the new proposed household utility function as the tness function; this was employed to generate initial individual daily plans for each household in the synthetic population. Speci cally, in the GA, each chromosome represented a household's set of daily plans and each gene represented a family member's daily plan. During evolution (including mutation, crossover and selection), each chromosome was scored; only those with higher household utilities remained. Then, a set of daily plans with the highest household utility function were selected and allocated to the household. Similarly, other daily household plans in the synthetic population were generated, one by one. It should also be noted that the travel time in the initial daily plans was estimated. Therefore, elements like travel time and activity duration in the initial daily plans would be adapted (optimized) when executed in MATSim.
In Scenario 2, the GA incorporated the individual utility function to search for each agent's (family member's) plans.

Activity Locations, Network and Transport Modes
Activity Locations Five typical activity types, including work, home, leisure, education and shopping, were taken into account in the scenarios. The activity facilities numbers for these ve types were: 1 647, 462, 246, 372 and 445, respectively.

Transport Network
The scenarios contained two network types, including road and public transit networks. Figure

Transport Modes
The simulated transport modes included car, public transport, bike and walk. Car drivers and public transport passengers used the road network and transit network. Because agents who traveled by bike or on foot had no access to the transport network, they were teleported from origin to destination and assigned no exact routes, but their travel time was calculated.

Historical Validation
Historic validation. composed of the following two steps, was carried out to assess MATSim's performance and applied to both scenarios.
Step 1: Comparison of both real and simulated car ows and comparison of real and simulated transit passenger ows were carried out in each scenario, to assess MATSim's performance for car and transit simulation. The MRE (Mean Relative Error), calculated by the equation (61.1), was employed to assess performance.
where, F simulated and F real denotes the simulated and the real ow (car ow or passenger ow), respectively.
Step 2: Comparison of both scenarios' performance for car and transit simulation, based on results from step 1.

Comparison of Two Scenarios: Car Tra c
Car ow data on six road links (equal to 12 links in MATSim scenario) from 7 am to 9 am, was used for comparison of car simulation and was manually counted in 2007.  .2(a) demonstrated car simulation performance for both scenarios. Four dots were approximately located in the y = x line and the other two dots, below the line, also were very close to it. Mean relative error margins of Scenario 1 and Scenario 2 were 44.8 % and 47.5 %, respectively. It can thus be concluded that the performance of Scenario 1 (using household utility function) was slightly better than Scenario 2 (using individual utility function).

Comparison of Two Scenarios: Transit Tra c
Data (passenger ow for nine transit lines from 7 am to 9 am) used for transit simulation comparison was also manually counted in 2007. Figure 61.2(b) illustrated both transit simulation scenarios' performance. Clearly, most dots did locate close to the y = x line, however, two dots below the line were signi cantly distant from it. Also, mean relative errors of Scenario 1 and Scenario 2 were 38.7 % and 47.9 %, suggesting that Scenario 1 better represented transit passenger ows than Scenario 2.

Achieved Results
A proposed MATSim household utility function was tested comparing two scenarios using household and individual utility function. Historical validation con rmed that MATSim improved its own car and transit simulation performance by using the new utility function. However, more case studies are needed to further con rm this new proposed utility function's advantages.
More information on the Baoding scenario can be found in Zhuge (2014) (in Chinese).