The rise of MoD services like Uber and Lyft has significantly altered urban mobility. Research on these systems has focused on efficient design and management, aiming for minimal fleet size, waiting times, and vehicle miles traveled (VMT). Early studies developed heuristic-based taxi dispatching and fare management systems (Ma et al., 2013), incorporating ride-pooling (Santi et al., 2014; Alonso-Mora et al., 2017) to improve efficiency. The potential of autonomous MoD (AMoD) systems has also been explored through simulations, indicating substantial reductions in privately-owned vehicles (Fagnant et al., 2015; Dia and Javanshour, 2017). These simulations have quantified the impact of MoD and AMoD on the environment, congestion, and parking (Fagnant and Kockelman, 2014; Fiedler et al., 2017; Zhang et al., 2015). However, the interaction between MoD and existing public transit has largely been overlooked in these studies. While some research has focused on bimodal MoD systems for first/last-mile solutions (Vakayil et al., 2017; Ma, 2017; Shen et al., 2017; Moorthy et al., 2017), a crucial limitation in most existing research is the assumption of fixed, exogenous demand. These models often use a waiting time threshold, assuming that passengers who can be served by MoD will always choose it, neglecting the competition with other modes. This study addresses this gap by incorporating endogenous demand, where MoD demand depends on its attributes and those of competing modes, reflecting individual preferences. Optimizing under exogenous demand also fails to address broader policy implications, such as the impact of MoD on transit ridership, vehicle ownership, and parking demand (Basu et al., 2018; Hao and Yamamoto, 2017; Zhang and Guhathakurta, 2017). While some studies have considered endogenous demand (Hörl et al., 2016; Basu et al., 2018), they often rely on scenario-based analysis and synthetic mode choice models. Others have analyzed supply-demand interactions (Djavadian and Chow, 2017a; Djavadian and Chow, 2017b), but primarily focus on evaluating existing policies rather than optimizing supply-side parameters. This research aims to develop a framework that integrates a mode choice model with a state-of-the-art MoD simulation system to address these limitations. Specifically, this study develops a multi-scale MoD fleet management system for Manhattan, where passengers choose among ride-hailing, ride-pooling, micro-transit, and public transit, using a stated preference survey to calibrate the mode choice model. Furthermore, it incorporates Bayesian Optimization to find optimal supply-side parameters, offering a more efficient alternative to heuristic or grid search methods.

Existing literature on Mobility-on-Demand (MoD) system design has primarily focused on optimizing operational efficiency under the assumption of exogenous demand. Studies have explored heuristic-based taxi dispatching (Ma et al., 2013), ride-pooling strategies (Santi et al., 2014; Alonso-Mora et al., 2017), and the potential of autonomous vehicles (Fagnant et al., 2015; Dia and Javanshour, 2017). Simulations have assessed the environmental, congestion, and parking impacts of MoD and AMoD systems (Fagnant and Kockelman, 2014; Fiedler et al., 2017; Zhang et al., 2015). Some research has begun to consider the integration of MoD with public transit for first/last-mile solutions (Vakayil et al., 2017; Ma, 2017; Shen et al., 2017; Moorthy et al., 2017). However, a major limitation is the assumption of fixed demand, neglecting the interplay between MoD services and other transportation modes. A few studies have addressed endogenous demand, incorporating mode choice models into agent-based simulation platforms like MATSim and SimMobility (Hörl et al., 2016; Basu et al., 2018). But these studies suffer from limitations, such as scenario-based analysis, lack of supply-side optimization, and reliance on synthetic mode choice models. Studies examining supply-demand interactions in multimodal systems with on-demand services have employed agent-based stochastic user equilibrium with day-to-day adjustments (Djavadian and Chow, 2017b), but these focus on evaluating policy sensitivity rather than optimization. This paper addresses the gap in the literature by developing a unified framework that integrates mode choice modeling with an advanced MoD simulation system and utilizes Bayesian optimization for optimal supply-side parameter determination.

This study proposes a unified framework that integrates mode choice modeling with a state-of-the-art MoD simulation system to design and optimize MoD operations within a multimodal transportation network. The framework consists of nested inner and outer loops. The inner loop simulates the daily interaction between supply and demand within the multimodal system, reaching equilibrium when mode choice shares stabilize. The outer loop uses Bayesian Optimization (BO) to find optimal supply-side parameters. **Mode Choice Model:** A multinomial logit (MNL) model is used to predict passenger mode choice, calibrated using stated preference (SP) survey data collected in New York City. The survey incorporates attributes like walking/waiting time, in-vehicle travel time, cost, parking cost, powertrain type, and automation level for Uber, UberPool, and the respondent's current mode. The MNL model parameters are estimated to quantify the willingness-to-pay for each attribute. The alternative specific constants (ASCs) for the mode choice model are calibrated using a grid search method targeting a realistic transit market share in Manhattan. **MoD Simulation:** The MoD simulation system, based on Alonso-Mora et al. (2017), models a fleet of vehicles with varying passenger capacities (1, 4, 10). It involves two main tasks: (i) matching travel requests to vehicles and (ii) rebalancing idle vehicles. The matching process uses an anytime optimal algorithm that constructs a request-vehicle graph to identify feasible trips and solves an Integer Linear Program (ILP) to assign vehicles to trips while minimizing total delay and penalties for unmet requests. The rebalancing of idle vehicles is optimized via a linear program. **Public Transit Simulation:** The simulation incorporates existing public transit data from the General Transit Feed Specification (GTFS) dataset. A combined road and transit network is created, calculating walk-transit-walk paths for all origin-destination (OD) pairs using a shortest-path algorithm. **Inner Loop Iteration:** The inner loop iteratively updates mode-specific attributes (waiting and travel times), using historical data to reflect passenger learning and preferences. K-means clustering is employed to group OD pairs and update attribute information. The loop stops when the average difference in mode shares between consecutive iterations falls below a threshold (0.01). A penalty parameter adjusts the utility of MoD services in the next iteration if a request was not satisfied in the current iteration, reflecting passengers' aversion to unsatisfied demand. **Outer Loop Optimization (Bayesian Optimization):** The outer loop uses Bayesian optimization (BO) to find optimal supply-side parameters (fleet sizes and fares for each MoD service type). The inner loop simulation acts as a black-box function evaluated by the BO algorithm. A Gaussian process (GP) serves as the surrogate model to approximate the objective function (MoD operator's profit), while the Upper Confidence Bound (UCB) acquisition function guides the exploration of the parameter space. The objective function is defined as the difference between revenue (based on fares with discount factors applied for ride-pooling and micro-transit) and operating costs (leasing, driver salary, and operating cost per mile).

The numerical experiments demonstrate several key findings: 1. **Equilibrium Convergence:** The multimodal supply-demand system converges to an equilibrium state where mode shares stabilize after several iterations, showcasing the model's numerical stability and the learning process of passengers. Experiments show that mode choice shares can fluctuate slightly at equilibrium, representing simulation noise inherent in the probabilistic mode choice model. 2. **Bayesian Optimization Performance:** The Bayesian optimization (BO) algorithm significantly outperforms random search in optimizing supply-side parameters. In a smaller test case (10% of the Manhattan data), BO achieved a near-optimal solution (2.5% profit gap compared to exhaustive search). In the real-scale experiment, BO yielded a solution with 15% higher profit than random search, showcasing its efficiency in high-dimensional optimization. 3. **Impact of Discounting:** Experiments reveal that offering discounts on ride-pooling and micro-transit services doesn't always increase overall profit. In the base case scenario where no discount factor function is used, high-capacity MoD services attain a larger portion of market share. The BO algorithm suggests zero discount factors for high capacity MoD services, indicating that the cost savings from sharing rides may not sufficiently offset passengers' potential disutility in this case. Scenario analysis involving a discount factor function that captures passenger preferences highlights the trade-off between increasing market share of high-capacity services by offering discounts and maximizing overall profit. This shows that simply offering discounts doesn't necessarily lead to increased profitability; rather, careful consideration of passenger preferences is crucial. 4. **Policy Analysis (Per-Ride Tax):** The framework successfully simulates a policy intervention—a per-ride tax on ride-hailing services—quantifying its impact. The tax leads to a significant decrease in MoD profit (30.5%), a reduction in VMT (10.5%), and an increase in transit ridership (1.6%). This demonstrates the framework's ability to assess the effects of transportation policies on multiple stakeholders. 5. **Calibration of ASCs:** The calibration of Alternative Specific Constants (ASCs) for the transit mode is crucial for obtaining realistic transit market shares when the initial travel demand is biased (i.e., when initial travel mode shares doesn't represent actual mode shares). Using a grid search to adjust the transit ASC resulted in a more realistic market share for transit and more accurate prediction of other mode shares.

This study's findings offer significant contributions to the understanding and design of MoD systems. The integration of mode choice modeling into the MoD optimization framework allows for a more realistic representation of passenger behavior and the interaction between MoD and other transport modes. The use of Bayesian Optimization enhances the efficiency and effectiveness of parameter optimization, providing a more powerful tool than traditional methods. The results of the policy analysis demonstrate the applicability of the framework for evaluating the impacts of various policy interventions on different stakeholders, offering valuable insights for policymakers and transportation planners. The superior performance of BO compared to the random search method supports the utilization of such advanced optimization techniques in tackling complex transportation problems. The scenario analysis based on the discount factor function indicates that passenger preferences concerning high-capacity MoD services and discounting play a significant role in the design and profitability of these systems. Therefore, future studies should focus on improved modeling of passenger preferences beyond simply considering level-of-service attributes. The observed sensitivity of optimization results to the parameters of the mode choice model highlights the importance of robust and accurate mode choice models for the effective design and policy analysis of MoD systems.

This paper presents a novel framework for designing and optimizing Mobility-on-Demand (MoD) systems within a multimodal context. It integrates mode choice modeling with advanced MoD simulation and uses Bayesian optimization to efficiently determine optimal supply-side parameters. The framework's ability to capture endogenous demand and quantify the impact of policy interventions makes it a valuable tool for both researchers and policymakers. Future work should focus on enhancing the mode choice model to capture more nuanced passenger preferences, particularly concerning the perception of discounts and sharing rides. Additionally, incorporating a more sophisticated transit assignment model could further improve the accuracy and realism of the simulation.

Several limitations of the current study should be considered. First, the study considers a single MoD operator and does not account for competition between multiple providers. The competitive dynamics between operators could significantly influence the results. Second, the mode choice model, while calibrated using stated preference data, may not perfectly capture all aspects of passenger behavior. More complex models or inclusion of latent variables could provide more accurate predictions. Third, the assumption that unsatisfied MoD demand automatically shifts to public transit may not always hold true in real-world scenarios. Fourth, this research uses a simple transit routing model; incorporating a full-blown transit assignment model may alter the results. Finally, the study focuses on a specific geographic area (Manhattan), and the generalizability of the findings to other urban settings needs further investigation.