MoDES: Urban Mobility Optimization

• MoDES is a comprehensive simulation and optimization framework for multimodal urban transportation that integrates Mobility-on-Demand services with endogenous mode choice.
• It employs a bi-level architecture with detailed supply‐side simulation and Bayesian Optimization to efficiently explore fleet configurations and discount factors.
• Empirical evaluations demonstrate its practical use in policy scenario analysis, optimizing system-level outcomes such as profit, VMT, and transit performance.

MoDES (Mobility-on-Demand plus mode Choice) is a comprehensive simulation and optimization framework for the joint design and operational analysis of multimodal urban transportation systems, integrating Mobility-on-Demand (MoD) services with endogenous mode choice and state-of-the-art supply-side simulation. It provides a structured methodology to quantify and optimize how riders choose among transit, ride-hailing, pooled, and micro-transit options as a function of level-of-service, and supports system-level objectives (such as profit or sustainability) and scenario analysis (including policy interventions) (Liu et al., 2018).

1. Unified Multimodal Supply–Demand Architecture

The MoDES framework is characterized by a bi-level architecture. The outer loop defines the system supply through decision variables such as fleet sizes $n_m$ and discount factors $\gamma_m$ for each MoD service class $m$ (with discrete capacities, e.g., 1, 4, or 10). The inner loop models the urban transport state at a finer temporal and spatial resolution:

• Each vehicle $v_j$ has capacity $c_j$; requests $r_k$ are tracked with realized waiting times $w_r$ and in-vehicle delays $\delta_r$.
• Historical level-of-service attributes $H^n_{ijm}$ are maintained for each origin-destination (OD) cluster-pair $(i,j)$ and mode $\gamma_m$0, capturing average waiting, travel times, and service rates at each iteration $\gamma_m$1.

A day-to-day equilibrium process iterates between trip assignment (MoD matching using shareability graphs, ILP assignment, and rebalancing; transit via shortest-path), travel experience update, and recomputation of mode-choice until convergence in mode-share vector $\gamma_m$2. This inner equilibrium is embedded in an outer Bayesian Optimization (BO) layer exploring $\gamma_m$3 for system objectives (Liu et al., 2018).

2. Integrated Mode Choice Modeling

Endogenous user mode-choice is modeled via a Multinomial Logit (MNL), estimated from a stated preference discrete-choice experiment (SP-DCE) with 1,507 New York City commuters. For each OD pair $\gamma_m$4 and mode $\gamma_m$5, utility is calculated as

$\gamma_m$6

where coefficients ($\gamma_m$7, $\gamma_m$8, $\gamma_m$9, etc.) reflect user sensitivities to out-of-vehicle time, in-vehicle time, price, parking, electrification, and automation. Choice probabilities are softmaxed over alternatives. ASC for transit is calibrated by grid search to match empirical transit mode shares.

Economic interpretation yields estimated willingness-to-pay of $m$0 for OVTT and $m$1 for IVTT (derived as ratios of cost/time coefficients) (Liu et al., 2018).

3. Bayesian Optimization for Supply-Side Design

MoDES formulates the system design as a black-box optimization: $m$2 where $m$3 is the fare for passenger $m$4 (a function of base fare, in-vehicle time, distance, and discount factor), $m$5 is fleet leasing cost, $m$6 driver salary, $m$7 operating cost, $m$8 total VMT. The optimization uses a Gaussian Process surrogate with Matérn kernel and GP-UCB acquisition.

BO leverages real simulation results as batch queries, making it highly data- and computation-efficient relative to grid search or random search. Small-scale enumeration shows BO achieves near-optimal profit faster (2.5% suboptimality). In full-scale tests, BO achieves a 15% profit advantage over random search (Liu et al., 2018).

4. Convergence, Calibration, and Equilibrium Computation

Mode-share equilibrium is defined when

$m$9

with $v_j$0 typically set to 0.01. Empirical tests demonstrate convergence within 5–10 inner-loop iterations across different $v_j$1. Demand and supply calibration leverage granular Manhattan taxi pickup data (5.9% of daily demand at 8–9am) mapped to a 4,092-node road network with GTFS subway. Clustering is performed to aggregate demand and maintain tractable simulation scopes (Liu et al., 2018).

5. Empirical Results and Scenario Analysis

Exhaustive experiments compare MoDES outcomes under fixed versus optimized configurations. For typical scenarios:

• Profit-maximizing fleets (with fixed discounts) found via brute-force enumeration achieve \$v_j$212,674 in a fraction of the time.</li> <li>In full-scale deployment, BO achieves \$145,015 profit under real demand, exceeding random search by 15%.
• Policy sensitivity: introducing passenger disutility for high-capacity modes alters optimal discount rates and mode shares; higher disutility reduces pool/micro-transit, shifting back to single-occupancy ride-hailing.

A policy experiment imposing a \$2/trip tax on capacity-1 (UberX-style) ride-hailing yields:

• Fleet moves from $v_j$3 to $v_j$4;
• Profit drops by 30%, VMT by 10.5%;
• Mode shares shift from (61.0, 13.5, 19.2, 6.3) to (36.4, 50.6, 5.1, 7.9) for (RH, RP, MT, transit);
• Public transit gains \$14,340 in fare revenue (Liu et al., 2018).

These results underscore MoDES’s capability to capture nuanced trade-offs between operator profit, total VMT, passenger-time metrics, and public-transit outcomes.

6. Scenario Flexibility and Policy Evaluation

MoDES supports rich what-if scenario and policy analysis: various forms of passenger utility, congestion or emissions pricing, and exogenous constraints can be introduced by adjusting utility coefficients, adding fares/costs, or constraining fleet variables. Each scenario can be re-optimized via BO, enabling rapid assessment of policy impacts at the system level—incorporating full equilibrium feedback, which fixed-demand MoD models inherently miss (Liu et al., 2018).

7. Significance and Outlook

MoDES advances multimodal transportation system design by tightly coupling endogenous mode-choice (learned from user preferences) with detailed, state-of-the-art MoD operations, and optimizing supply using statistical surrogates. Its capability to simulate, calibrate, and optimize full-scale, city-level multimodal systems allows for principled quantification of future MoD/transit deployments and policy interventions.

This tightly layered approach—bottom-up state dynamics, endogenous behavioral modeling, and top-down optimization—establishes a paradigm for comprehensive urban mobility systems analysis, with direct applicability to subsidy design, congestion pricing, and regulatory impact assessment (Liu et al., 2018).