Multimodal mobility systems provide seamless travel by integrating different types of transportation modes. Most existing studies model service operations and users’ travel choices independently or iteratively and constrained with pre-defined multimodal travel options. The paper proposes a choice-based optimization approach that optimizes service operations with explicitly embedded travelers’ choices described by the multinomial logit (MNL) model. It allows the flexible combination of travel modes and routes in multimodal mobility systems. We propose a computationally efficient linearization method for transformed MNL constraints with bounded errors to solve the choice-based optimization model. The model is validated using a mobility on demand and public transport network by comparing it with a simulation sampling-based MNL linearization method. The results show that the mixed-integer formulation provides a high-quality solution in terms of both the estimated choice probability errors and computational speed. We also conduct an error analysis and a sensitivity analysis to explore the behavior of the proposed approach. The real-world case study in Stockholm further illustrates that the analytical formulation achieves a better system operation performance than the traditional iterative supply–demand updating optimization method. The choice-based optimization model and solution formulation are highly adaptable for operations decision support integrating stochastic travel choices in multimodal mobility systems.

This study proposes an integer linear program model for ride-sharing, electric, autonomous mobility on demand (RE-AMoD) system operations and develops a model predictive control (MPC) algorithm to optimize the decisions of ride matching, vehicle routing, rebalancing, and charging. The system ensures that electric autonomous vehicles provide transportation services for up to two customers to share a ride and that they can be charged automatically during the operating period. The RE-AMoD problem is formulated as a network flow optimization problem considering ride-sharing and charging control. The objective is to minimize the customers' waiting time while minimizing the system's energy consumption. An iterative MPC is developed to compute the optimal control policy for real-time control. The case study uses real-world data from San Francisco to validate the model performance by comparing benchmark models in an RE-AMoD simulation platform and investigating the impact of ride-sharing and smart charging strategies on system performance by comparing models with no ride-sharing and heuristic charging strategies. The results show that the smart charging policy is critical for realizing ride-sharing's full advantages in RE-AMoD systems. Allowing the sharing of trips significantly improves system performance in terms of reducing fleet sizes and energy consumption while improving the customer level of service.

Multimodal mobility systems provide seamless service by integrating various travel modes like driving, cycling, Mobility-on-Demand (MoD) services, and Public Transit (PT) services. With the advancement in autonomous driving and electric vehicles, MoD services show their significant potential in coordinating with other travel modes, especially for PT services. To make the best use of its potential, it is essential to investigate the planning and operations of MoD and PT services in the multimodal mobility system.

In the multimodal mobility system, service operations on the supply side should focus on intermodal coordination. On the demand side, customers decide on routes and modes according to service levels such as travel time and price.However, research gaps exist in the planning and operations of integrated MoD and PT services. First, existing literature lacks in optimizing service operations that conform to customer behavior for multimodal mobility systems. Second, existing methods are not applicable to solve such an optimization problem with consistent 'expected' (from service operations) and 'actual' customer behavior. Third, there is a lack of operational optimization models with temporal dynamics for electric MoD vehicles integrated with PT service. To address the above issues, the included papers propose (1) service operation planning in multimodal mobility systems, (2) a generic mathematical solution algorithm for the choice-based optimization problem, and (3) electric MoD operation in multimodal mobility systems.

Paper I proposes a choice-based optimization model for planning MoD services in the multimodal system with the consideration of customer behavior. The optimization of service operations embeds the travelers' choices over modes and routes through a multinomial logit (MNL) model. An efficient linearization method is proposed for transformed MNL constraints to solve the choice-based optimization model. The case study and numerical experiments demonstrate the method's accuracy, efficiency, and advantages compared to existing methods. Paper II further extends the approach to propose the generic outer-inner approximation methods to solve the choice-based optimization problem, which is applicable to problems, such as, location planning, network expansion, and pricing.  

Paper III optimizes the integrated operations between MoD and PT services through a network flow model describing the interactions among customer flows, MoD vehicles, and PT services. It embeds the temporal dynamics and charging actions of MoD vehicles using the expanded network with each dimension representing a location, a moment, a state of charge, or a mode. The case study uses real data in Färingsö island, Stockholm. The results show that, compared to existing PT services, the integration of 10 MoD vehicles generally reduces 11.35% average travel time and 1.90% average travel distance. It also significantly (around 40%) reduces maximum travel time, average waiting time, average initial waiting time, and average/maximum transfer time for customers.  The intermodal transfers mainly happen in limited locations, suggesting that only minor modifications to the existing infrastructure are required for the integration.

Multimodala transportsystem erbjuder sömlösa tjänster genom att integrera olika reseformer som bilkörning, cykling, Mobility-on-Demand (MoD)-tjänster och kollektivtrafik (PT). Med framstegen inom autonom körning och elfordon visar MoD-tjänster betydande potential för samordning med andra reseformer, särskilt kollektivtrafiken. För att utnyttja denna potential fullt ut är det nödvändigt att undersöka planering och drift av MoD och PT i ett multimodalt system.

I det multimodala transportsystemet bör serviceoperationer på utbudssidan fokusera på intermodell samordning. På efterfrågesidan väljer kunder rutter och färdmedel baserat på servicekvalitet såsom restid och pris. Dock existerar forskningsluckor i planering och drift av integrerade MoD- och PT-tjänster. Först och främst saknar befintlig litteratur optimering av serviceoperationer som anpassas till kundbeteende i multimodala system. För det andra är befintliga metoder inte lämpliga för att lösa optimeringsproblem som balanserar förväntat beteende (från serviceoperationer) och äkta kundbeteende. För det tredje saknas operativa optimeringsmodeller med tidsdynamik för elburna MoD-fordon integrerade med PT. För att adressera dessa problem presenterar artiklarna: (1) planering av serviceoperationer i multimodala system, (2) en generisk matematisk lösningsalgoritm för valbaserade optimeringsproblem, och (3) drift av elburna MoD-fordon i multimodala system.

Artikel I presenterar en valbaserad optimeringsmodell för MoD-planering i multimodala system med hänsyn till kundbeteende. Optimeringen integrerar resenärers val av färdmedel och rutter via en multinomial logit (MNL)-modell. En effektiv lineariseringsmetod för transformerade MNL-begränsningar föreslås för att lösa modellen. Fallstudier och numeriska experiment demonstrerar metodens precision, effektivitet och fördelar jämfört med befintliga metoder. Artikel II utvidgar tillvägagångssättet genom att föreslå generiska yttre-inre approximationsmetoder för att lösa valbaserade optimeringsproblem, tillämpbara på problem som lokaliseringsplanering, nätverksutbyggnad och prissättning.

Artikel III optimerar samverkan mellan MoD och PT genom en nätverksflödesmodell som beskriver interaktioner mellan kundflöden, MoD-fordon och PT. Modellen integrerar tidsdynamik och laddningsbeteende för MoD-fordon via ett expanderat nätverk där varje dimension representerar plats, tidpunkt, laddningstillstånd eller färdmedel. En fallstudie med verkliga data från Färingsö i Stockholm visar att integrering av 10 MoD-fordon generellt minskar genomsnittlig restid med 11,35% och reslängd med 1,90%. Dessutom minskar maximal restid, genomsnittlig väntetid, inledande väntetid samt genomsnittlig/maximal bytestid markant (40%). Intermodella byten äger huvudsakligen rum på begränsade platser, vilket indikerar att endast små infrastrukturanpassningar krävs för integrationen.

Multimodal mobility systems provide seamless travel by integrating different types of transportation modes. Most existing studies model service operations and travelers’ choices independently or limited in multimodal travel options. We propose a choice-based optimization model for optimal operations of multimodal mobility systems with embedded travelers’ choices using a multinomial logit (MNL) model. We derive a mixed-integer linear formulation for the problem by linearizing transformed MNL constraints with bounded errors. The preliminary experimental test for a small mobility on demand and public transport network shows the model provides a good solution quality.

Different urban transportation flows (e.g., passenger journeys, freight distribution, and waste management) are conventionally separately handled by corresponding single-purpose vehicles (SVs). The multi-purpose vehicle (MV) is a novel vehicle concept that can enable the sequential sharing of different transportation flows by changing the so-called modules, thus theoretically improving the efficiency of urban transportation through the utilization of higher vehicles. In this study, a variant of the pick-up and delivery problem with time windows is established to describe the sequential sharing problem considering both MVs and SVs with features of multiple depots, partial recharging strategies, and fleet sizing. MVs can change their load modules to carry all item types that can also be carried by SVs. To solve the routing problem, an adaptive large neighborhood search (ALNS) algorithm is developed with new problem-specific heuristics. The proposed ALNS is tested on 15 small-size cases and evaluated using a commercial MIP solver. Results show that the proposed algorithm is time-efficient and able to generate robust and high-quality solutions. We investigate the performance of the ALNS algorithm by analyzing convergence and selection probabilities of the heuristic solution that destroy and repair operators. On 15 large-size instances, we compare results for pure SV, pure MV, and mixed fleets, showing that the introduction of MVs can allow smaller fleet sizes while approximately keeping the same total travel distance as for pure SVs.

Choice-based optimization problem integrates demand modeling into optimal supply decisions, which is generic for decision-making applications. Solving the problem is challenging given the nonlinear discrete choice model constraints. Existing solution methods are limited to specific problem structures, such as binary or discrete supply decisions and fixed option attributes. This paper proposes an outer-inner approximation method for the generic choice-based optimization problem without specific problem structural requirements. We validated the method using a network expansion problem on the SiouxFalls network, aiming to reduce the overall system congestion by optimally expanding road capacities considering the road expansion cost. The results show that the expansion cost is significantly lower than the total travel time savings. More experiments are expected to benchmark with existing models using more case studies, e.g., service frequency and pricing in multimodal transportation systems.

This paper optimizes the vehicle operation and charging for integrated electric mobility-on-demand services and public transit in the multimodal mobility system. The advancement in automatic driving and electric vehicles introduces challenges in operating MoD services jointly with PT services. However, existing literature on optimizing multimodal mobility systems lacks (1) the energy capacity and en-route charging behavior of MoD services, and (2) the temporal dynamics. We propose an generic network flow model to optimize an electric multimodal mobility system by representing the temporal interactions among customers, electric MoD vehicles, and PT services. The model captures (1) the traveling, waiting, and inter-/intra-mode transfers of customers, (2) the routing, rebalancing, waiting, and charging of MoD vehicles, and (3) the schedules and routes of PT services. We perform a case study based on a real dataset from Färingsö island, Stockholm. We compare the existing PT services and the electric multimodal mobility system integrating MoD with PT. The results suggest the integration can overall reduce 11.35% average travel time and 1.90% average travel distance for customers. It also significantly decreases the average initial waiting time (44.59%), maximum travel time (50.00%), and average transfer time (38.20%) for customers. Moreover, the intermodal transfers mainly occur in one location on the island, indicating a minor modification of existing infrastructure for the challenging service coordination problem in the multimodal mobility systems.