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The introduction of autonomous vehicles (AVs) to consumer markets will expedite the trend of car sharing and enable co‐owning or co‐leasing a car. In this paper, we consider a combinatorial auction market for fractional ownership of AVs, which is unique in two aspects. First, items are neither predefined nor discrete; rather, items are continuous time slots defined by bidders. Second, the spatial information of bidders should be incorporated within the winner determination problem (WDP) so that sharing a vehicle is indeed a viable plan. The consideration of spatial information increases the computational complexity significantly. We formulate the WDP, which plays a critical role in various auction designs and pricing schemes, for both discrete‐ and continuous‐time settings. In terms of social welfare maximization, we show that the continuous‐time model is superior to the discrete‐time model. We provide a conflict‐based reformulation of the continuous‐time model, for which we develop an effective solution approach based on a heuristic and maximal clique based reformulations. Using samples of the 2010–2012 California Household Travel Survey, we verify that the proposed solution methods provide effective computational tools for the combinatorial auction with bidder‐defined items.

This study designs a new market for fractional ownership of autonomous vehicles (AVs), in which an AV is co‐leased by a group of individuals. We present a practical iterative auction based on the combinatorial clock auction to match the interested customers together and determine their payments. In designing such an auction, we consider continuous‐time items (time slots) that are defined by bidders and naturally exploit driverless mobility of AVs to form co‐leasing groups. To relieve the computational burdens of both bidders and the auctioneer, we devise user agents who generate packages and bid on behalf of bidders. Through numerical experiments using the California 2010–2012 travel survey, we test the performance of the auction design. We also compare various bidding strategies and study the effect of activity rules on the bidders' payoffs. We find that the designed activity rules successfully remove the strategic behavior of bidders. We also find that core‐selecting payment rule brings the largest revenue to the auctioneer in most cases.

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Reinforcement learning has recently shown promise in learning quality solutions in many combinatorial optimization problems. In particular, the attention-based encoder-decoder models show high effectiveness on various routing problems, including the Traveling Salesman Problem (TSP). Unfortunately, they perform poorly for the TSP with Drone (TSP-D), requiring routing a heterogeneous fleet of vehicles in coordination-a truck and a drone. In TSP-D, the two vehicles are moving in tandem and may need to wait at a node for the other vehicle to join. State-less attention-based decoder fails to make such coordination between vehicles. We propose an attention encoder-LSTM decoder hybrid model, in which the decoder's hidden state can represent the sequence of actions made. We empirically demonstrate that such a hybrid model improves upon a purely attention-based model for both solution quality and computational efficiency. Our experiments on the min-max Capacitated Vehicle Routing Problem (mmCVRP) also confirm that the hybrid model is more suitable for coordinated routing of multiple vehicles than the attention-based model.