Data-driven Distributionally Robust Optimization For Vehicle Balancing of Mobility-on-Demand Systems

Abstract

With the transformation to smarter cities and the development of technologies, a large amount of data is collected from sensors in real time. Services provided by ride-sharing systems such as taxis, mobility-on-demand autonomous vehicles, and bike sharing systems are popular. This paradigm provides opportunities for improving transportation systems’ performance by allocating ride-sharing vehicles toward predicted demand proactively. However, how to deal with uncertainties in the predicted demand probability distribution for improving the average system performance is still a challenging and unsolved task. Considering this problem, in this work, we develop a data-driven distributionally robust vehicle balancing method to minimize the worst-case expected cost. We design efficient algorithms for constructing uncertainty sets of demand probability distributions for different prediction methods and leverage a quad-tree dynamic region partition method for better capturing the dynamic spatial-temporal properties of the uncertain demand. We then derive an equivalent computationally tractable form for numerically solving the distributionally robust problem. We evaluate the performance of the data-driven vehicle balancing algorithm under different demand prediction and region partition methods based on four years of taxi trip data for New York City (NYC). We show that the average total idle driving distance is reduced by 30% with the distributionally robust vehicle balancing method using quad-tree dynamic region partitions, compared with vehicle balancing methods based on static region partitions without considering demand uncertainties. This is about a 60-million-mile or a 8-million-dollar cost reduction annually in NYC.

A Robust and Constrained Multi-Agent Reinforcement Learning Framework for Electric Vehicle AMoD Systems

“…We consider both the mobility supply-demand ratio [17], [23], [44] and the charging utilization rate [8], [9], [16], [45] in each region as service quality metrics for the EV AMoD system. However, with limited supply volume in a city, achieving high supply-demand ratios in all regions may not be possible.…”

“…The fairness metrics u s (s, a) and u m (s, a) are calculated given the EVs rebalancing action a, and the larger the better. One advantage of the proposed robust and constrained MARL formulation is that the form of the reward/cost function does not need to satisfy the requirements as those of the robust optimization methods [17], [35], e.g., the objective/constraints do not need to be convex of the decision variable or concave of the uncertain parameters.…”

“…Heuristics can lead to sub-optimal rebalancing solutions [19]. Other major categories of AMoD system rebalancing methods include optimization-based algorithms [17], Model Predictive Control (MPC) [20] and Reinforcement Learning (RL) [21].…”

Data-Driven Distributionally Robust Electric Vehicle Balancing for Mobility-on-Demand Systems under Demand and Supply Uncertainties

“…Instead of assuming we know the true probability distributions of r and c from data, in this work we construct uncertainty sets F r and F c that describe possible probability distributions of r and c by applying the Algorithm 2 proposed in [10] which constructs distributional sets with a general prediction model. Here we use the autoregressive integrated moving average model (ARIMA model) [18] as the prediction model to capture the spatial and temporal correlations for the predictions.…”

“…Since we don't have true value of the difference δ r = r − r (δ c = c − ĉ), we use estimation residuals to capture the information from these difference. Σr ( Σc ) is the estimated covariance, γ1r , γ2r (γ 1c , γ2c ) are two estimated threshold values of δ r (δ c ) by Algorithm 2 in [10] based on the concept of bootstrapping. More discussions about uncertainty set construction refer to [2], [10].…”