Large-scale ride-hailing systems often combine real-time routing at the individual request level with a macroscopic Model Predictive Control (MPC) optimization for dynamic pricing and vehicle relocation. The MPC relies on a demand forecast and optimizes over a longer time horizon to compensate for the myopic nature of the routing optimization. However, the longer horizon increases computational complexity and forces the MPC to operate at coarser spatial-temporal granularity, degrading the quality of its decisions. This paper addresses these computational challenges by learning the MPC optimization. The resulting machine-learning model then serves as the optimization proxy and predicts its optimal solutions. This makes it possible to use the MPC at higher spatial-temporal fidelity, since the optimizations can be solved and learned offline. Experimental results show that the proposed approach improves quality of service on challenging instances from the New York City dataset.
A critical aspect of power systems research is the availability of suitable data, access to which is limited by privacy concerns and the sensitive nature of energy infrastructure. This lack of data, in turn, hinders the development of modern research avenues such as machine learning approaches or stochastic formulations. To overcome this challenge, this paper proposes a systematic, data-driven framework for reconstructing high-fidelity time series, using publicly-available grid snapshots and historical data published by transmission system operators. The proposed approach, from geo-spatial data and generation capacity reconstruction, to time series disaggregation, is applied to the French transmission grid. Thereby, synthetic but highly realistic time series data, spanning multiple years with a 5-minute granularity, is generated at the individual component level.
The Jobs shop Scheduling Problem (JSP) is a canonical combinatorial optimization problem that is routinely solved for a variety of industrial purposes. It models the optimal scheduling of multiple sequences of tasks, each under a fixed order of operations, in which individual tasks require exclusive access to a predetermined resource for a specified processing time. The problem is NP-hard and computationally challenging even for medium-sized instances. Motivated by the increased stochasticity in production chains, this paper explores a deep learning approach to deliver efficient and accurate approximations to the JSP. In particular, this paper proposes the design of a deep neural network architecture to exploit the problem structure, its integration with Lagrangian duality to capture the problem constraints, and a post-processing optimization to guarantee solution feasibility.The resulting method, called JSP-DNN, is evaluated on hard JSP instances from the JSPLIB benchmark library. Computational results show that JSP-DNN can produce JSP approximations of high quality at negligible computational costs.
Optimization problems are ubiquitous in our societies and are present in almost every segment of the economy. Most of these optimization problems are NP-hard and computationally demanding, often requiring approximate solutions for large-scale instances. Machine learning frameworks that learn to approximate solutions to such hard optimization problems are a potentially promising avenue to address these difficulties, particularly when many closely related problem instances must be solved repeatedly. Supervised learning frameworks can train a model using the outputs of pre-solved instances. However, when the outputs are themselves approximations, when the optimization problem has symmetric solutions, and/or when the solver uses randomization, solutions to closely related instances may exhibit large differences and the learning task can become inherently more difficult. This paper demonstrates this critical challenge, connects the volatility of the training data to the ability of a model to approximate it, and proposes a method for producing (exact or approximate) solutions to optimization problems that are more amenable to supervised learning tasks. The effectiveness of the method is tested on hard non-linear nonconvex and discrete combinatorial problems.
Many special events, including sport games and concerts, often cause surges in demand and congestion for transit systems. Therefore, it is important for transit providers to understand their impact on disruptions, delays, and fare revenues. This paper proposes a suite of data-driven techniques that exploit Automated Fare Collection (AFC) data for evaluating, anticipating, and managing the performance of transit systems during recurring congestion peaks due to special events. This includes an extensive analysis of ridership of the two major stadiums in downtown Atlanta using rail data from the Metropolitan Atlanta Rapid Transit Authority (MARTA). The paper first highlights the ridership predictability at the aggregate level for each station on both event and non-event days. It then presents an unsupervised machine-learning model to cluster passengers and identify which train they are boarding. The model makes it possible to evaluate system performance in terms of fundamental metrics such as the passenger load per train and the wait times of riders. The paper also presents linear regression and random forest models for predicting ridership that are used in combination with historical throughput analysis to forecast demand. Finally, simulations are performed that showcase the potential improvements to wait times and demand matching by leveraging proposed techniques to optimize train frequencies based on forecasted demand.
Large-scale ride-sharing systems combine real-time dispatching and routing optimization over a rolling time horizon with a model predictive control(MPC) component that relocates idle vehicles to anticipate the demand. The MPC optimization operates over a longer time horizon to compensate for the inherent myopic nature of the real-time dispatching. These longer time horizons are beneficial for the quality of the decisions but increase computational complexity. To address this computational challenge, this paper proposes a hybrid approach that combines machine learning and optimization. The machine-learning component learns the optimal solution to the MPC optimization on the aggregated level to overcome the sparsity and high-dimensionality of the MPC solutions. The optimization component transforms the machine-learning predictions back to the original granularity via a tractable transportation model. As a consequence, the original NP-hard MPC problem is reduced to a polynomial time prediction and optimization. Experimental results show that the hybrid approach achieves 27% further reduction in rider waiting time than the MPC optimization, thanks to its ability to model a longer time horizon within the computational limits.
Agencies, such as the U.S. Census Bureau, release data sets and statistics about groups of individuals that are used as input to a number of critical decision processes. To conform to privacy and confidentiality requirements, these agencies are often required to release privacy-preserving versions of the data. This paper studies the release of differentially private data sets and analyzes their impact on some critical resource allocation tasks under a fairness perspective. {The paper shows that, when the decisions take as input differentially private data}, the noise added to achieve privacy disproportionately impacts some groups over others. The paper analyzes the reasons for these disproportionate impacts and proposes guidelines to mitigate these effects. The proposed approaches are evaluated on critical decision problems that use differentially private census data.
This paper surveys the recent attempts at leveraging machine learning to solve constrained optimization problems. It focuses on surveying the work on integrating combinatorial solvers and optimization methods with machine learning architectures. These approaches hold the promise to develop new hybrid machine learning and optimization methods to predict fast, approximate, solutions to combinatorial problems and to enable structural logical inference. This paper presents a conceptual review of the recent advancements in this emerging area.
This paper proposes a novel machine-learning approach for predicting AC-OPF solutions that features a fast and scalable training. It is motivated by the two critical considerations: (1) the fact that topology optimization and the stochasticity induced by renewable energy sources may lead to fundamentally different AC-OPF instances; and (2) the significant training time needed by existing machine-learning approaches for predicting AC-OPF. The proposed approach is a 2-stage methodology that exploits a spatial decomposition of the power network that is viewed as a set of regions. The first stage learns to predict the flows and voltages on the buses and lines coupling the regions, and the second stage trains, in parallel, the machine-learning models for each region. Experimental results on the French transmission system (up to 6,700 buses and 9,000 lines) demonstrate the potential of the approach. Within a short training time, the approach predicts AC-OPF solutions with very high fidelity and minor constraint violations, producing significant improvements over the state-of-the-art. The results also show that the predictions can seed a load flow optimization to return a feasible solution within 0.03% of the AC-OPF objective, while reducing running times significantly.