Integer Programming for Learning Directed Acyclic Graphs from Continuous Data

Learning directed acyclic graphs (DAGs) from data is a challenging task both in theory and in practice, because the number of possible DAGs scales superexponentially with the number of nodes. In this paper, we study the problem of learning an optimal DAG from continuous observational data. We cast this problem in the form of a mathematical programming model that can naturally incorporate a superstructure to reduce the set of possible candidate DAGs. We use a negative log-likelihood score function with both l0 and l1 penalties and propose a new mixed-integer quadratic program, referred to as a layered network (LN) formulation. The LN formulation is a compact model that enjoys as tight an optimal continuous relaxation value as the stronger but larger formulations under a mild condition. Computational results indicate that the proposed formulation outperforms existing mathematical formulations and scales better than available algorithms that can solve the same problem with only l1 regularization. In particular, the LN formulation clearly outperforms existing methods in terms of computational time needed to find an optimal DAG in the presence of a sparse superstructure.

Predictively Coordinated Vehicle Acceleration and Lane Selection Using Mixed Integer Programming

Autonomous vehicle technology provides the means to optimize motion planning beyond human capacity. In particular, the problem of navigating multi-lane traffic optimally for trip time, energy efficiency, and collision avoidance presents challenges beyond those of single-lane roadways. For example, the host vehicle must simultaneously track multiple obstacles, the drivable region is non-convex, and automated vehicles must obey social expectations. Furthermore, reactive decision-making may result in becoming stuck in an undesirable traffic position. This paper presents a fundamental approach to these problems using model predictive control with a mixed integer quadratic program at its core. Lateral and longitudinal movements are coordinated to avoid collisions, track a velocity and lane, and minimize acceleration. Vehicle-to-vehicle connectivity provides a preview of surrounding vehicles’ motion. Simulation results show a 79% reduction in congestion-induced travel time and an 80% decrease in congestion-induced fuel consumption compared to a rule-based approach.

Domiciling Truck Drivers More Strategically in a Transportation Network

The authors propose a method to better domicile truck drivers in a relay-point highway transportation network to obtain better solutions for the truck driver domiciling and sourcing problem. The authors exploit characteristics of the truckload driver routing problem over a transportation network and introduce a new approach to domicile, source, and route truck drivers while more inclusively considering performance and cost measures related to the driver, transportation carrier, and customer. Driver domicile and relay-point locations are exploited to balance driver pay and recruiting costs and driving time. A mixed integer quadratic program will determine where driver domiciles are located to base drivers, source drivers, route drivers, etc. while considering key costs related to transporting truckload freight over long distances. A method to improve driver domicile locations is introduced to enhance driving jobs and driver sourcing, but not at the expense of the transportation carrier and customer. A numerical experiment will be conducted.

Domiciling Truck Drivers More Strategically in a Transportation Network

The authors propose a method to better domicile truck drivers in a relay-point highway transportation network to obtain better solutions for the truck driver domiciling and sourcing problem. The authors exploit characteristics of the truckload driver routing problem over a transportation network and introduce a new approach to domicile, source, and route truck drivers while more inclusively considering performance and cost measures related to the driver, transportation carrier, and customer. Driver domicile and relay-point locations are exploited to balance driver pay and recruiting costs and driving time. A mixed integer quadratic program will determine where driver domiciles are located to base drivers, source drivers, route drivers, etc. while considering key costs related to transporting truckload freight over long distances. A method to improve driver domicile locations is introduced to enhance driving jobs and driver sourcing, but not at the expense of the transportation carrier and customer. A numerical experiment will be conducted.