Achieving Consistency with Cutting Planes

Cutting planes accelerate branch-and-bound search primarily by cutting off fractional solutions of the linear programming (LP) relaxation, resulting in tighter bounds for pruning the search tree. Yet cutting planes can also reduce backtracking by excluding inconsistent partial assignments that occur in the course of branching. A partial assignment is inconsistent with a constraint set when … Read more

Consistency for 0-1 programming

Concepts of consistency have long played a key role in constraint programming but never developed in integer programming (IP). Consistency nonetheless plays a role in IP as well. For example, cutting planes can reduce backtracking by achieving various forms of consistency as well as by tightening the linear programming (LP) relaxation. We introduce a type … Read more

Seamless Multimodal Transportation Scheduling

Ride-hailing services have expanded the role of shared mobility in passenger transportation systems, creating new markets and creative planning solutions for major urban centers. In this paper, we consider their use for last-mile passenger transportation in coordination with a mass transit service to provide a seamless multimodal transportation experience for the user. A system that … Read more

The Integrated Last-Mile Transportation Problem

Last-mile transportation (LMT) refers to any service that moves passengers from a hub of mass transportation (MT), such as air, boat, bus, or train, to destinations, such as a home or an office. In this paper, we introduce the problem of scheduling passengers jointly on MT and LMT services, with passengers sharing a car, van, … Read more

Compact Representation of Near-Optimal Integer Programming Solutions

It is often useful in practice to explore near-optimal solutions of an integer programming problem. We show how all solutions within a given tolerance of the optimal value can be efficiently and compactly represented in a weighted decision diagram, once the optimal value is known. The structure of a decision diagram facilitates rapid processing of … Read more

Modeling with Metaconstraints and Semantic Typing of Variables

Recent research in hybrid optimization shows that a combination of technologies that exploits their complementary strengths can significantly speed up computation. The use of high-level metaconstraints in the problem formulation can achieve a substantial share of these computational gains by better communicating problem structure to the solver. During the solution process, however, metaconstraints give rise … Read more