19,426 research outputs found
A General Large Neighborhood Search Framework for Solving Integer Programs
This paper studies how to design abstractions of large-scale combinatorial optimization problems that can leverage existing state-of-the-art solvers in general purpose ways, and that are amenable to data-driven design. The goal is to arrive at new approaches that can reliably outperform existing solvers in wall-clock time. We focus on solving integer programs, and ground our approach in the large neighborhood search (LNS) paradigm, which iteratively chooses a subset of variables to optimize while leaving the remainder fixed. The appeal of LNS is that it can easily use any existing solver as a subroutine, and thus can inherit the benefits of carefully engineered heuristic approaches and their software implementations. We also show that one can learn a good neighborhood selector from training data. Through an extensive empirical validation, we demonstrate that our LNS framework can significantly outperform, in wall-clock time, compared to state-of-the-art commercial solvers such as Gurobi
The Voice of Optimization
We introduce the idea that using optimal classification trees (OCTs) and
optimal classification trees with-hyperplanes (OCT-Hs), interpretable machine
learning algorithms developed by Bertsimas and Dunn [2017, 2018], we are able
to obtain insight on the strategy behind the optimal solution in continuous and
mixed-integer convex optimization problem as a function of key parameters that
affect the problem. In this way, optimization is not a black box anymore.
Instead, we redefine optimization as a multiclass classification problem where
the predictor gives insights on the logic behind the optimal solution. In other
words, OCTs and OCT-Hs give optimization a voice. We show on several realistic
examples that the accuracy behind our method is in the 90%-100% range, while
even when the predictions are not correct, the degree of suboptimality or
infeasibility is very low. We compare optimal strategy predictions of OCTs and
OCT-Hs and feedforward neural networks (NNs) and conclude that the performance
of OCT-Hs and NNs is comparable. OCTs are somewhat weaker but often
competitive. Therefore, our approach provides a novel insightful understanding
of optimal strategies to solve a broad class of continuous and mixed-integer
optimization problems
Human-Machine Collaborative Optimization via Apprenticeship Scheduling
Coordinating agents to complete a set of tasks with intercoupled temporal and
resource constraints is computationally challenging, yet human domain experts
can solve these difficult scheduling problems using paradigms learned through
years of apprenticeship. A process for manually codifying this domain knowledge
within a computational framework is necessary to scale beyond the
``single-expert, single-trainee" apprenticeship model. However, human domain
experts often have difficulty describing their decision-making processes,
causing the codification of this knowledge to become laborious. We propose a
new approach for capturing domain-expert heuristics through a pairwise ranking
formulation. Our approach is model-free and does not require enumerating or
iterating through a large state space. We empirically demonstrate that this
approach accurately learns multifaceted heuristics on a synthetic data set
incorporating job-shop scheduling and vehicle routing problems, as well as on
two real-world data sets consisting of demonstrations of experts solving a
weapon-to-target assignment problem and a hospital resource allocation problem.
We also demonstrate that policies learned from human scheduling demonstration
via apprenticeship learning can substantially improve the efficiency of a
branch-and-bound search for an optimal schedule. We employ this human-machine
collaborative optimization technique on a variant of the weapon-to-target
assignment problem. We demonstrate that this technique generates solutions
substantially superior to those produced by human domain experts at a rate up
to 9.5 times faster than an optimization approach and can be applied to
optimally solve problems twice as complex as those solved by a human
demonstrator.Comment: Portions of this paper were published in the Proceedings of the
International Joint Conference on Artificial Intelligence (IJCAI) in 2016 and
in the Proceedings of Robotics: Science and Systems (RSS) in 2016. The paper
consists of 50 pages with 11 figures and 4 table
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