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

Efficient Benchmarking of Algorithm Configuration Procedures via Model-Based Surrogates

The optimization of algorithm (hyper-)parameters is crucial for achieving peak performance across a wide range of domains, ranging from deep neural networks to solvers for hard combinatorial problems. The resulting algorithm configuration (AC) problem has attracted much attention from the machine learning community. However, the proper evaluation of new AC procedures is hindered by two key hurdles. First, AC benchmarks are hard to set up. Second and even more significantly, they are computationally expensive: a single run of an AC procedure involves many costly runs of the target algorithm whose performance is to be optimized in a given AC benchmark scenario. One common workaround is to optimize cheap-to-evaluate artificial benchmark functions (e.g., Branin) instead of actual algorithms; however, these have different properties than realistic AC problems. Here, we propose an alternative benchmarking approach that is similarly cheap to evaluate but much closer to the original AC problem: replacing expensive benchmarks by surrogate benchmarks constructed from AC benchmarks. These surrogate benchmarks approximate the response surface corresponding to true target algorithm performance using a regression model, and the original and surrogate benchmark share the same (hyper-)parameter space. In our experiments, we construct and evaluate surrogate benchmarks for hyperparameter optimization as well as for AC problems that involve performance optimization of solvers for hard combinatorial problems, drawing training data from the runs of existing AC procedures. We show that our surrogate benchmarks capture overall important characteristics of the AC scenarios, such as high- and low-performing regions, from which they were derived, while being much easier to use and orders of magnitude cheaper to evaluate

The Configurable SAT Solver Challenge (CSSC)

It is well known that different solution strategies work well for different types of instances of hard combinatorial problems. As a consequence, most solvers for the propositional satisfiability problem (SAT) expose parameters that allow them to be customized to a particular family of instances. In the international SAT competition series, these parameters are ignored: solvers are run using a single default parameter setting (supplied by the authors) for all benchmark instances in a given track. While this competition format rewards solvers with robust default settings, it does not reflect the situation faced by a practitioner who only cares about performance on one particular application and can invest some time into tuning solver parameters for this application. The new Configurable SAT Solver Competition (CSSC) compares solvers in this latter setting, scoring each solver by the performance it achieved after a fully automated configuration step. This article describes the CSSC in more detail, and reports the results obtained in its two instantiations so far, CSSC 2013 and 2014

Handling software upgradeability problems with MILP solvers

Upgradeability problems are a critical issue in modern operating systems. The problem consists in finding the "best" solution according to some criteria, to install, remove or upgrade packages in a given installation. This is a difficult problem: the complexity of the upgradeability problem is NP complete and modern OS contain a huge number of packages (often more than 20 000 packages in a Linux distribution). Moreover, several optimisation criteria have to be considered, e.g., stability, memory efficiency, network efficiency. In this paper we investigate the capabilities of MILP solvers to handle this problem. We show that MILP solvers are very efficient when the resolution is based on a linear combination of the criteria. Experiments done on real benchmarks show that the best MILP solvers outperform CP solvers and that they are significantly better than Pseudo Boolean solvers.Comment: In Proceedings LoCoCo 2010, arXiv:1007.083

ASlib: A Benchmark Library for Algorithm Selection

The task of algorithm selection involves choosing an algorithm from a set of algorithms on a per-instance basis in order to exploit the varying performance of algorithms over a set of instances. The algorithm selection problem is attracting increasing attention from researchers and practitioners in AI. Years of fruitful applications in a number of domains have resulted in a large amount of data, but the community lacks a standard format or repository for this data. This situation makes it difficult to share and compare different approaches effectively, as is done in other, more established fields. It also unnecessarily hinders new researchers who want to work in this area. To address this problem, we introduce a standardized format for representing algorithm selection scenarios and a repository that contains a growing number of data sets from the literature. Our format has been designed to be able to express a wide variety of different scenarios. Demonstrating the breadth and power of our platform, we describe a set of example experiments that build and evaluate algorithm selection models through a common interface. The results display the potential of algorithm selection to achieve significant performance improvements across a broad range of problems and algorithms.Comment: Accepted to be published in Artificial Intelligence Journa

An ADMM Based Framework for AutoML Pipeline Configuration

We study the AutoML problem of automatically configuring machine learning pipelines by jointly selecting algorithms and their appropriate hyper-parameters for all steps in supervised learning pipelines. This black-box (gradient-free) optimization with mixed integer & continuous variables is a challenging problem. We propose a novel AutoML scheme by leveraging the alternating direction method of multipliers (ADMM). The proposed framework is able to (i) decompose the optimization problem into easier sub-problems that have a reduced number of variables and circumvent the challenge of mixed variable categories, and (ii) incorporate black-box constraints along-side the black-box optimization objective. We empirically evaluate the flexibility (in utilizing existing AutoML techniques), effectiveness (against open source AutoML toolkits),and unique capability (of executing AutoML with practically motivated black-box constraints) of our proposed scheme on a collection of binary classification data sets from UCI ML& OpenML repositories. We observe that on an average our framework provides significant gains in comparison to other AutoML frameworks (Auto-sklearn & TPOT), highlighting the practical advantages of this framework