Mining companies have complex supply chains that start from the mining location and stretch thousands of kilometers to the end customer in a different country and continent. The logistics of moving the materials from mines to ship is composed of series of optimization problems like berth allocation , ship scheduling , stockyard scheduling , and rail scheduling , which are individually NP-hard. In this paper, we present a scheduling application, called as IBM Optimization: Mine to Ship , for end-to-end integrated operations scheduling. The application is built on IBM ILOG ODM Enterprise with advanced features like rescheduling under deviations and disturbances, and maintenance scheduling. The modeling and computational complexity of integrated scheduling optimization is tamed using hybrid optimization technique that leverages mathematical programming and constraint programming. The application will benefit the mining companies with increased resource usage, higher throughput, reduced cost of operations, and higher revenue.

Flight controllers manage the orientation and modes of eight large solar arrays that power the International Space Station (ISS). The task requires generating plans that balance complex constraints and preferences. These considerations include context-dependent constraints on viable solar array configurations, temporal limits on transitions between configurations, and preferences on which considerations have priority. The Solar Array Constraint Engine (SACE) treats this operations planning problem as a sequence of tractable constrained optimization problems. SACE uses constraint management and automated planning capabilities to reason about the constraints, to find optimal array configurations subject to these constraints and solution preferences, and to automatically generate solar array operations plans.

We describe the Fast Greedy Sparse Subspace Clustering (FGSSC) algorithm providing an efficient method for clustering data belonging to a few low-dimensional linear or affine subspaces. The main difference of our algorithm from predecessors is its ability to work with noisy data having a high rate of erasures (missed entries with the known coordinates) and errors (corrupted entries with unknown coordinates). We discuss here how to implement the fast version of the greedy algorithm with the maximum efficiency whose greedy strategy is incorporated into iterations of the basic algorithm. We provide numerical evidences that, in the subspace clustering capability, the fast greedy algorithm outperforms not only the existing state-of-the art SSC algorithm taken by the authors as a basic algorithm but also the recent GSSC algorithm. At the same time, its computational cost is only slightly higher than the cost of SSC. The numerical evidence of the algorithm significant advantage is presented for a few synthetic models as well as for the Extended Yale B dataset of facial images. In particular, the face recognition misclassification rate turned out to be 6-20 times lower than for the SSC algorithm. We provide also the numerical evidence that the FGSSC algorithm is able to perform clustering of corrupted data efficiently even when the sum of subspace dimensions significantly exceeds the dimension of the ambient space.

Ideas from the image processing literature have recently motivated a new set of clustering algorithms that rely on the concept of total variation. While these algorithms perform well for bi-partitioning tasks, their recursive extensions yield unimpressive results for multiclass clustering tasks. This paper presents a general framework for multiclass total variation clustering that does not rely on recursion. The results greatly outperform previous total variation algorithms and compare well with state-of-the-art NMF approaches.

Latent Gaussian models (LGMs) are widely used in statistics and machine learning. Bayesian inference in non-conjugate LGMs is difficult due to intractable integrals involving the Gaussian prior and non-conjugate likelihoods. Algorithms based on variational Gaussian (VG) approximations are widely employed since they strike a favorable balance between accuracy, generality, speed, and ease of use. However, the structure of the optimization problems associated with these approximations remains poorly understood, and standard solvers take too long to converge. We derive a novel dual variational inference approach that exploits the convexity property of the VG approximations. We obtain an algorithm that solves a convex optimization problem, reduces the number of variational parameters, and converges much faster than previous methods. Using real-world data, we demonstrate these advantages on a variety of LGMs, including Gaussian process classification, and latent Gaussian Markov random fields.

We show an efficient algorithm for the following problem: Given uniformly random points from an arbitrary n-dimensional simplex, estimate the simplex. The size of the sample and the number of arithmetic operations of our algorithm are polynomial in n. This answers a question of Frieze, Jerrum and Kannan [FJK]. Our result can also be interpreted as efficiently learning the intersection of n+1 half-spaces in R^n in the model where the intersection is bounded and we are given polynomially many uniform samples from it. Our proof uses the local search technique from Independent Component Analysis (ICA), also used by [FJK]. Unlike these previous algorithms, which were based on analyzing the fourth moment, ours is based on the third moment. We also show a direct connection between the problem of learning a simplex and ICA: a simple randomized reduction to ICA from the problem of learning a simplex. The connection is based on a known representation of the uniform measure on a simplex. Similar representations lead to a reduction from the problem of learning an affine transformation of an n-dimensional l_p ball to ICA.

Although nonnegative matrix factorization (NMF) is NP-hard in general, it has been shown very recently that it is tractable under the assumption that the input nonnegative data matrix is close to being separable (separability requires that all columns of the input matrix belongs to the cone spanned by a small subset of these columns). Since then, several algorithms have been designed to handle this subclass of NMF problems. In particular, Bittorf, Recht, R\'e and Tropp (`Factoring nonnegative matrices with linear programs', NIPS 2012) proposed a linear programming model, referred to as Hottopixx. In this paper, we provide a new and more general robustness analysis of their method. In particular, we design a provably more robust variant using a post-processing strategy which allows us to deal with duplicates and near duplicates in the dataset.

In this paper is proposed a new heuristic approach belonging to the field of evolutionary Estimation of Distribution Algorithms (EDAs). EDAs builds a probability model and a set of solutions is sampled from the model which characterizes the distribution of such solutions. The main framework of the proposed method is an estimation of distribution algorithm, in which an adaptive Gibbs sampling is used to generate new promising solutions and, in combination with a local search strategy, it improves the individual solutions produced in each iteration. The Estimation of Distribution Algorithm with Adaptive Gibbs Sampling we are proposing in this paper is called AGEDA. We experimentally evaluate and compare this algorithm against two deterministic procedures and several stochastic methods in three well known test problems for unconstrained global optimization. It is empirically shown that our heuristic is robust in problems that involve three central aspects that mainly determine the difficulty of global optimization problems, namely high-dimensionality, multi-modality and non-smoothness.

We address a dynamic repair shop scheduling problem in the context of military aircraft fleet management where the goal is to maintain a full complement of aircraft over the long-term. A number of flights, each with a requirement for a specific number and type of aircraft, are already scheduled over a long horizon. We need to assign aircraft to flights and schedule repair activities while considering the flights requirements, repair capacity, and aircraft failures. The number of aircraft awaiting repair dynamically changes over time due to failures and it is therefore necessary to rebuild the repair schedule online. To solve the problem, we view the dynamic repair shop as successive static repair scheduling sub-problems over shorter time periods. We propose a complete approach based on the logic-based Benders decomposition to solve the static sub-problems, and design different rescheduling policies to schedule the dynamic repair shop. Computational experiments demonstrate that the Benders model is able to find and prove optimal solutions on average four times faster than a mixed integer programming model. The rescheduling approach having both aspects of scheduling over a longer horizon and quickly adjusting the schedule increases aircraft available in the long term by 10% compared to the approaches having either one of the aspects alone.

We developed a new quantum annealing (QA) algorithm for Dirichlet process mixture (DPM) models based on the Chinese restaurant process (CRP). QA is a parallelized extension of simulated annealing (SA), i.e., it is a parallel stochastic optimization technique. Existing approaches [Kurihara et al. UAI2009, Sato et al. UAI2009] and cannot be applied to the CRP because their QA framework is formulated using a fixed number of mixture components. The proposed QA algorithm can handle an unfixed number of classes in mixture models. We applied QA to a DPM model for clustering vertices in a network where a CRP seating arrangement indicates a network partition. A multi core processor was used for running QA in experiments, the results of which show that QA is better than SA, Markov chain Monte Carlo inference, and beam search at finding a maximum a posteriori estimation of a seating arrangement in the CRP. Since our QA algorithm is as easy as to implement the SA algorithm, it is suitable for a wide range of applications.