26,631 research outputs found

    Evolutionary Synthesis of HVAC System Configurations: Algorithm Development.

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    This paper describes the development of an optimization procedure for the synthesis of novel heating, ventilating, and air-conditioning (HVAC) system configurations. Novel HVAC system designs can be synthesized using model-based optimization methods. The optimization problem can be considered as having three sub-optimization problems; the choice of a component set; the design of the topological connections between the components; and the design of a system operating strategy. In an attempt to limit the computational effort required to obtain a design solution, the approach adopted in this research is to solve all three sub-problems simultaneously. Further, the computational effort has been limited by implementing simplified component models and including the system performance evaluation as part of the optimization problem (there being no need in this respect to simulation the system performance). The optimization problem has been solved using a Genetic Algorithm (GA), with data structures and search operators that are specifically developed for the solution of HVAC system optimization problems (in some instances, certain of the novel operators may also be used in other topological optimization problems. The performance of the algorithm, and various search operators has been examined for a two-zone optimization problem (the objective of the optimization being to find a system design that minimizes the system energy use). In particular, the performance of the algorithm in finding feasible system designs has been examined. It was concluded that the search was unreliable when the component set was optimized, but if the component set was fixed as a boundary condition on the search, then the algorithm had an 81% probability of finding a feasible system design. The optimality of the solutions is not examined in this paper, but is described in an associated publication. It was concluded that, given a candidate set of system components, the algorithm described here provides an effective tool for exploring the novel design of HVAC systems. (c) HVAC & R journa

    Hybrid Algorithms Based on Integer Programming for the Search of Prioritized Test Data in Software Product Lines

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    In Software Product Lines (SPLs) it is not possible, in general, to test all products of the family. The number of products denoted by a SPL is very high due to the combinatorial explosion of features. For this reason, some coverage criteria have been proposed which try to test at least all feature interactions without the necessity to test all products, e.g., all pairs of features (pairwise coverage). In addition, it is desirable to first test products composed by a set of priority features. This problem is known as the Prioritized Pairwise Test Data Generation Problem. In this work we propose two hybrid algorithms using Integer Programming (IP) to generate a prioritized test suite. The first one is based on an integer linear formulation and the second one is based on a integer quadratic (nonlinear) formulation. We compare these techniques with two state-of-the-art algorithms, the Parallel Prioritized Genetic Solver (PPGS) and a greedy algorithm called prioritized-ICPL. Our study reveals that our hybrid nonlinear approach is clearly the best in both, solution quality and computation time. Moreover, the nonlinear variant (the fastest one) is 27 and 42 times faster than PPGS in the two groups of instances analyzed in this work.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech. Partially funded by the Spanish Ministry of Economy and Competitiveness and FEDER under contract TIN2014-57341-R, the University of Málaga, Andalucía Tech and the Spanish Network TIN2015-71841-REDT (SEBASENet)

    Best Subset Selection via a Modern Optimization Lens

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    In the last twenty-five years (1990-2014), algorithmic advances in integer optimization combined with hardware improvements have resulted in an astonishing 200 billion factor speedup in solving Mixed Integer Optimization (MIO) problems. We present a MIO approach for solving the classical best subset selection problem of choosing kk out of pp features in linear regression given nn observations. We develop a discrete extension of modern first order continuous optimization methods to find high quality feasible solutions that we use as warm starts to a MIO solver that finds provably optimal solutions. The resulting algorithm (a) provides a solution with a guarantee on its suboptimality even if we terminate the algorithm early, (b) can accommodate side constraints on the coefficients of the linear regression and (c) extends to finding best subset solutions for the least absolute deviation loss function. Using a wide variety of synthetic and real datasets, we demonstrate that our approach solves problems with nn in the 1000s and pp in the 100s in minutes to provable optimality, and finds near optimal solutions for nn in the 100s and pp in the 1000s in minutes. We also establish via numerical experiments that the MIO approach performs better than {\texttt {Lasso}} and other popularly used sparse learning procedures, in terms of achieving sparse solutions with good predictive power.Comment: This is a revised version (May, 2015) of the first submission in June 201

    The Discrete Dantzig Selector: Estimating Sparse Linear Models via Mixed Integer Linear Optimization

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    We propose a novel high-dimensional linear regression estimator: the Discrete Dantzig Selector, which minimizes the number of nonzero regression coefficients subject to a budget on the maximal absolute correlation between the features and residuals. Motivated by the significant advances in integer optimization over the past 10-15 years, we present a Mixed Integer Linear Optimization (MILO) approach to obtain certifiably optimal global solutions to this nonconvex optimization problem. The current state of algorithmics in integer optimization makes our proposal substantially more computationally attractive than the least squares subset selection framework based on integer quadratic optimization, recently proposed in [8] and the continuous nonconvex quadratic optimization framework of [33]. We propose new discrete first-order methods, which when paired with state-of-the-art MILO solvers, lead to good solutions for the Discrete Dantzig Selector problem for a given computational budget. We illustrate that our integrated approach provides globally optimal solutions in significantly shorter computation times, when compared to off-the-shelf MILO solvers. We demonstrate both theoretically and empirically that in a wide range of regimes the statistical properties of the Discrete Dantzig Selector are superior to those of popular â„“1\ell_{1}-based approaches. We illustrate that our approach can handle problem instances with p = 10,000 features with certifiable optimality making it a highly scalable combinatorial variable selection approach in sparse linear modeling
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