Boolean query optimization and the 0-1 hyperbolic sum problem

Hansen, Pierre; Aragão, Marcus V. Poggi De; Ribeiro, Celso C.

doi:10.1007/bf01531072

Cited by 25 publications

(10 citation statements)

References 13 publications

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“…Multiple-ratio FP is nondeterministic polynomial-time hard (NP-hard) even for two ratios and strictly positive denominators (Hansen et al 1990;Prokopyev et al 2005a, b). For solving multiple-ratio FP, there exist several mixed-integer linear programming (MILP) reformulations of FP.…”

Section: Introductionmentioning

confidence: 99%

On Robust Fractional 0-1 Programming

Mehmanchi

Gillen

Gómez

et al. 2020

INFORMS Journal on Optimization

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We study single- and multiple-ratio robust fractional 0-1 programming problems (RFPs). In particular, this work considers RFPs under a wide range of disjoint and joint uncertainty sets, where the former implies separate uncertainty sets for each numerator and denominator and the latter accounts for different forms of interrelatedness between them. We first demonstrate that unlike the deterministic case, a single-ratio RFP is nondeterministic polynomial-time hard under general polyhedral uncertainty sets. However, if the uncertainty sets are imbued with a certain structure, variants of the well-known budgeted uncertainty, the disjoint and joint single-ratio RFPs are polynomially solvable when the deterministic counterpart is. We also propose mixed-integer linear programming (MILP) formulations for multiple-ratio RFPs. We conduct extensive computational experiments using test instances based on real and synthetic data sets to evaluate the performance of our MILP reformulations as well as to compare the disjoint and joint uncertainty sets. Finally, we demonstrate the value of the robust approach by examining the robust solution in a deterministic setting and vice versa.

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Section: Introductionmentioning

confidence: 99%

On Robust Fractional 0-1 Programming

Mehmanchi

Gillen

Gómez

et al. 2020

INFORMS Journal on Optimization

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“…This model is an integer nonlinear programming problem in which the objective function is a sum of ratios with a particular structure: Numerators and denominators of a ratio di er only by the constants. Similar problems with a sum of ratios as objective have been studied by Hansen et al [68] and Benati and Hansen [69]. Benati [70] proved that the problem was NP-hard.…”

Section: The Proposed Modelmentioning

confidence: 72%

A Mathematical Model for Competitive Location Problem with Product Selection

et al. 2018

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In this paper, a new competitive location problem for a chain is considered. The owner of the chain can o er a variety of products. The objective of the model is to determine both the location of new facilities and the optimal product type for each opened facility. The patronizing behavior of the customers is based on Hu rule and the location of new facilities is selected from a set of potential sites. As a result, the proposed model is a nonlinear integer programming problem and for solving it, the problem is reformulated as a mixed integer linear programming one. Therefore, a standard optimization solver can be used for obtaining the optimal solutions to small-and medium-size problems. To cope with large-size problems, we develop two methods: 1) a heuristic method for a special case and 2) a hybrid heuristic-re y algorithm for general cases. By using the proposed model, it is numerically shown that in multi-product industries in which the owner of the facilities is able to o er di erent types of products, in addition to the optimal location, it is necessary to determine the best products. At the end, a real-world case study for locating a new bakery is presented.

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“…We consider a relaxed form of (9) , known as unconstrained fractional 0–1 programming, problem ( Hammer et al , 1968 ) and frequently encountered in the fields of scheduling or database query optimization ( Hansen et al , 1990 ): where n is the number of non-zero values for the itemset being considered. and .…”

Section: Methodsmentioning

confidence: 99%

Discovering combinatorial interactions in survival data

et al. 2013

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Motivation: Although several methods exist to relate high-dimensional gene expression data to various clinical phenotypes, finding combinations of features in such input remains a challenge, particularly when fitting complex statistical models such as those used for survival studies.Results: Our proposed method builds on existing ‘regularization path-following’ techniques to produce regression models that can extract arbitrarily complex patterns of input features (such as gene combinations) from large-scale data that relate to a known clinical outcome. Through the use of the data’s structure and itemset mining techniques, we are able to avoid combinatorial complexity issues typically encountered with such methods, and our algorithm performs in similar orders of duration as single-variable versions. Applied to data from various clinical studies of cancer patient survival time, our method was able to produce a number of promising gene-interaction candidates whose tumour-related roles appear confirmed by literature.Availability: An R implementation of the algorithm described in this article can be found at https://github.com/david-duverle/regularisation-path-followingContact: dave.duverle@aist.go.jpSupplementary information: Supplementary data are available at Bioinformatics online.

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Boolean query optimization and the 0-1 hyperbolic sum problem

Cited by 25 publications

References 13 publications

On Robust Fractional 0-1 Programming

On Robust Fractional 0-1 Programming

A Mathematical Model for Competitive Location Problem with Product Selection

Discovering combinatorial interactions in survival data

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