This paper deals with the k-way normalized cut problem in complex networks. It presents a methodology that uses mathematical optimization to provide mixed-integer linear programming formulations for the problem. The p...
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This paper deals with the k-way normalized cut problem in complex networks. It presents a methodology that uses mathematical optimization to provide mixed-integer linear programming formulations for the problem. The paper also develops a branch-and-price algorithm for the above-mentioned problem which scales better than the compact formulations. Additionally, a heuristic algorithm which is able to approximate largescale image problems in those cases where the exact methods are not applicable is presented. Extensive computational experiments assess the usefulness of these methods to solve the k-way normalized cut problem. Finally, we have applied the minimum normalized cut objective function to the segmentation of actual images, showing the applicability of the introduced methodology.
Background: Applying machine learning methods on microarray gene expression profiles for disease classification problems is a popular method to derive biomarkers, i.e. sets of genes that can predict disease state or o...
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Background: Applying machine learning methods on microarray gene expression profiles for disease classification problems is a popular method to derive biomarkers, i.e. sets of genes that can predict disease state or outcome. Traditional approaches where expression of genes were treated independently suffer from low prediction accuracy and difficulty of biological interpretation. Current research efforts focus on integrating information on protein interactions through biochemical pathway datasets with expression profiles to propose pathway-based classifiers that can enhance disease diagnosis and prognosis. As most of the pathway activity inference methods in literature are either unsupervised or applied on two-class datasets, there is good scope to address such limitations by proposing novel methodologies. Results: A supervised multiclass pathway activity inference method using optimisation techniques is reported. For each pathway expression dataset, patterns of its constituent genes are summarised into one composite feature, termed pathway activity, and a novel mathematical programming model is proposed to infer this feature as a weighted linear summation of expression of its constituent genes. Gene weights are determined by the optimisation model, in a way that the resulting pathway activity has the optimal discriminative power with regards to disease phenotypes. Classification is then performed on the resulting low-dimensional pathway activity profile. Conclusions: The model was evaluated through a variety of published gene expression profiles that cover different types of disease. We show that not only does it improve classification accuracy, but it can also perform well in multiclass disease datasets, a limitation of other approaches from the literature. Desirable features of the model include the ability to control the maximum number of genes that may participate in determining pathway activity, which may be pre-specified by the user. Overall, this work highlig
The triangular norm-based operations in fuzzy logic usually lead to non-L-R type fuzzy sets. This study considers mathematical programming problems with non-L-R type fuzzy parameters. It shows that the fuzzy solutions...
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The triangular norm-based operations in fuzzy logic usually lead to non-L-R type fuzzy sets. This study considers mathematical programming problems with non-L-R type fuzzy parameters. It shows that the fuzzy solutions to such problems can be obtained by solving an optimization problem on a mixed domain. The necessary and sufficient conditions for solving the resulting optimization problems are investigated by employing the theory of convex optimization on mixed domains. This is the first attempt to solve the fuzzy optimization problem with non-L-R type membership functions in view of optimization problems on a mixed domain.
This study applies a genetic algorithm embedded with mathematical programming techniques to solve a synchronized and integrated two-level lot sizing and scheduling problem motivated by a real-world problem that arises...
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This study applies a genetic algorithm embedded with mathematical programming techniques to solve a synchronized and integrated two-level lot sizing and scheduling problem motivated by a real-world problem that arises in soft drink production. The problem considers a production process compounded by raw material preparation/storage and soft drink bottling. The lot sizing and scheduling decisions should be made simultaneously for raw material preparation/storage in tanks and soft drink bottling in several production lines minimizing inventory, shortage and setup costs. The literature provides mixed-integer programming models for this problem, as well as solution methods based on evolutionary algorithms and relax-and-fix approaches. The method applied by this paper uses a new approach which combines a genetic algorithm (GA) with mathematical programming techniques. The GA deals with sequencing decisions for production lots, so that an exact method can solve a simplified linear programming model, responsible for lot sizing decisions. The computational results show that this evolutionary/mathematical programming approach outperforms the literature methods in terms of production costs and run times when applied to a set of real-world problem instances provided by a soft drink company. (C) 2014 Elsevier Ltd. All rights reserved.
The optimal placement of turbines in a wind farm is critical to the maximization of power production. In this paper, we develop a new mathematical programming approach for wind farm layout optimization. We use Jensen&...
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The optimal placement of turbines in a wind farm is critical to the maximization of power production. In this paper, we develop a new mathematical programming approach for wind farm layout optimization. We use Jensen's wake decay model to represent multi-turbine wake effects. We develop mixed integer linear and quadratic optimization formulations and apply them to several example layout cases in the literature. Compared to previous approaches, our models produce layouts that tend to be more symmetric and that generate slightly more power. Our formulations solve quickly, allowing a decision maker to efficiently explore the impact of different turbine densities in a wind farm. (C) 2013 Elsevier Ltd. All rights reserved.
This article deals with a class of constrained nonsmooth multiobjective programming problems (NMOPP) in the setting of Hadamard manifolds. The generalized Guignard constraint qualification (GGCQ), Abadie constraint qu...
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This article deals with a class of constrained nonsmooth multiobjective programming problems (NMOPP) in the setting of Hadamard manifolds. The generalized Guignard constraint qualification (GGCQ), Abadie constraint qualification (ACQ), and the generalized ACQ (GACQ) are introduced in the framework of Hadamard manifolds for NMOPP using the notion of Clarke subdifferentials. Subsequently, by employing GGCQ and geodesic quasiconvexity assumptions, we establish Karush-Kuhn-Tucker (abbreviated as, KKT)-type necessary criteria of Pareto efficiency for NMOPP. Moreover, we establish that ACQ and GACQ are sufficient criteria for satisfaction of GGCQ. Several nontrivial numerical examples are furnished in manifold settings to demonstrate the validity of the derived results. To the best of our knowledge, this is the first time that ACQ, GACQ, GGCQ, and KKT-type necessary criteria of Pareto efficiency for NMOPP have been studied in manifold setting using Clarke subdifferentials.
A major risk for many existing and planned wood-based bioenergy facilities is the uncertainty regarding future feedstock supply. Many bioenergy projects use waste generated from primary sectors such as lumber, and, th...
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A major risk for many existing and planned wood-based bioenergy facilities is the uncertainty regarding future feedstock supply. Many bioenergy projects use waste generated from primary sectors such as lumber, and, therefore, carry the inherent risk of supply fluctuations if these industries change. To assess the long-term viability of a wood-based bioenergy facility, it is necessary to understand how biomass feedstock fluctuates with other sectors and at what cost supply can be made available. We address these issues by constructing a positive mathematical programming (PMP) model of the Alberta forest sector that focuses on optimizing fibre transfer routes. Through the use of PMP, we derive a marginal cost function for harvesting and hauling fibre to each processing facility. The results indicate that woody residual supply is quite sensitive to market conditions in the primary sector. For the most part, to support bioenergy expansion, feedstock will need to be sourced from the forest, as very few surplus mill residues are available even at high lumber prices. However, we estimate the marginal cost of delivering harvesting residues to be significant, which suggests that policy support will be needed for further bioenergy development.
This paper presents a novel mathematical programming approach for the static stability analysis of structures with uncertainties within the framework of FEM. The considered uncertain parameters are material properties...
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This paper presents a novel mathematical programming approach for the static stability analysis of structures with uncertainties within the framework of FEM. The considered uncertain parameters are material properties, geometry of element cross section, and loading conditions, all of which are described by an interval model. The proposed method formulates the two cases of interest, namely, worst and best buckling load calculation, into a pair of mathematical programming problems. Two straightforward advantages are exhibited by such formulations. The first advantage is that the proposed formulation can overcome the interference on the sharpness of bounds of the buckling load due to the interval dependence issue. The second benefit is that the information of uncertain parameters causing the extremities of buckling load can always be retrieved as by-products of the uncertain stability analysis. Some numerical examples are presented to illustrate the capability of the proposed method on various structures and the sharpness of the bounds of the buckling load factors. The efficiency and effectiveness of the proposed method are also demonstrated through comparison with the classical Monte Carlo simulation method. Copyright (c) 2014 John Wiley & Sons, Ltd.
This paper addresses the workload balancing problem in identical parallel machines context. The problem consists of assigning n different jobs to m identical parallel machines in order to minimize the workload imbalan...
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This paper addresses the workload balancing problem in identical parallel machines context. The problem consists of assigning n different jobs to m identical parallel machines in order to minimize the workload imbalance among the different machines. This problem is formulated as a linear mixed integer program to minimize the difference between the greatest and smallest workload assigned to each machine. Based on some numerical examples reported in the literature, we establish that the classical formulation which consists of minimizing the greatest machine completion time does not provide the optimal workload repartition. That is why we consider a new mathematical formulation based on the minimization of the difference between the workload of the bottleneck machine and the workload of the fastest machine. The proposed programming method is also used to provide optimal solutions in reasonable computational times for different test problems presented in the literature by Raghavendra and Murthy (10) to test their genetic algorithm.
The sectorization problem is a particular case of partitioning problems occurring in cartography. The aim is to partition a territory into sectors such that the statistical activity measure of each sector is as close ...
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The sectorization problem is a particular case of partitioning problems occurring in cartography. The aim is to partition a territory into sectors such that the statistical activity measure of each sector is as close as possible to a given target value. We model this as a problem of minimizing the maximum deviation among all the sectors between their activity measure and their target value. We propose a mathematical programming formulation for the problem, we add some valid inequalities to restrict the solution space and develop a preprocessing procedure to reduce the number of variables. Computational results on different maps highlight the strong efficiency of this reduction procedure.
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