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.
An interactive method is developed for solving the general nonlinear multiple objective mathematical programming problems. The method asks the decision maker to provide partial information (local tradeoff ratios) abou...
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An interactive method is developed for solving the general nonlinear multiple objective mathematical programming problems. The method asks the decision maker to provide partial information (local tradeoff ratios) about his utility (preference) function at each iteration. Using the information, the method generates an efficient solution and presents it to the decision maker. In so doing, the best compromise solution is sought in a finite number of iterations. This method differs from the existing feasible direction methods in that (i) it allows the decision maker to consider only efficient solutions throughout, (ii) the requirement of line search is optional, and (iii) it solves the problems with linear objective functions and linear utility function in one iteration. Using various problems selected from the literature, five line search variations of the method are tested and compared to one another. The nonexisting decision maker is simulated using three different recognition levels, and their impact on the method is also investigated.
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
A new mathematical programming model for the three-group classification problem is presented. This model is shown to be computationally more efficient than the General Single Function Classification (GSFC) model for a...
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A new mathematical programming model for the three-group classification problem is presented. This model is shown to be computationally more efficient than the General Single Function Classification (GSFC) model for a variety of data configurations. Theoretical characteristics of the classificatory performance of the two models are also investigated. Copyright (C) 1997 Elsevier Science Ltd
A new dual gradient method is given to solve linearly constrained, strongly convex, separable mathematical programming problems. The dual problem can be decomposed into one-dimensional problems whose solutions can be ...
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A new dual gradient method is given to solve linearly constrained, strongly convex, separable mathematical programming problems. The dual problem can be decomposed into one-dimensional problems whose solutions can be computed extremely easily. The dual objective function is shown to have a Lipschitz continuous gradient, and therefore a gradient-type algorithm can be used for solving the dual problem. The primal optimal solution can be obtained from the dual optimal solution in a straightforward way. Convergence proofs and computational results are given.
In this paper, an approach to steady-state rolling, based on the boundary element method and mathematical programming techniques is presented. The algorithm solves the problem by an enchained iteration with the NORM a...
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In this paper, an approach to steady-state rolling, based on the boundary element method and mathematical programming techniques is presented. The algorithm solves the problem by an enchained iteration with the NORM and TANG parts of the problem. These two parts are solved by different methods because of the different nature of the nonlinearities inside each one of them. The normal part has a weak non-linearity and can be solved as a linear complementary problem by the Lemke method, but the tangential part, with a stronger non-linearity, needs other methods. This work presents three different ways to solve this part by using mathematical programming techniques, showing their flexibility and reliability by solving various classic problems. (C) 2000 Civil-Comp Ltd. and Elsevier Science Ltd. All rights reserved.
Hydrogen production is a vital development trend to improve the economics and penetration rate of offshore wind farms (OWFs), and distributed hydrogen production (DHP) is a preferred solution for deep and far sea OWFs...
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Hydrogen production is a vital development trend to improve the economics and penetration rate of offshore wind farms (OWFs), and distributed hydrogen production (DHP) is a preferred solution for deep and far sea OWFs without expensive submarine cables and offshore substations. The export pathway of OWF-DHP consists of collection pipelines, transmission pipelines, and offshore compressor stations. In this paper, mathematical programming is introduced to explore the export pathway planning problem of OWF-DHP. Firstly, the area of OWF is discretized into multiple grids with the center of the grids being the candidate locations of the offshore compressor station. Then, a binary integer quadratic programming problem is established to optimize both the offshore compressor station location and pipeline construction with different topologies. Further, the mathematical model is solved by the branch and cut algorithm integrated with the proposed dimension reduction methods. Finally, the effectiveness of the proposed export pathway planning approach is verified by the actual data of Baltic Eagle OWF in Germany, which would support the construction of the OWF-DHP project.
Economic development, variation in weather patterns and natural disasters focus attention on the management of water resources. This paper reviews the literature on the development of mathematical programming models f...
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Economic development, variation in weather patterns and natural disasters focus attention on the management of water resources. This paper reviews the literature on the development of mathematical programming models for water resource management under uncertainty between 2010 and 2017. A systematic search of the academic literature identified 448 journal articles on water resource management for examination. Bibliometric analysis is employed to investigate the methods that researchers are currently using to address this problem and to identify recent trends in research in the area. The research reveals that stochastic dynamic programming and multistage stochastic programming are the methods most commonly applied. Water resource allocation, climate change, water quality and agricultural irrigation are amongst the most frequently discussed topics in the literature. A more detailed examination of the literature on each of these topics is included. The findings suggest that there is a need for mathematical programming models of large-scale water systems that deal with uncertainty and multiobjectives in an effective and computationally efficient way.
Two mathematical programming procedures for treating nonlinear problems involving mixed variables are presented. One involves a relatively simple concept. First an optimum is located treating all variables as continuo...
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Two mathematical programming procedures for treating nonlinear problems involving mixed variables are presented. One involves a relatively simple concept. First an optimum is located treating all variables as continuous. Adjacent discrete points are then evaluated in order of increasing distance from the all-continuous optimum, each evaluation requiring an optimization of the continuous variables, if any, until a satisfactory design is found. The other method utilizes an optimal discrete search to locate the optimum. These procedures are applied to the minimum weight design of stiffened, cylindrical shells where they prove to be effective.
Subset selection for multiple linear regression aims to construct a regression model that minimizes errors by selecting a small number of explanatory variables. Once a model is built, various statistical tests and dia...
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Subset selection for multiple linear regression aims to construct a regression model that minimizes errors by selecting a small number of explanatory variables. Once a model is built, various statistical tests and diagnostics are conducted to validate the model and to determine whether the regression assumptions are met. Most traditional approaches require human decisions at this step. For example, the user may repeat adding or removing a variable until a satisfactory model is obtained. However, this trial-and-error strategy cannot guarantee that a subset that minimizes the errors while satisfying all regression assumptions will be found. In this paper, we propose a fully automated model building procedure for multiple linear regression subset selection that integrates model building and validation based on mathematical programming. The proposed model minimizes mean squared errors while ensuring that the majority of the important regression assumptions are met. We also propose an efficient constraint to approximate the constraint for the coefficient t-test. When no subset satisfies all of the considered regression assumptions, our model provides an alternative subset that satisfies most of these assumptions. Computational results show that our model yields better solutions (i.e., satisfying more regression assumptions) compared to the state-of-the-art benchmark models while maintaining similar explanatory power. (C) 2020 Elsevier Ltd. All rights reserved.
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