This paper deals with inequality relations in fuzzy mathematical programming problem (FMP) not necessarily linear. Moreover, fuzzy parameters may have nonlinear membership functions. A new approach for comparing fuzzy...
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This paper deals with inequality relations in fuzzy mathematical programming problem (FMP) not necessarily linear. Moreover, fuzzy parameters may have nonlinear membership functions. A new approach for comparing fuzzy sets is proposed, which is more general than the well known proposals in the literature.
Graph mining methods enumerate frequently appearing subgraph patterns, which can be used as features for subsequent classification or regression. However, frequent patterns are not necessarily informative for the give...
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Graph mining methods enumerate frequently appearing subgraph patterns, which can be used as features for subsequent classification or regression. However, frequent patterns are not necessarily informative for the given learning problem. We propose a mathematical programming boosting method (gBoost) that progressively collects informative patterns. Compared to AdaBoost, gBoost can build the prediction rule with fewer iterations. To apply the boosting method to graph data, a branch-and-bound pattern search algorithm is developed based on the DFS code tree. The constructed search space is reused in later iterations to minimize the computation time. Our method can learn more efficiently than the simpler method based on frequent substructure mining, because the output labels are used as an extra information source for pruning the search space. Furthermore, by engineering the mathematical program, a wide range of machine learning problems can be solved without modifying the pattern search algorithm.
In this paper, we propose two kinds of ranking criteria for fuzzy numbers, and a simple and systematical method for producing these criteria. We show that any ranking proposed by Dubois is one of the rankings of each ...
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In this paper, we propose two kinds of ranking criteria for fuzzy numbers, and a simple and systematical method for producing these criteria. We show that any ranking proposed by Dubois is one of the rankings of each kind. That is, we show that the proposed rankings of each kind are generalization of the rankings proposed by Dubois. We also show the application of that to a fuzzy mathematical programming problem (FMP)with imprecise resources and technological coefficients. In the proposed method, a DM can easily select ranking criteria which can reflect the DM's subtle request. A DM also can have clearly the information about selected ranking criteria although so far in many cases a DM was difficult to know the meaning of using ranking criteria. Hence, when applied to an FMP with imprecise resources and technological coefficients, a DM can easily set the way of solving the FMP approximately, and also have clearly the information how the FMP is solved approximately. This information is very useful especially when a DM makes decision by using the solution of the FMP. (C) 1998 Published by Elsevier Science B.V.
Forecasting future productivity is a critical task to every organization. However, the existing methods for productivity forecasting have two problems. First, the logarithmic or log-sigmoid value, rather than the orig...
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Forecasting future productivity is a critical task to every organization. However, the existing methods for productivity forecasting have two problems. First, the logarithmic or log-sigmoid value, rather than the original value, of productivity is dealt with. Second, the objective functions are not consistent with those adopted in practice. To address these problems, a fuzzy polynomial fitting and mathematical programming (FPF-MP) approach are proposed in this study. The FPF-MP approach solves two polynomial programming problems, based on the original value of productivity, in two steps to optimize accuracy and precision of forecasting future productivity, respectively. A real case was adopted to validate the effectiveness of the proposed methodology. According to the experimental results, the proposed FPF-MP approach outperformed six existing methods in improving the forecasting accuracy and precision.
In the contemporary literature on deterministic machine scheduling, problems are formulated from three different, but equivalent, perspectives. Algebraic models provide a rigorous problem statement in the language of ...
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In the contemporary literature on deterministic machine scheduling, problems are formulated from three different, but equivalent, perspectives. Algebraic models provide a rigorous problem statement in the language of set theory and are typical of the more abstract development of scheduling theory in mathematics and computer science. mathematical programming models rely on familiar concepts of nonlinear optimization and are generally the most accessible. Network models (disjunctive graphs) are best suited to the development of solution approaches and figure prominently in discussions of algorithm design and analysis. In this tutorial, it is shown how the minimum-makespan job-shop problem (n/m/G/C(max)) is realized in each of these three model forms. A common notation is developed and how the underlying structure and fundamental difficulty of the problem are expressed in each model is demonstrated.
This paper considers the hybrid flow shop scheduling problem, where jobs are processed in $m$ stages with the same route of the stage. Each stage has identical parallel machines for processing jobs. Some mathematical ...
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This paper considers the hybrid flow shop scheduling problem, where jobs are processed in $m$ stages with the same route of the stage. Each stage has identical parallel machines for processing jobs. Some mathematical programming formulations and lower bound calculations have been proposed in the literature for such cases. Nevertheless, there is a lack of complete comparisons of these mathematical programming formulations and lower bounds in the hybrid flow shop literature. This paper proposes a new mixed integer programming model and two new lower bounds based on the bin-packing concept for the considered problem. To evaluate the proposed model, two sets of small and small-to-medium problems are used to compare our model with the existing models. Moreover, two propositions are discussed for lower bounds. The experimental results show that the proposed mixed integer programming model efficiently found optimal solutions because it needs a smaller number of binary variables and a smaller number of constraints, and the proposed lower bound can also serve as a strong indicator to evaluate the distances between the solutions obtained by heuristic algorithms and the optimal solution.
mathematical programming (MP) problems depending on a small parameter are investigated. Attention is paid to the cases where the solutions to the reduced program and/or the solutions to the dual reduced program are no...
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mathematical programming (MP) problems depending on a small parameter are investigated. Attention is paid to the cases where the solutions to the reduced program and/or the solutions to the dual reduced program are not unique. Conditions are given for the convergence of perturbed solutions to a point of the reduced problem solution set, if the small parameter tends to zero. It is shown how to find this point and how to construct an approximate solution to the perturbed program. A singular situation may appear if the dual solution set is unbounded. In this case, a gap between perturbed and reduced solutions may arise. However, it is shown that the perturbed solutions are close to the solutions of some modified reduced problem. The practical usefulness of perturbation theory is demonstrated by considering the two LP problems. Decomposition and aggregation procedures are constructed on the base of general results to find suboptimal solutions of these problems.
Tandem queueing models play an important role in many real world systems such as computer systems, production lines, and service systems. This paper proposes a procedure to construct the membership functions of the pe...
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Tandem queueing models play an important role in many real world systems such as computer systems, production lines, and service systems. This paper proposes a procedure to construct the membership functions of the performance measures in tandem queueing systems, in that the arrival rate and service rates are fuzzy numbers. The basic idea is to transform a fuzzy tandem queue to a family of crisp tandem queues by applying the alpha-cut approach. Then on the basis of alpha-cut representation and the extension principle, a pair of mathematical programs is formulated to describe this family of crisp tandem queues, via which the membership functions of the performance measures are derived. Two numerical examples arc solved successfully to demonstrate the validity of the proposed approach. Since the performance measures are expressed by membership functions rather than by crisp values, the fuzziness of input information is completely conserved. Thus the proposed approach for fuzzy systems can represent the system more accurately, and more information is provided for designing queueing systems. The successful extension of tandem queues to fuzzy environments permits tandem queueing models to have wider applications.
Regression is a predictive analysis tool that examines the relationship between independent and dependent variables. The goal of this analysis is to fit a mathematical function that describes how the value of the resp...
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Regression is a predictive analysis tool that examines the relationship between independent and dependent variables. The goal of this analysis is to fit a mathematical function that describes how the value of the response changes when the values of the predictors vary. The simplest form of regression is linear regression which in the case multiple regression, tries to explain the data by simply fitting a hyperplane minimising the absolute error of the fitting. Piecewise regression analysis partitions the data into multiple regions and a regression function is fitted to each one. Such an approach is the OPLRA (Optimal Piecewise Linear Regression Analysis) model (Yang, Liu, Tsoka, & Papage, 2016) which is a mathematical programming approach that optimally partitions the data into multiple regions and fits a linear regression functions minimising the Mean Absolute Error between prediction and truth. However, using many regions to describe the data can lead to overfitting and bad results. In this work an extension of the OPLRA model is proposed that deals with the problem of selecting the optimal number of regions as well as overfitting. To achieve this result, information criteria such as the Akaike and the Bayesian are used that reward predictive accuracy and penalise model complexity. (C) 2018 Published by Elsevier Ltd.
Most of the research on cellular manufacturing focuses on cell formation, the initial step of setting up a cellular manufacturing system. Numerous methods exist for organizing efficient manufacturing cells for existin...
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Most of the research on cellular manufacturing focuses on cell formation, the initial step of setting up a cellular manufacturing system. Numerous methods exist for organizing efficient manufacturing cells for existing equipment and parts. However, when cell redesign is not possible or desired, opportunities still exist for further optimization and cost savings with the existing cell formation. Exceptional elements (EEs) in cellular manufacturing are bottleneck machines and exceptional parts that span two or more manufacturing cells. This paper develops a mathematical programming model that retains the original cell formation, which is assumed to be optimal in the long term, and minimizes total costs of a cellular manufacturing system with exceptional elements through (1) intercellular transfer, (2) machine duplication, and (3) subcontracting while taking machine capacities into account to avoid capacity violations. (C) 2014 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.
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