The paper deals with the holonomic behavior of slackened-elastic-plastic (SEP) skeletal structures (beams, frames, trusses) using the quadratic programming formulations. The considerations are restricted to 'frict...
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The paper deals with the holonomic behavior of slackened-elastic-plastic (SEP) skeletal structures (beams, frames, trusses) using the quadratic programming formulations. The considerations are restricted to 'frictionless' quasi-static processes, small strains and piecewise linear approximations of the yield and clearance surfaces. The results of numerical experiments for several illustrative examples are presented, including the unilateral contact problem between an elastic-perfectly plastic beam and an elastic-perfectly plastic foundation. In the analysis the discrete FEM-oriented mathematical model [A. Gawecki, Elasto-plasticity of slackened systems, Arch. Mech. 1992;44:363-390 was employed. (C) 1998 Elsevier Science Ltd. All rights reserved.
Given a role-based access control (RBAC), resiliency checking problem (RCP) aims at determining whether every permission is executed by a user and all authorization constraints are satisfied when some users become abs...
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Given a role-based access control (RBAC), resiliency checking problem (RCP) aims at determining whether every permission is executed by a user and all authorization constraints are satisfied when some users become absent. Although the problem is computationally hard, desirable solutions are still expected so as to guarantee the continuity of access control. In this article, we solve RCP for RBAC based on constraint enforcement and mathematical programming. We use Petri nets (PNs) to formalize RBAC. It is shown that each separation of duty constraint imposed on a PN modeling of RBAC can be enforced by a maximally permissive PN-based control structure. After implementing such control structure on the PN modeling of RBAC, we can obtain an admissible RBAC. We show that RCP of RBAC can be transformed into another problem, which determines whether each permission can be executed by a user in the admissible RBAC against the absence of some users. An integer linear programming-based approach is presented to accomplish such verification. The comparison between our approach and the existing one is given to illustrate the effectiveness and efficiency of ours.
The solutions of the time-independent Schrodinger equation provide a quantum description of the stationary state of electrons in atoms and molecules. The Hartree-Fock problem consists in expressing these solutions by ...
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The solutions of the time-independent Schrodinger equation provide a quantum description of the stationary state of electrons in atoms and molecules. The Hartree-Fock problem consists in expressing these solutions by means of finite dimensional approximations thereof. These are themselves linear combinations of an existing linearly independent set;best approximations are obtained when a certain energy function is minimized. In Lavor et al. (Europhys Lett 5(77):50006p1-50006p5, 2007) we proposed a new mathematical programming (MP) approach which enhanced the likelihood of attaining globally optimal approximations, limited to closed-shell atomic systems. In this paper, we discuss an extension to open-shell systems: this is nontrivial as it requires the expression of a rank constraint within an MP formulation. We achieve this by explicitly modelling eigenvalues and requiring them to be nonzero. Although our approach might not necessarily scale well, we show it works on two open-shell systems (lithium and boron).
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.
This study focuses on the linkage between decision layers that have different time scales. The resulting expansion of the boundary of decision-making process can provide more robust and flexible management and operati...
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This study focuses on the linkage between decision layers that have different time scales. The resulting expansion of the boundary of decision-making process can provide more robust and flexible management and operation strategies by resolving inconsistencies between different levels. For this, we develop a multi-timescale decision-making model that combines Markov decision process (MDP) and mathematical programming (MP) in a complementary way and introduce a computationally tractable solution algorithm based on reinforcement learning (RL) to solve the MP-embedded MDP problem. To support the integration of the decision hierarchy, a data-driven uncertainty prediction model is suggested which is valid across all time scales considered. A practical example of refinery procurement and production planning is presented to illustrate the proposed method, along with numerical results of a benchmark case study. (C) 2018 Elsevier Ltd. All rights reserved.
The problem of computing a schedule of maximum robustness for the Mars Express mission is formulated and solved via linear programming (LP). We also provide a characterization of "easy" and "difficult&q...
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The problem of computing a schedule of maximum robustness for the Mars Express mission is formulated and solved via linear programming (LP). We also provide a characterization of "easy" and "difficult" instances such that the former ones can be solved to optimality directly, without having recourse to any optimization algorithm. In both cases, provably optimal solutions are obtained in shorter computing time compared to previously published approaches. Starting from the simplified model already described in the literature, we extend it to consider real constraints. For this purpose, we define an integer LP model with four different objective functions and develop a decision support system based on hierarchical optimization of the first two objectives and multi-criteria optimization of the other two.
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.
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.
In this study, for solving multi-group classification problems, a new two-stage hybrid classification method based on regression analysis and mathematical programming has been developed. In the first step of the propo...
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In this study, for solving multi-group classification problems, a new two-stage hybrid classification method based on regression analysis and mathematical programming has been developed. In the first step of the proposed method, the classification score of each unit is estimated with the help of the linear regression equation for each unit. In the second step, the classification of the units is performed by the mathematical programming model based on clustering analysis. The proposed method combines the strengths of regression analysis and mathematical programming method. From the 10 real data sets taken the well-known literature and simulation study results, it is observed that the proposed method outperforms the regression analysis, mathematical programming and artificial neural network based classification methods.
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.
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