As urban traffic congestion is on the increase worldwide, many cities are increasingly looking to inexpensive public transit options such as light rail that operate at street-level and require coordination with conven...
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As urban traffic congestion is on the increase worldwide, many cities are increasingly looking to inexpensive public transit options such as light rail that operate at street-level and require coordination with conventional traffic networks and signal control. A major concern in light rail installation is whether enough commuters will switch to it to offset the additional constraints it places on traffic signal control and the resulting decrease in conventional vehicle traffic capacity. In this study, the authors study this problem and ways to mitigate it through a novel model of optimised traffic signal control subject to light rail schedule constraints solved in a mixed-integer linear programming (MILP) framework. The authors' key results show that while this MILP approach provides a novel way to optimise fixed-time control schedules subject to light rail constraints, it also enables a novel optimised adaptive signal control method that virtually nullifies the impact of the light rail presence, reducing average delay times in microsimulations by up to 58.7% versus optimal fixed-time control.
Data Warehouse (DW) and OLAP systems are first citizens of Business Intelligence tools. They are widely used in the academic and industrial communities for numerous different fields of application. Despite the maturit...
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Data Warehouse (DW) and OLAP systems are first citizens of Business Intelligence tools. They are widely used in the academic and industrial communities for numerous different fields of application. Despite the maturity of DW and OLAP systems, with the advent of Big Data, more and more sources of data are available, and warehousing this data can lead to important quality issues. In this work, we focus on missing numerical and categorical in presence of aggregated facts. Motivated by the lack of a formal approach for the imputation of this kind of data taking into account all type of aggregation functions (distributive, algebraic and holistic), we propose an new methodology based on linear programming. Our methodology allows dealing with the relaxed constraints over classical SQL aggregation functions. The proposed approach is tested on two well-known datasets. Experiments show the effectiveness of the proposed approach.
Fuzzy set theory has been extensively employed in mathematical programming, especially in linear programming problems. As a generalization of fuzzy sets, a hesitant fuzzy set is a very useful tool in places where ther...
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Fuzzy set theory has been extensively employed in mathematical programming, especially in linear programming problems. As a generalization of fuzzy sets, a hesitant fuzzy set is a very useful tool in places where there are some hesitations in determining the membership of an element to a set. There are few studies on hesitant fuzzy linear programming problems;therefore, in this paper, we have studied such problems. For this purpose, at first, the motivation of this paper is explained;then, types of hesitant fuzzy linear programming models are introduced. Since it is not easy to examine all of the hesitant fuzzy models for the linear programming problems in one paper, we have restricted ourselves to symmetric and right-hand-side hesitant fuzzy linear programming problems with the flexible approach and then proposed two new approaches to solve them. Finally, to illustrate the applicability of the proposed approaches, three examples under hesitant fuzzy information are given.
Powerful interior-point methods (IPM) based commercial solvers, such as Gurobi and Mosek, have been hugely successful in solving large-scale linear programming (LP) problems. The high efficiency of these solvers depen...
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Powerful interior-point methods (IPM) based commercial solvers, such as Gurobi and Mosek, have been hugely successful in solving large-scale linear programming (LP) problems. The high efficiency of these solvers depends critically on the sparsity of the problem data and advanced matrix factorization techniques. For a large scale LP problem with data matrix A that is dense (possibly structured) or whose corresponding normal matrix AAT has a dense Cholesky factor (even with reordering), these solvers may require excessive computational cost and/or extremely heavy memory usage in each interior-point iteration. Unfortunately, the natural remedy, i.e., the use of iterative methods based IPM solvers, although it can avoid the explicit computation of the coefficient matrix and its factorization, is often not practically viable due to the inherent extreme ill-conditioning of the large scale normal equation arising in each interior-point iteration. While recent progress has been made to alleviate the ill-conditioning issue via sophisticated preconditioning techniques, the difficulty remains a challenging one. To provide a better alternative choice for solving large scale LPs with dense data or requiring expensive factorization of its normal equation, we propose a semismooth Newton based inexact proximal augmented Lagrangian (SNIPAL) method. Different from classical IPMs, in each iteration of SNIPAL, iterative methods can efficiently be used to solve simpler yet better conditioned semismooth Newton linear systems. Moreover, SNIPAL not only enjoys a fast asymptotic superlinear convergence but is also proven to enjoy a finite termination property. Numerical comparisons with Gurobi have demonstrated encouraging potential of SNIPAL for handling large-scale LP problems where the constraint matrix A has a dense representation or AAT has a dense factorization even with an appropriate reordering. For a few large LP instances arising from correlation clustering, our algorithm can be u
We evaluate the practical usefulness of incorporating maximum ramping rates and minimum environmental flows into a linear programming based water value calculator for hydropower plants that participate in the day-ahea...
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We evaluate the practical usefulness of incorporating maximum ramping rates and minimum environmental flows into a linear programming based water value calculator for hydropower plants that participate in the day-ahead electricity market. The methodology consists of three steps: first computing the water value once with and once without environmental constraints, then simulating the plant operations using each water value, and finally comparing the simulation profits. A set of nine representative hydropower plants formed by combinations of three real locations (in Colombia, Norway and Spain) and three turbine configurations (from one to three Francis units) are individually analyzed. Each plant is simulated in two synthetic 10-year long series subject to fifteen combinations of maximum ramping rates and minimum flows with the two above-mentioned water values, totaling 540 simulations. The results indicate that incorporating the analyzed environmental constraints into a linear programming based water value calculator can be significantly profitable only when the hydropower plants have only one or at most two turbines.
linear discriminant analysis (LDA) is widely used for various binary classification problems. In contrast to the LDA that estimates the precision matrix Omega and the mean difference vector delta in the classification...
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linear discriminant analysis (LDA) is widely used for various binary classification problems. In contrast to the LDA that estimates the precision matrix Omega and the mean difference vector delta in the classification rule separately, the linear programming discriminant (LPD) rule estimates the product Omega delta directly through a constrained l(1) minimization. The LPD rule has very good classification performance on many high-dimensional binary classification problems. However, to estimate beta* = Omega delta, the LPD rule uses equal weights for all the elements of beta* in the constrained l(1) minimization. It may not deliver the optimal estimate of beta*, and therefore the estimated discriminant direction can be suboptimal. In order to obtain better estimates of beta* and the discriminant direction, we can heavily penalize beta(j) in the constrained l(1) minimization if we suspect the jth feature is useless for the classification while moderately penalize beta(j) if we suspect the jth feature is useful. In this paper, based on the LPD rule and some popular feature screening methods, we propose a new weighted linear programming discriminant (WLPD) rule for the high-dimensional binary classification problem. The screening statistics used in the marginal two-sample t-test screening, Kolmogorov-Smirnov filter, and the maximum marginal likelihood screening will be used to construct appropriate weights for different elements of beta* flexibly. Besides the linear programming algorithm, we develop a new alternating direction method of multipliers algorithm to solve the high-dimensional constrained l(1) minimization problem efficiently. Our numerical studies show that our proposed WLPD rule can outperform LPD and serve as an effective binary classification tool.
linear discriminant analysis (LDA) is an important conventional model for data classification. Classical theory shows that LDA is Bayes consistent for a fixed data dimensionality p and a large training sample size n. ...
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linear discriminant analysis (LDA) is an important conventional model for data classification. Classical theory shows that LDA is Bayes consistent for a fixed data dimensionality p and a large training sample size n. However, in high-dimensional settings when p >> n, LDA is difficult due to the inconsistent estimation of the covariance matrix and the mean vectors of populations. Recently, a linear programming discriminant (LPD) rule was proposed for high-dimensional linear discriminant analysis, based on the sparsity assumption over the discriminant function. It is shown that the LPD rule is Bayes consistent in high-dimensional settings. In this paper, we further show that the LPD rule is sign consistent under the sparsity assumption. Such sign consistency ensures the LPD rule to select the optimal discriminative features for high-dimensional data classification problems. Evaluations on both synthetic and real data validate our result on the sign consistency of the LPD rule. (C) 2019 Elsevier Ltd. All rights reserved.
This paper presents an innovative method for solving Pythagorean fuzzy (PF) multicriteria group decision-making problems with completely unknown weight information about criteria using entropy weight model, linear pro...
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This paper presents an innovative method for solving Pythagorean fuzzy (PF) multicriteria group decision-making problems with completely unknown weight information about criteria using entropy weight model, linear programming (LP) and modified technique for ordering preference by similarity to ideal solution (TOPSIS). At first, a new distance measure for PF sets is defined considering their degree of hesitancy and based on weighted Hamming distance and Hausdorff metric. To handle the fuzziness in criteria weights, PF entropy weight model is used to find the initial weights of the criteria in PF format. Following the concept of TOPSIS, an LP model is constructed on the basis of the view point that the chosen alternative should have the smallest distance from the positive ideal solution and the largest distance from the negative ideal solution. Then, the LP model is utilized to find optimal weights of the criteria. Using the newly defined distance measure, entropy weight model and LP model, TOPSIS is extended in PF environments. The existing methods are able to find criteria weights in the form of crisp values only, whereas proposed method is able to obtain those weights in PF format. Thus, the proposed method can overcome the drawback in computing criteria weight for multicriteria group decision-making in PF environments and reduce the information loss significantly. Several numerical examples are considered and solved to validate the superiority of the proposed methodology.
This paper deals with the finite-time interval observer design method for discrete-time switched systems subjected to disturbances. The disturbances of the system are unknown but bounded. The framework of the finite-t...
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This paper deals with the finite-time interval observer design method for discrete-time switched systems subjected to disturbances. The disturbances of the system are unknown but bounded. The framework of the finite-time interval observer is established and the sufficient conditions are derived by the multiple linear copositive Lyapunov function. Furthermore, the conditions which are expressed by the forms of linear programming are numerically tractable by standard computing software. One example is simulated to illustrate the validity of the designed observer.
In the field of constraint satisfaction problems (CSPs), promise CSPs are an exciting new direction of study. In a promise CSP, each constraint comes in two forms: "strict" and "weak," and in the a...
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In the field of constraint satisfaction problems (CSPs), promise CSPs are an exciting new direction of study. In a promise CSP, each constraint comes in two forms: "strict" and "weak," and in the associated decision problem one must distinguish between being able to satisfy all the strict constraints versus not being able to satisfy all the weak constraints. The most commonly cited example of a promise CSP is the approximate graph coloring problem-which has recently seen exciting progress [Bulin, Krokhin, and Oprsal, Proceedings of the Symposium on Theory of Computing, 2019, pp. 602-613 and Wrochna and Zivny, Proceedings of the Symposium on Discrete Algorithms, 2020, pp. 1426-1435] benefiting from a systematic algebraic approach to promise CSPs based on "polymorphisms," operations that map tuples in the strict form of each constraint to tuples in the corresponding weak form. In this work, we present a simple algorithm which in polynomial time solves the decision problem for all promise CSPs that admit infinitely many symmetric polymorphisms, which are invariant under arbitrary coordinate permutations. This generalizes previous work of the first two authors [Brakensiek and Guruswami, Proceedings of the Symposium on Discrete Algorithms, 2019, pp. 436-455]. We also extend this algorithm to a more general class of block-symmetric polymorphisms. As a corollary, this single algorithm solves all polynomial-time tractable Boolean CSPs simultaneously. These results give a new perspective on Schaefer's classic dichotomy theorem and shed further light on how symmetries of polymorphisms enable algorithms. Finally, we show that block symmetric polymorphisms are not only sufficient but also necessary for this algorithm to work, thus establishing its precise power.
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