Inspired by the results obtained in Liu et al. (2008, 2009), this study extends the constrained control problem to singular linear positive discrete-time systems with delay. By using the singular value decomposition a...
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Inspired by the results obtained in Liu et al. (2008, 2009), this study extends the constrained control problem to singular linear positive discrete-time systems with delay. By using the singular value decomposition approach, delay-dependent sufficient conditions for the regularity, causality, positivity and exponential stabilisation with a given decay rate of the system are established in terms of linear programming problem. A numerical example to demonstrate the effectiveness of the proposed method is given.
Transportation problems (TP) have multiple applications in supply chain management to reduce costs. Efficient methods have been developed to address TP when all factors, including supply, demand, and unit transportati...
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Transportation problems (TP) have multiple applications in supply chain management to reduce costs. Efficient methods have been developed to address TP when all factors, including supply, demand, and unit transportation costs, are precisely known. However, due to uncertainty in practical applications, it is necessary to study TP in an uncertain environment. In this paper, we define the Trapezoidal Fermatean Fuzzy Number (TrFFN) and its arithmetic operations. Then we introduce a new approach to solve TP, where transportation cost, supply, and demand are treated as TrFFN, and we call it Fermatean Fuzzy TP (FFTP). We illustrate the feasibility and superiority of this method with two application examples, and compare the performance of this method with existing methods. Furthermore, the advantages of the proposed method over existing methods are described to address TP in uncertain environments.
A general model of a virtual circuit network consisting of a number of servers and a number of traffic classes is considered, A traffic class is identified by the sequence of servers that should be visited and the cor...
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A general model of a virtual circuit network consisting of a number of servers and a number of traffic classes is considered, A traffic class is identified by the sequence of servers that should be visited and the corresponding service rates before a message (customer) of the class leaves the network. The following cases are distinguished: 1) the messages need nonpreemptive service: 2) the service of a message can be preempted at any time;3) pipelining of the service in a sequence of servers is allowed;and 4) pipelining is not allowed. All of these cases arise in different transmission slr itching techniques and scheduling schemes. A fluid model that emerges when both preemption and pipelining are allowed is considered, Scheduling schemes in the quid model are compared with corresponding ones in the network with nonpreemptive service and no pipelining, The problem of evacuating the network from an initial backlog without further arrival is identified in the fluid model. Rased on that, a policy with nearly optimal evacuation time is identified for the store-and-forward case. Finally, scheduling with deadlines is considered and it is shown that in the fluid model, the evacuation problem is equivalent to a linear programming problem. The evacuation times under different work-conserving policies are considered in specific examples.
Recently in Dufrenois [1], a new Fisher type contrast measure has been proposed to extract a target population in a dataset contaminated by outliers. Although mathematically sound, this work presents some further shor...
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Recently in Dufrenois [1], a new Fisher type contrast measure has been proposed to extract a target population in a dataset contaminated by outliers. Although mathematically sound, this work presents some further shortcomings in both the formalism and the field of use. First, we propose to re-express this problem from the formalism of proximal support vector machines as introduced in Mangasarian and Wild [2]. This change is far from harmless since it introduces a suited writing for solving the problem. Another limiting factor of the method is that its performance relies on the assumption that the density between the target and outliers are different. This consideration can easily prove to be over-optimistic for real world datasets making the method unreliable, at least directly. The computation of the decision boundary is a time consuming part of the algorithm since it is based on solving a generalized eigenvalue problem (GEP). This method is therefore limited to medium sized data sets. In this paper, we propose appropriate strategies to unlock all these shortcomings and fully benefit from the interest of the approach. Firstly, we show under some conditions that generating appropriate artificial outliers allows to stay within the constraints of the method and thus enlarges the conditions of use. Secondly, we show that the GEP can be advantageously replaced by a conjugate gradient solution (CG) significantly decreasing the computational cost. Lastly, the proposed algorithm is compared with recent novelty detectors on synthetic and real datasets. (C) 2015 Elsevier Ltd. All rights reserved.
In this paper, a novel 1-norm extreme learning machine (ELM) for regression and multiclass classification is proposed as a linear programming problem whose solution is obtained by solving its dual exterior penalty pro...
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In this paper, a novel 1-norm extreme learning machine (ELM) for regression and multiclass classification is proposed as a linear programming problem whose solution is obtained by solving its dual exterior penalty problem as an unconstrained minimization problem using a fast Newton method. The algorithm converges from any starting point and can be easily implemented in MATLAB. The main advantage of the proposed approach is that it leads to a sparse model representation meaning that many components of the optimal solution vector will become zero and therefore the decision function can be determined using much less number of hidden nodes in comparison to ELM. Numerical experiments were performed on a number of interesting real-world benchmark datasets and their results are compared with ELM using additive and radial basis function (RBE) hidden nodes, optimally pruned ELM (OP-ELM) and support vector machine (SVM) methods. Similar or better generalization performance of the proposed method on the test data over ELM, OP-ELM and SVM clearly illustrates its applicability and usefulness. (C) 2013 Elsevier B.V. All rights reserved.
Fuzzy linear Fractional programmingproblem has been used as an important planning tool for the different disciplines such as engineering, business, finance, economics, etc. In this paper, a new algorithm is developed...
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Fuzzy linear Fractional programmingproblem has been used as an important planning tool for the different disciplines such as engineering, business, finance, economics, etc. In this paper, a new algorithm is developed to solve the Fuzzy linear Fractional programmingproblem (FLFPP) where the cost of the objective function, the resources and the technological coefficients are triangular fuzzy numbers. For this, the FLFPP is transformed into an equivalent deterministic Multi Objective linear Fractional programmingproblem (MOLFPP) and solved them each objective function. From the obtained solutions, we define an imprecise and aspiration level for each objectives. Hence, the objectives are transformed as fuzzy goal. Then the goal programming approach is used to achieve the highest degree of each of the membership goals by minimizing their deviational variables. Finally, two real examples and one case study problem will be used to illustrate our algorithm and compare it with the existing method.
This paper shows that the minimum ratio canceling algorithm of Wallacher (Unpublished manuscript, Institut fur Ange-wandte Mathematik, Technische Universitat, Braunschweig (1989)) (and a faster relaxed version) can be...
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This paper shows that the minimum ratio canceling algorithm of Wallacher (Unpublished manuscript, Institut fur Ange-wandte Mathematik, Technische Universitat, Braunschweig (1989)) (and a faster relaxed version) can be generalized to an algorithm for general linear programs with geometric convergence. This implies that when we have a negative cycle oracle, this algorithm will compute an optimal solution in (weakly) polynomial time. We then specialize the algorithm to linearprogramming on unimodular linear spaces, and to the minimum cost flow and (dual) tension problems. We construct instances proving that even in the network special cases the algorithm is not strongly polynomial. (C) 2000 Elsevier Science B.V. All rights reserved.
In this study, the asynchronous l positive filtering problem for a class of switched positive system with detection delay is investigated. The switched sequence satisfies modal-dwell-time (MDT) condition and the detec...
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In this study, the asynchronous l positive filtering problem for a class of switched positive system with detection delay is investigated. The switched sequence satisfies modal-dwell-time (MDT) condition and the detection delay is both time-varying and allowed to be overlapped with each other. A new linear copositive Lyapunov function, which is time-dependent, mode-dependent and MDT-dependent, is constructed and the stability of the underlying filtering error system is established. Based on the established stability result, conditions guaranteeing the l stability of the corresponding filtering error system are further derived. The allowable total running time of the unmatched sub-filters is presented to be upper bounded by a linear combination of those running on matched sub-filters. An asynchronous positive filter with l disturbance suppression performance for the underlying switched positive system with overlapped detection delay is designed by solving a linear programming problem. The effectiveness of the proposed filter is illustrated by a numerical example.
The first part of this two-part paper proposes tri-level transmission expansion planning (TTEP) under physical intentional attacks. In the first level, the network planner looks for an optimal transmission expansion p...
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The first part of this two-part paper proposes tri-level transmission expansion planning (TTEP) under physical intentional attacks. In the first level, the network planner looks for an optimal transmission expansion plan to fortify the power network. In the second level, the attacker tries to maximise damages to the network. In the third level, the adverse effects of the attacks on the network operation are minimised by the network operator. Since the third level problem is a linearprogramming (LP) problem, the second and third levels are converted into a single-level model by using primal-dual transformation, and consequently, TTEP is converted into a bi-level programmingproblem. To achieve a single-level model, instead of assuming a unique attacker, a cooperative game of multiple virtual attackers (VAs) of which every VA is to maximise the damage by attacking one transmission line is introduced and modelled. The conditions that enforce Nash and Pareto equilibria of this game are derived as linear constraints which are lower level equivalent. By using this equivalence, the aforementioned bi-level TTEP model is converted into a single-level model that can be recast as a mixed integer LP problem. The numerical results are provided in the second part.
It is shown that the holes of the objects in an input image with a CT-CNN [1] or a DT-CNN [2] may be obtained in a single transient using just one linear parameter configuration. A set of local rules is given that des...
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It is shown that the holes of the objects in an input image with a CT-CNN [1] or a DT-CNN [2] may be obtained in a single transient using just one linear parameter configuration. A set of local rules is given that describe how a CNN with a linear configuration may extract the hole of the objects of an input image in a single transient. The parameter configuration for DT-CNNs or for CT-CNNs is obtained as the solution of a single linear programming problem, including robustness as an objective. The tolerances to multiplicative and additive errors caused by circuit inaccuracies for the linear hole-extraction configurations proposed have been deduced. These tolerable errors have been corroborated by simulations. The tolerance to errors and the speed of the CT-CNN linear configuration proposed for hole extraction are compared with those of the CT-CNN nonlinear configuration found in the bibliography [3].
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