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Solvability of the power flow problem in DC overhead wire circuit modeling

Jakub Ševčík, Lukáš Adam, Jan Přikryl, Václav Šmídl (2021)

Applications of Mathematics

Proper traffic simulation of electric vehicles, which draw energy from overhead wires, requires adequate modeling of traction infrastructure. Such vehicles include trains, trams or trolleybuses. Since the requested power demands depend on a traffic situation, the overhead wire DC electrical circuit is associated with a non-linear power flow problem. Although the Newton-Raphson method is well-known and widely accepted for seeking its solution, the existence of such a solution is not guaranteed. Particularly...

Solving a class of non-convex quadratic problems based on generalized KKT conditions and neurodynamic optimization technique

Alaeddin Malek, Najmeh Hosseinipour-Mahani (2015)

Kybernetika

In this paper, based on a generalized Karush-Kuhn-Tucker (KKT) method a modified recurrent neural network model for a class of non-convex quadratic programming problems involving a so-called Z -matrix is proposed. The basic idea is to express the optimality condition as a mixed nonlinear complementarity problem. Then one may specify conditions for guaranteeing the global solutions of the original problem by using results from the S-lemma. This process is proved by building up a dynamic system from...

Solving a permutation problem by a fully polynomial-time approximation scheme

Stanisław Gawiejnowicz, Wiesław Kurc, Lidia Pankowska (2010)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

For a problem of optimal discrete control with a discrete control set composed of vertices of an n-dimensional permutohedron, a fully polynomial-time approximation scheme is proposed.

Solving a possibilistic linear program through compromise programming.

Mariano Jiménez López, María Victoria Rodríguez Uría, María del Mar Arenas Parra, Amelia Bilbao Terol (2000)

Mathware and Soft Computing

In this paper we propose a method to solve a linear programming problem involving fuzzy parameters whose possibility distributions are given by fuzzy numbers. To address the above problem we have used a preference relationship of fuzzy numbers that leads us to a solving method that produces the so-called α-degree feasible solutions. It must be pointed out that the final solution of the problem depends critically on this degree of feasibility, which is in conflict with the optimal value of the objective...

Solving convex program via Lagrangian decomposition

Matthias Knobloch (2004)

Kybernetika

We consider general convex large-scale optimization problems in finite dimensions. Under usual assumptions concerning the structure of the constraint functions, the considered problems are suitable for decomposition approaches. Lagrangian-dual problems are formulated and solved by applying a well-known cutting-plane method of level-type. The proposed method is capable to handle infinite function values. Therefore it is no longer necessary to demand the feasible set with respect to the non-dualized...

Solving maximum independent set by asynchronous distributed hopfield-type neural networks

Giuliano Grossi, Massimo Marchi, Roberto Posenato (2006)

RAIRO - Theoretical Informatics and Applications

We propose a heuristic for solving the maximum independent set problem for a set of processors in a network with arbitrary topology. We assume an asynchronous model of computation and we use modified Hopfield neural networks to find high quality solutions. We analyze the algorithm in terms of the number of rounds necessary to find admissible solutions both in the worst case (theoretical analysis) and in the average case (experimental Analysis). We show that our heuristic is better than the...

Solving multi-agent scheduling problems on parallel machines with a global objective function

F. Sadi, A. Soukhal, J.-C. Billaut (2014)

RAIRO - Operations Research - Recherche Opérationnelle

In this study, we consider a scheduling environment with m(m ≥ 1) parallel machines. The set of jobs to schedule is divided into K disjoint subsets. Each subset of jobs is associated with one agent. The K agents compete to perform their jobs on common resources. The objective is to find a schedule that minimizes a global objective function f0, while maintaining the regular objective function of each agent, fk, at a level no greater than a fixed value, εk (fk ∈ {fkmax, ∑fk}, k = 0, ..., K). This...

Solving multi-objective fuzzy matrix games via multi-objective linear programming approach

Abha Aggarwal, Imran Khan (2016)

Kybernetika

A class of multi-objective fuzzy matrix games is studied and it is shown that solving such a game is equivalent to solving a pair of multi-objective linear programming problems. This work generalizes an earlier study of Fernandez et al. [7] from crisp scenario to fuzzy scenario on the lines of Bector et al. [4]. Further certain difficulties with similar studies reported in the literature are also discussed.

Solving systems of two–sided (max, min)–linear equations

Martin Gavalec, Karel Zimmermann (2010)

Kybernetika

A finite iteration method for solving systems of (max, min)-linear equations is presented. The systems have variables on both sides of the equations. The algorithm has polynomial complexity and may be extended to wider classes of equations with a similar structure.

Solving the Cahn-Hilliard variational inequality with a semi-smooth Newton method

Luise Blank, Martin Butz, Harald Garcke (2011)

ESAIM: Control, Optimisation and Calculus of Variations

The Cahn-Hilliard variational inequality is a non-standard parabolic variational inequality of fourth order for which straightforward numerical approaches cannot be applied. We propose a primal-dual active set method which can be interpreted as a semi-smooth Newton method as solution technique for the discretized Cahn-Hilliard variational inequality. A (semi-)implicit Euler discretization is used in time and a piecewise linear finite element discretization of splitting type is used in space leading...

Solving the Cahn-Hilliard variational inequality with a semi-smooth Newton method

Luise Blank, Martin Butz, Harald Garcke (2011)

ESAIM: Control, Optimisation and Calculus of Variations

The Cahn-Hilliard variational inequality is a non-standard parabolic variational inequality of fourth order for which straightforward numerical approaches cannot be applied. We propose a primal-dual active set method which can be interpreted as a semi-smooth Newton method as solution technique for the discretized Cahn-Hilliard variational inequality. A (semi-)implicit Euler discretization is used in time and a piecewise linear finite element discretization of splitting type is used in space...

Solving the Crop Allocation Problem using Hard and Soft Constraints

Mahuna Akplogan, Simon de Givry, Jean-Philippe Métivier, Gauthier Quesnel, Alexandre Joannon, Frédérick Garcia (2013)

RAIRO - Operations Research - Recherche Opérationnelle

Application tools for the crop allocation problem (CAP) are required for agricultural advisors to design more efficient farming systems. Despite the extensive treatment of this issue by agronomists in the past, few methods tackle the crop allocation problem considering both the spatial and the temporal aspects of the CAP. In this paper, we precisely propose an original formulation addressing the crop allocation planning problem while taking farmers’ management choices into account. These choices...

Solving the Minimum Independent Domination Set Problem in Graphs by Exact Algorithm and Greedy Heuristic

Christian Laforest, Raksmey Phan (2013)

RAIRO - Operations Research - Recherche Opérationnelle

In this paper we present a new approach to solve the Minimum Independent Dominating Set problem in general graphs which is one of the hardest optimization problem. We propose a method using a clique partition of the graph, partition that can be obtained greedily. We provide conditions under which our method has a better complexity than the complexity of the previously known algorithms. Based on our theoretical method, we design in the second part of this paper an efficient algorithm by including...

Solving the sensor cover energy problem via integer linear programming

Pingke Li (2021)

Kybernetika

This paper demonstrates that the sensor cover energy problem in wireless communication can be transformed into a linear programming problem with max-plus linear inequality constraints. Consequently, by a well-developed preprocessing procedure, it can be further reformulated as a 0-1 integer linear programming problem and hence tackled by the routine techniques developed in linear and integer optimization. The performance of this two-stage solution approach is evaluated on a set of randomly generated...

Solving the simple plant location problem by genetic algorithm

Jozef Kratica, Dušan Tošic, Vladimir Filipović, Ivana Ljubić (2001)

RAIRO - Operations Research - Recherche Opérationnelle

The simple plant location problem (SPLP) is considered and a genetic algorithm is proposed to solve this problem. By using the developed algorithm it is possible to solve SPLP with more than 1000 facility sites and customers. Computational results are presented and compared to dual based algorithms.

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