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Semidefinite Programming Based Algorithms for the Sparsest Cut Problem

Luis A.A. Meira, Flávio K. Miyazawa (2011)

RAIRO - Operations Research

In this paper we analyze a known relaxation for the Sparsest Cut problem based on positive semidefinite constraints, and we present a branch and bound algorithm and heuristics based on this relaxation. The relaxed formulation and the algorithms were tested on small and moderate sized instances. It leads to values very close to the optimum solution values. The exact algorithm could obtain solutions for small and moderate sized instances, and the best heuristics obtained optimum or near optimum...

Semidefinite Programming Based Algorithms for the Sparsest Cut Problem

Luis A.A. Meira, Flávio K. Miyazawa (2011)

RAIRO - Operations Research

In this paper we analyze a known relaxation for the Sparsest Cut problem based on positive semidefinite constraints, and we present a branch and bound algorithm and heuristics based on this relaxation. The relaxed formulation and the algorithms were tested on small and moderate sized instances. It leads to values very close to the optimum solution values. The exact algorithm could obtain solutions for small and moderate sized instances, and the best heuristics obtained optimum or near optimum...

Simulated Annealing and Tabu Search for Discrete-Continuous Project Scheduling with Discounted Cash Flows

Grzegorz Waligóra (2014)

RAIRO - Operations Research - Recherche Opérationnelle

Discrete-continuous project scheduling problems with positive discounted cash flows and the maximization of the NPV are considered. We deal with a class of these problems with an arbitrary number of discrete resources and one continuous, renewable resource. Activities are nonpreemptable, and the processing rate of an activity is a continuous, increasing function of the amount of the continuous resource allotted to the activity at a time. Three common payment models – Lump Sum Payment, Payments at...

Solution of a fractional combinatorial optimization problem by mixed integer programming

Alain Billionnet, Karima Djebali (2006)

RAIRO - Operations Research

Fractionnal mathematical programs appear in numerous operations research, computer science and economic domains. We consider in this paper the problem of maximizing the sum of 0–1 hyperbolic ratios (SRH). In contrast to the single ratio problem, there has been little work in the literature concerning this problem. We propose two mixed-integer linear programming formulations of SRH and develop two different strategies to solve them. The first one consists in using directly a general-purpose mixed-integer...

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 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 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.

Solving the simple plant location problem by genetic algorithm

Jozef Kratica, Dušan Tošic, Vladimir Filipović, Ivana Ljubić (2010)

RAIRO - Operations Research

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.

Stability of scheduling with random processing times on one machine

Paweł Rajba, Mieczysław Wodecki (2012)

Applicationes Mathematicae

We consider a strong NP-hard single-machine scheduling problem with deadlines and minimizing the total weight of late jobs on a single machine ( 1 | | w i U i ). Processing times are deterministic values or random variables having Erlang distributions. For this problem we study the tolerance to random parameter changes for solutions constructed according to tabu search metaheuristics. We also present a measure (called stability) that allows an evaluation of the algorithm based on its resistance to random parameter...

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