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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.

Solving the Task Assignment Problem with a Variable Neighborhood Search

Kratica, Jozef, Savić, Aleksandar, Filipović, Vladimir, Milanović, Marija (2010)

Serdica Journal of Computing

In this paper a variable neighborhood search (VNS) approach for the task assignment problem (TAP) is considered. An appropriate neighborhood scheme along with a shaking operator and local search procedure are constructed specifically for this problem. The computational results are presented for the instances from the literature, and compared to optimal solutions obtained by the CPLEX solver and heuristic solutions generated by the genetic algorithm. It can be seen that the proposed VNS approach reaches...

Sur les α -flots

W. Bienia, V. Letrouit (1997)

RAIRO - Operations Research - Recherche Opérationnelle

The adaptation of the k -means algorithm to solving the multiple ellipses detection problem by using an initial approximation obtained by the DIRECT global optimization algorithm

Rudolf Scitovski, Kristian Sabo (2019)

Applications of Mathematics

We consider the multiple ellipses detection problem on the basis of a data points set coming from a number of ellipses in the plane not known in advance, whereby an ellipse E is viewed as a Mahalanobis circle with center S , radius r , and some positive definite matrix Σ . A very efficient method for solving this problem is proposed. The method uses a modification of the k -means algorithm for Mahalanobis-circle centers. The initial approximation consists of the set of circles whose centers are determined...

The color-balanced spanning tree problem

Štefan Berežný, Vladimír Lacko (2005)

Kybernetika

Suppose a graph G = ( V , E ) whose edges are partitioned into p disjoint categories (colors) is given. In the color-balanced spanning tree problem a spanning tree is looked for that minimizes the variability in the number of edges from different categories. We show that polynomiality of this problem depends on the number p of categories and present some polynomial algorithm.

The inverse maximum flow problem considering l∞ norm

Adrian Deaconu (2008)

RAIRO - Operations Research

The problem is to modify the capacities of the arcs from a network so that a given feasible flow becomes a maximum flow and the maximum change of the capacities on arcs is minimum. A very fast O(m⋅log(n)) time complexity algorithm for solving this problem is presented, where m is the number of arcs and n is the number of nodes of the network. The case when both, lower and upper bounds of the flow can be modified so that the given feasible flow becomes a maximum flow is also discussed. The algorithm...

The Lazy Travelling Salesman Problem in ℝ 2

Paz Polak, Gershon Wolansky (2007)

ESAIM: Control, Optimisation and Calculus of Variations

We study a parameter (σ) dependent relaxation of the Travelling Salesman Problem on  ℝ 2 . The relaxed problem is reduced to the Travelling Salesman Problem as σ → 0. For increasing σ it is also an ordered clustering algorithm for a set of points in ℝ 2 . A dual formulation is introduced, which reduces the problem to a convex optimization, provided the minimizer is in the domain of convexity of the relaxed functional. It is shown that this last condition is generically satisfied, provided σ is large enough. ...

The partial inverse minimum cut problem with L1-norm is strongly NP-hard

Elisabeth Gassner (2010)

RAIRO - Operations Research

The partial inverse minimum cut problem is to minimally modify the capacities of a digraph such that there exists a minimum cut with respect to the new capacities that contains all arcs of a prespecified set. Orlin showed that the problem is strongly NP-hard if the amount of modification is measured by the weighted L1-norm. We prove that the problem remains hard for the unweighted case and show that the NP-hardness proof of Yang [RAIRO-Oper. Res.35 (2001) 117–126] for this problem with additional bound...

The periodic Vehicle routing problem: classification and heuristic

M. Mourgaya, F. Vanderbeck (2006)

RAIRO - Operations Research

Periodic Vehicle Routing Problem: classification and heuristic for tactical planning. The Periodic Vehicle Routing Problem (PVRP) consists in assigning customer visits to vehicle routes in some periods of a time horizon so as to satisfy some service level requirements that can take the form of frequency of visit, constraint on time lag between visits, or pre-defined visit patterns. We present different variants of this problem and propose a classification. Then, we consider a model for tactical...

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