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In this paper we will describe a new class of coloring problems, arising from military frequency assignment, where we want to minimize the number of distinct -uples of colors used to color a given set of -complete-subgraphs of a graph. We will propose two relaxations based on Semi-Definite Programming models for graph and hypergraph coloring, to approximate those (generally) NP-hard problems, as well as a generalization of the works of Karger et al. for hypergraph coloring, to find good feasible...
In this paper we will describe a new class of coloring
problems, arising from military frequency assignment, where we want to
minimize the number of distinct n-uples of colors used to color a given
set of n-complete-subgraphs of a graph.
We will propose two relaxations based on
Semi-Definite Programming models for graph and hypergraph
coloring, to approximate those (generally) NP-hard problems, as well as
a generalization of the works of Karger et al. for hypergraph coloring,
to find good feasible...
Let and for . Max-algebra is an analogue of linear algebra developed on the pair of operations extended to matrices and vectors. The system of equations and inequalities have each been studied in the literature. We consider a problem consisting of these two systems and present necessary and sufficient conditions for its solvability. We also develop a polynomial algorithm for solving max-linear program whose constraints are max-linear equations and inequalities.
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...
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.
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...
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...
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.
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.
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...
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