• Corpus ID: 211989492

The discrete optimization problems with interval objective function on graphs and hypergraphs and the interval greedy algorithm

@article{Prolubnikov2020TheDO,
  title={The discrete optimization problems with interval objective function on graphs and hypergraphs and the interval greedy algorithm},
  author={Alexander V. Prolubnikov},
  journal={ArXiv},
  year={2020},
  volume={abs/2003.01937}
}
  • A. Prolubnikov
  • Published 4 March 2020
  • Computer Science, Mathematics
  • ArXiv
We consider the discrete optimization problems with interval objective function on graphs and hypergraphs. For the problems, we need to find either a strong optimal solution or a set of all possible weak solutions. A strong solution of the problem is a solution that is optimal for all possible values of the objective function's coefficients that belong to predefined intervals. A weak solution is a solution that is optimal for some of the possible values of the coefficients. We characterize the… 

References

SHOWING 1-10 OF 25 REFERENCES
A tabu search algorithm for the minmax regret minimum spanning tree problem with interval data
TLDR
The obtained results suggest that the proposed tabu search algorithm quickly outputs optimal solutions for the smaller instances, previously discussed in the existing literature.
Discrete Optimization Problems with Interval Data: Pareto Set of Solutions or Set of Weak Solutions?
  • G. Kozina
  • Mathematics, Computer Science
    Reliab. Comput.
  • 2004
TLDR
This paper analyzes the relation between these two concepts of optimality, and provides arguments in favor of the Pareto approach.
Discrete optimization problems with interval parameters
Optimization problems on graphs with interval parameters are considered, and exponential and polynomial bounds for their computational complexity are obtained. For a certain subclass of polynomially
Interval Spanning Trees Problem: Solvability and Computational Complexity
The optimization Spanning Trees Problem on graphs with interval weights is presented. The interval function is defined as the sum of interval weights of feasible spanning tree edges. The relation
A Greedy Heuristic for the Set-Covering Problem
  • V. Chvátal
  • Mathematics, Computer Science
    Math. Oper. Res.
  • 1979
TLDR
It turns out that the ratio between the two grows at most logarithmically in the largest column sum of A when all the components of cT are the same, which reduces to a theorem established previously by Johnson and Lovasz.
Approximation of min-max and min-max regret versions of some combinatorial optimization problems
TLDR
This paper investigates, for the first time in the literature, the approximation of min–max (regret) versions of classical problems like shortest path, minimum spanning tree, and knapsack, using dynamic programming and classical trimming techniques to establish fully polynomial-time approximation schemes.
Discrete Optimization with Interval Data - Minmax Regret and Fuzzy Approach
  • A. Kasperski
  • Computer Science, Mathematics
    Studies in Fuzziness and Soft Computing
  • 2008
Minmax Regret Combinatorial Optimization Problems with Interval Data.- Problem Formulation.- Evaluation of Optimality of Solutions and Elements.- Exact Algorithms.- Approximation Algorithms.- Minmax
Combinatorial Optimization: Algorithms and Complexity
This clearly written , mathematically rigorous text includes a novel algorithmic exposition of the simplex method and also discusses the Soviet ellipsoid algorithm for linear programming; efficient
Interval Methods for Data Fitting under Uncertainty: A Probabilistic Treatment
How to estimate parameters from observations subject to errors and uncertainty? Very often, the measurement errors are random quantities that can be adequately described by the probability theory.
Robust Discrete Optimization and its Applications
TLDR
This paper presents four approaches to handle Uncertainty in Decision Making using a Robust Discrete Optimization Framework and results show how these approaches can be applied to real-world problems.
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