Detail publikace

Genetic Algorithms for Scenario Generation in Stochastic Programming: Motivation and General Framework

Originální název

Genetic Algorithms for Scenario Generation in Stochastic Programming: Motivation and General Framework

Anglický název

Genetic Algorithms for Scenario Generation in Stochastic Programming: Motivation and General Framework

Jazyk

en

Originální abstrakt

Stochastic programs have been developed as useful tools for modeling of various application problems. The developed algorithms usually require a solution of large-scale linear and nonlinear programs because the deterministic reformulations of the original stochastic programs are based on empirical or sampling discrete probability distributions, i.e. on so-called scenario sets. The scenario sets are often large, so the reformulated programs must be solved. Therefore, the suitable scenario set generation techniques are required. Hence, randomly selected reduced scenario sets are often employed. Related confidence intervals for the optimal objective function values have been derived and are often presented as tight enough. However, there is also demand for goal-oriented scenario generation to learn more about the extreme cases. Traditional deterministic max-min and min-min techniques are significantly limited by the size of scenario set. Therefore, this text introduces a general framework how to generate and modify suitable scenario sets by using genetic algorithms. As an example, the search of absolute lower and upper bounds by using GA is presented and further enhancements are discussed. The proposed technique is implemented in C++ and GAMS and then tested on real-data examples.

Anglický abstrakt

Stochastic programs have been developed as useful tools for modeling of various application problems. The developed algorithms usually require a solution of large-scale linear and nonlinear programs because the deterministic reformulations of the original stochastic programs are based on empirical or sampling discrete probability distributions, i.e. on so-called scenario sets. The scenario sets are often large, so the reformulated programs must be solved. Therefore, the suitable scenario set generation techniques are required. Hence, randomly selected reduced scenario sets are often employed. Related confidence intervals for the optimal objective function values have been derived and are often presented as tight enough. However, there is also demand for goal-oriented scenario generation to learn more about the extreme cases. Traditional deterministic max-min and min-min techniques are significantly limited by the size of scenario set. Therefore, this text introduces a general framework how to generate and modify suitable scenario sets by using genetic algorithms. As an example, the search of absolute lower and upper bounds by using GA is presented and further enhancements are discussed. The proposed technique is implemented in C++ and GAMS and then tested on real-data examples.

Dokumenty

BibTex


@inbook{BUT55260,
  author="Jan {Roupec} and Pavel {Popela}",
  title="Genetic Algorithms for Scenario Generation in Stochastic Programming: Motivation and General Framework",
  annote="Stochastic programs have been developed as useful tools for modeling of various application problems. The developed algorithms usually require a solution of large-scale linear and nonlinear programs because the deterministic reformulations of the original stochastic programs are based on empirical or sampling discrete probability distributions, i.e. on so-called scenario sets. The scenario sets are often large, so the reformulated programs must be solved. Therefore, the suitable scenario set generation techniques are required. Hence, randomly selected reduced scenario sets are often employed. Related confidence intervals for the optimal objective function values have been derived and are often presented as tight enough. However, there is also demand for goal-oriented scenario generation to learn more about the extreme cases. Traditional deterministic max-min and min-min techniques are significantly limited by the size of scenario set. Therefore, this text introduces a general framework how to generate and modify suitable scenario sets by using genetic algorithms. As an example, the search of absolute lower and upper bounds by using GA is presented and further enhancements are discussed. The proposed technique is implemented in C++ and GAMS and then tested on real-data examples.",
  address="Springer",
  booktitle="Lecture Notes in Electrical Engineering, book series: Advances in Computational Algorithms and Data Analysis, Vol. 14 Ao, S.L., Rieger, B., Chen, S.S. (Eds.).",
  chapter="55260",
  edition="1",
  howpublished="print",
  institution="Springer",
  year="2008",
  month="september",
  pages="527--536",
  publisher="Springer",
  type="book chapter"
}