Effective Probabilistic Stopping Rules for Randomized Metaheuristics: GRASP Implementations

  • Celso C. Ribeiro
  • Isabel Rosseti
  • Reinaldo C. Souza
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6683)


The main drawback of most metaheuristics is the absence of effective stopping criteria. Most implementations stop after performing a given maximum number of iterations or a given maximum number of consecutive iterations without improvement in the best known solution value, or after the stabilization of the set of elite solutions found along the search. We propose probabilistic stopping rules for randomized metaheuristics such as GRASP and VNS. We first show experimentally that the solution values obtained by GRASP fit a Normal distribution. Next, we use this approximation to obtain an online estimation of the number of solutions that might be at least as good as the best known at the time of the current iteration. This estimation is used to implement effective stopping rules based on the trade off between solution quality and the time needed to find a solution that might improve the best found to date. This strategy is illustrated and validated by a computational study reporting results obtained with some GRASP heuristics.


Combinatorial Optimization Problem Test Instance Elite Solution Restricted Candidate List Online Estimation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Celso C. Ribeiro
    • 1
  • Isabel Rosseti
    • 1
  • Reinaldo C. Souza
    • 2
  1. 1.Department of Computer ScienceUniversidade Federal FluminenseNiteróiBrazil
  2. 2.Department of Electrical EngineeringPontifícia Universidade Católica do Rio de JaneiroBrazil

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