Reward-based selection

Reward-based selection is a technique used in evolutionary algorithms for selecting potentially useful solutions for recombination. The probability of being selected for an individual is proportional to the cumulative reward obtained by the individual. The cumulative reward can be computed as a sum of the individual reward and the reward inherited from parents.

Description

edit

Reward-based selection can be used within Multi-armed bandit framework for Multi-objective optimization to obtain a better approximation of the Pareto front. [1]

The newborn   and its parents receive a reward  , if   was selected for new population  , otherwise the reward is zero. Several reward definitions are possible:

  • 1.  , if the newborn individual   was selected for new population  .
  • 2.  , where   is the rank of newly inserted individual in the population of   individuals. Rank can be computed using a well-known non-dominated sorting procedure.[2]
  • 3.  , where   is the hypervolume indicator contribution of the individual   to the population  . The reward   if the newly inserted individual improves the quality of the population, which is measured as its hypervolume contribution in the objective space.
  • 4. A relaxation of the above reward, involving a rank-based penalization for points for  -th dominated Pareto front:  

Reward-based selection can quickly identify the most fruitful directions of search by maximizing the cumulative reward of individuals.

See also

edit

References

edit
  1. ^ Loshchilov, I.; M. Schoenauer; M. Sebag (2011). "Not all parents are equal for MO-CMA-ES" (PDF). Evolutionary Multi-Criterion Optimization 2011 (EMO 2011). Springer Verlag, LNCS 6576. pp. 31–45. Archived from the original (PDF) on 2012-06-04.
  2. ^ Deb, K.; Pratap, A.; Agarwal, S.; Meyarivan, T. (2002). "A fast and elitist multi-objective genetic algorithm: NSGA-II". IEEE Transactions on Evolutionary Computation. 6 (2): 182–197. CiteSeerX 10.1.1.17.7771. doi:10.1109/4235.996017.