MOFSRank: A Multiobjective Evolutionary Algorithm for Feature Selection in Learning to Rank

Algorithm 3

MOFS.

Input: :  maximum generations of multi-objective feature selection, :  population size of multi-objective

feature selection, :  crossover probability of multi-objective feature selection, :  mutation probability

of multi-objective feature selection, :  a set of non-dominated instance subsets;

Output: a set of non-dominated feature subsets , and their corresponding rankers set ;

  Initializing the population ;

  for   to   do

 /Evaluating by two proposed objectives with formula (2)/

 for   to   do

   calculating the number of non-zero features in ; the first objective value of -th individual

  ; select the ranker with the smallest value of

on the as the ranker of individual

  ; the second objective value of -th individual

 end for

  Binary Tournament ;

  calculating with formulas (3), (5) and (6);

  Variation ;

  Environmental ;

  end for

   selecting the solutions on the Pareto front;

   the corresponding ranker set of ;

  Return   and ;