In multiobjective optimization, how to calculate the distance to reference point?

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In multiobjective optimization, what does the distance exactly means, is it:



1) The distance from reference point (V) to an individual (Xi) (candidate solution) in the population (decision space).



 Euclidean Distance = d(Xi,V) 


OR



2) The distance from reference point (V) to the objective vector f(X) in the objective space, where f(Xi) = f(f1(Xi),...fm(Xi)). m is the number of objectives.



Euclidean Distance = d(f(Xi),V) 


In this paper "Harris’s Hawk Multi-Objective Optimizer for Reference
Point Problems", in the pseudo code, Section 4.2:



a-




Calculate distances to reference point v for each search agent(hawk)
Xi on all objectives ݂fm(Xi).




and



b-




Calculate distances to reference point vi for all ݂fm(Xi) on each
search agent in group




What is the difference between a and b?










share|cite|improve this question



























    up vote
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    down vote

    favorite












    In multiobjective optimization, what does the distance exactly means, is it:



    1) The distance from reference point (V) to an individual (Xi) (candidate solution) in the population (decision space).



     Euclidean Distance = d(Xi,V) 


    OR



    2) The distance from reference point (V) to the objective vector f(X) in the objective space, where f(Xi) = f(f1(Xi),...fm(Xi)). m is the number of objectives.



    Euclidean Distance = d(f(Xi),V) 


    In this paper "Harris’s Hawk Multi-Objective Optimizer for Reference
    Point Problems", in the pseudo code, Section 4.2:



    a-




    Calculate distances to reference point v for each search agent(hawk)
    Xi on all objectives ݂fm(Xi).




    and



    b-




    Calculate distances to reference point vi for all ݂fm(Xi) on each
    search agent in group




    What is the difference between a and b?










    share|cite|improve this question

























      up vote
      0
      down vote

      favorite









      up vote
      0
      down vote

      favorite











      In multiobjective optimization, what does the distance exactly means, is it:



      1) The distance from reference point (V) to an individual (Xi) (candidate solution) in the population (decision space).



       Euclidean Distance = d(Xi,V) 


      OR



      2) The distance from reference point (V) to the objective vector f(X) in the objective space, where f(Xi) = f(f1(Xi),...fm(Xi)). m is the number of objectives.



      Euclidean Distance = d(f(Xi),V) 


      In this paper "Harris’s Hawk Multi-Objective Optimizer for Reference
      Point Problems", in the pseudo code, Section 4.2:



      a-




      Calculate distances to reference point v for each search agent(hawk)
      Xi on all objectives ݂fm(Xi).




      and



      b-




      Calculate distances to reference point vi for all ݂fm(Xi) on each
      search agent in group




      What is the difference between a and b?










      share|cite|improve this question















      In multiobjective optimization, what does the distance exactly means, is it:



      1) The distance from reference point (V) to an individual (Xi) (candidate solution) in the population (decision space).



       Euclidean Distance = d(Xi,V) 


      OR



      2) The distance from reference point (V) to the objective vector f(X) in the objective space, where f(Xi) = f(f1(Xi),...fm(Xi)). m is the number of objectives.



      Euclidean Distance = d(f(Xi),V) 


      In this paper "Harris’s Hawk Multi-Objective Optimizer for Reference
      Point Problems", in the pseudo code, Section 4.2:



      a-




      Calculate distances to reference point v for each search agent(hawk)
      Xi on all objectives ݂fm(Xi).




      and



      b-




      Calculate distances to reference point vi for all ݂fm(Xi) on each
      search agent in group




      What is the difference between a and b?







      optimization algorithms euclidean-geometry






      share|cite|improve this question















      share|cite|improve this question













      share|cite|improve this question




      share|cite|improve this question








      edited Sep 8 at 12:37

























      asked Sep 8 at 12:30









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