On Mar 27, 5:20 am, "Ted Dunning"  wrote:   
   > On Mar 25, 6:33 am, "hegal...@gmail.com"  wrote:   
   >   
   > > I donot agree that fitness has to be scalar. In fact, it is when   
   > > either you are evaluating single objectively or weighted vevctor of   
   > > multiple values. This is not true for most of the real world problems.   
   > > A more intuitive way is to design a multiple objective vector which   
   > > can be used to evaluate choromosomes. This is what multiobjective EC   
   > > about. The "probability of passing genetic information to later   
   > > generations" can be decided by the comparisons of all objectives in a   
   > > dominating/non-dominating way. Optimization doesnt have to be within   
   > > one-dimension also, i.e. in the case of single objective.   
   >   
   > Probabilities are inherently scalar.  That really isn't a matter of   
   > debate.  As such, evolutionary algorithms are computing the fixed   
   > point of a Markov process   
   >   
      
   My claim was that utility might need to be a vector.   
   To quote von Neumann and Morgenstern (Theory of Games   
   and Economic Behavior, P.U.Press, 1944) "We have   
   conceded that one may doubt whether a person can always decide which   
   of two alternatives...he prefers... It leads to   
   what may be described as a many-dimensional vector concept   
   of utility."   
      
   I agree with von Neumann.   
      
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