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Optimization tool Multi objective Genetic Algorithm

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Asad Abbas
Asad Abbas 2016 年 8 月 23 日
コメント済み: Nathan S 2016 年 9 月 1 日
I am facing problem of multi objective optimization by Genetic Algorithm (By using Matlab Optimization tool) with give 4 objective functions and 13 variables. x is random generation population of 0 and 1. But when I optimize this file, the values of variable and population have change even with negative values. I am not getting my results. Please help me. If my question is not understandable please let me know. I will explain more.
function f=task1(x)
x=randi([0 1],1,V);

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Alan Weiss
Alan Weiss 2016 年 8 月 24 日
You didn't show us your call to gamultiobj, so we cannot check whether you correctly passed bounds to the solver. However, I can see that your objective function throws away the x that the solver passes, and instead creates a new x via the line
x=randi([0 1],1,V);
Remove that line from your objective function, you need to accept the x that the solver passes and work with it.
If you need your variables to be integer-valued, then you are out of luck, because gamultiobj works only with continuous variables. But if you have a vector of only 13 variables that are binary-valued, then why not simply do an exhaustive search over all the possible values? There are only 8192 values to examine.
Alan Weiss
MATLAB mathematical toolbox documentation

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Asad Abbas
Asad Abbas 2016 年 8 月 24 日
Sir you understand exactly what I want. From your suggestions I think gamultiobj is not useful for me because I want variables with binary values but not continuous variables. So can you please suggest me any other approach. One more thing I want specify goal as in goalattain algorithm for estimated solutions near to goal.
Thank you so much for your kind reply.
Alan Weiss
Alan Weiss 2016 年 8 月 24 日
As I told you on two occasions ( here is the other ), I think that you should generate all 8192 possible binary values for your 13 decision variables. Then take the resulting 8192 sets of 4-D objective function values and take the Pareto set among them.
I am not sure of the best algorithm to extract the Pareto points, but the following might work:
  1. Get the minimum objective function value in each of the 4 components. These points will definitely be on the Pareto set if they are unique. Keep them in a set of presumptive Pareto points.
  2. Go through the remaining points one at a time comparing their values to those in the presumptive Pareto set you are collecting. If the new point is better in every way than a presumptive Pareto point, then remove the presumptive point and include the new point. Make suer that you compare the new point to all existing presumptive points, because a new point can be better than several presumptive points.
Good luck,
Alan Weiss
MATLAB mathematical toolbox documentation
Nathan S
Nathan S 2016 年 9 月 1 日
Finding the Pareto optimal set from a collection of sample points is an active area of research. This paper presents an algorithm which is relatively simple to implement and also faster than many other approaches.

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