線形加重和法によるパレート最適値の計算

clear; close all;

x1 = -4:0.1:4;
x2 = -4:0.1:4;

f1 = 1-exp(-(x1-1/sqrt(2)).^2-(x2-1/sqrt(2)).^2);
f2 = 1-exp(-(x1+1/sqrt(2)).^2-(x2+1/sqrt(2)).^2);
plot(f1,f2,'rx');
hold on;

w1s = 0:0.1:1.0;
w2s = 0:0.1:1.0;
x1opts = [];
x2opts = [];
for i=1:length(w1s)
    w1 = w1s(i);
    for j=1:length(w2s)
      w2 = w2s(j);
      C = w1*f1+w2*f2;
      if length(find(C==min(C)))>2
          continue
      end
      x1opt = x1(find(C==min(C),1));
      x2opt = x2(find(C==min(C),1));
      
      x1opts(end+1)=x1opt;
      x2opts(end+1)=x1opt;      
    end
end

x1opts = unique(sort(x1opts))
x2opts = unique(sort(x2opts))
f1opts = 1-exp(-(x1opts-1/sqrt(2)).^2-(x2opts-1/sqrt(2)).^2);
f2opts = 1-exp(-(x1opts+1/sqrt(2)).^2-(x2opts+1/sqrt(2)).^2);
plot(f1opts,f2opts,'bo');

big;