多目的最適化におけるSTOMを利用した妥協解の計算

clear; close all;

x = -2:0.001:2;
f1 = @(x) exp(-x)+1.4*exp(-x.^2);
f2 = @(x) exp(x)+1.4*exp(-x.^2);
figure(1);
hold on;
% plot(f1(x),f2(x),'o');

x1 = 0:0.01:7;
y1 = interp1(f2(x),f1(x),x1,'spline');
plot(x1,y1,'-','DisplayName','Pareto Front');
xlim([0,7]);
ylim([0,7]);

f1i = 0;
f2i = 0;
f1a = 4;
f2a = 2;

w1 = 1/(f1a-f1i);
w2 = 1/(f2a-f2i);

C = max(w1*(f1(x)-f1a),w2*(f2(x)-f2a));
xopt = x(find(C==min(C)))
f1opt = f1(xopt)
f2opt = f2(xopt)

syms f1_symbol(t) f2_symbol(t)
f1_symbol(t) = @(t) exp(-t)+1.4*exp(-t.^2);
f2_symbol(t) = @(t) exp(t)+1.4*exp(-t.^2);
df1 = diff(f1_symbol);
df2 = diff(f2_symbol);
t12 = -df2/df1;

t12_val = eval(subs(t12,'t',xopt));
t21_val = 1/t12_val;
T = [-1 t12_val;
    t21_val -1]

C = (t12-0.5)^2;
figure(2);
plot(x,subs(C,t,x),'-');
title('D=(t_{1,2}-0.5)^2');
ylim([0 0.2]);
xA1 = fminsearch(C,-1.5)
xA2 = fminsearch(C,0)
xA3 = fminsearch(C,1)

f1_A1 = f1(xA1)
f2_A1 = f2(xA1)
f1_A2 = f1(xA2)
f2_A2 = f2(xA2)
f1_A3 = f1(xA3)
f2_A3 = f2(xA3)

figure(1);
plot(f1_A1,f2_A1,'o','DisplayName',sprintf('x=%.3g (t_{1,2}=0.5)',xA1));
plot(f1_A2,f2_A2,'o','DisplayName',sprintf('x=%.3g (t_{1,2}=0.5)',xA2));
plot(f1_A3,f2_A3,'o','DisplayName',sprintf('x=%.3g (t_{1,2}=0.5)',xA3));
legend();

t12_val = eval(subs(t12,'t',xA1));
t21_val = 1/t12_val;
T1 = [-1 t12_val;
    t21_val -1]

t12_val = eval(subs(t12,'t',xA2));
t21_val = 1/t12_val;
T2 = [-1 t12_val;
    t21_val -1]

t12_val = eval(subs(t12,'t',xA3));
t21_val = 1/t12_val;
T3 = [-1 t12_val;
    t21_val -1]

big;