GA for Mixed-Integer Nonlinear Programing

Dear all,

I am having a problem with solving a MINLP with GA solver. It keeps having the message of "Constraint function must return real value". I have double checked all the constraints and they should be fine. But this message still appeared. May I ask whether Matlab 2018b can show the contraint that has a problem? I would really appreciate your help.

Thank you so much,

Kind Regards,

Hoang Trinh,

[Ameer Hamza]

Can you share the code for the optimization problem? Alternatively, you can add a breakpoint inside nonlcon and find out if there is some issue with return values.

[Hoang Trinh]

Dear Ameer Hamza,

Yeah, I also think there is something wrong in the nonlcon constraints. But I do not know how to detect it. Here is the code of my nonlcon constraints:

function [c ceq] = nlcon(x) 
	tol = 1e-3  ; 
	c(1) = x(32) - 500*x(1)*6.5/(500*6.5  +  x(1)) - tol   ; 
	c(2) = x(33) - 50*(0.06*x(2) - 1)*(1 - exp(-1095)) - 520*(10950^0.8)*(1 - 0.008*x(2))*(0.8  +  1.2*exp(-0.005*x(32)))/(10950^0.8  +  0.15*x(32)) - tol   ; 
	c(3) = x(34)^2 - (x(1) - 41 - x(34))*(400*x(24))/x(5) - tol   ; 
	c(4) = 1000*x(44) - x(9)*x(10)*x(11)*x(12) - tol    ; 
	c(5) = x(51) - 0.6*(x(9)^2*x(10)*x(11)  +  2000*x(50))/1000 - tol   ; 
	c(6) = x(52) - 1/1000*(600*x(44)*x(45)  +  720*x(50)*(2*x(45)-x(9))/x(45))   - tol    ; 
	c(7) = x(53) - 1/1000000*(300*x(44)*x(45)*(x(9)-x(12)*x(45))  +  360*x(50)*(2*x(45)-x(9))^2/x(45)) - tol   ; 
	c(8) = x(54) - 1/1000*(3600*x(44)*x(45)/11  +  120*x(50)*(12*x(45) - 11*x(9))/x(45)) - tol    ; 
	c(9) = x(55) - 1/1000000*(9000*x(44)*x(45)*(x(9) - 6/11*x(12)*x(45))/55  +  660*x(50)*(2*x(45)-x(9))^2/x(45)) - tol   ; 
	c(10) = x(56) - 1/1000000*(800*x(45)*x(50)*(1 - 0.5*x(12)*x(57))  +  960*x(50)*(1 - (x(9)-x(45))/x(45)/x(57))*(0.5*x(12)*x(57)*x(45) - x(9)  +  x(45))) - tol   ; 
	c(11) = x(57)*(x(57)  +  200*x(50)/1000/x(44)/x(45)) - 1200*x(50)*(x(9)-x(45))/1000/x(44)/x(45)^2 - tol   ; 
	c(12) = 1000*x(58) - 7*(7*6.5*(0.03*x(1)  +  5.7)  +  30*(x(9)/1000)^2*(3.5 - x(1)/1000)) - tol   ; 
	c(13) = x(59)  -  0.05*x(9)*x(58) - tol   ; 
	c(14) = -x(32)  +  500*x(1)*6.5/(500*6.5  +  x(1)) - tol   ; 
	c(15) = -x(33)  +  50*(0.06*x(2) - 1)*(1 - exp(-1095))  +  520*(10950^0.8)*(1 - 0.008*x(2))*(0.8  +  1.2*exp(-0.005*x(32)))/(10950^0.8  +  0.15*x(32)) - tol   ; 
	c(16) = -x(34)^2  +  (x(1) - 41 - x(34))*(400*x(24))/x(5) - tol   ; 
	c(17) = -1000*x(44)  +  x(9)*x(10)*x(11)*x(12) - tol    ; 
	c(18) = -x(51)  +  0.6*(x(9)^2*x(10)*x(11)  +  2000*x(50))/1000 - tol   ; 
	c(19) = -x(52)  +  1/1000*(600*x(44)*x(45)  +  720*x(50)*(2*x(45) - x(9))/x(45))   - tol    ; 
	c(20) = -x(53)  +  1/1000000*(300*x(44)*x(45)*(x(9)-x(12)*x(45))  +  360*x(50)*(2*x(45)-x(9))^2/x(45)) - tol   ; 
	c(21) = -x(54)  +  1/1000*(18000/55*x(44)*x(45)  +  120*x(50)*(12*x(45) - 11*x(9))/x(45)) - tol    ; 
	c(22) = -x(55)  +  1/1000000*(9000/55*x(44)*x(45)*(x(9) - 6/11*x(12)*x(45))  +  660*x(50)*(2*x(45)-x(9))^2/x(45) ) - tol   ; 
	c(23) = -x(56)  +  1/1000000*(800*x(45)*x(50)*(1 - 0.5*x(12)*x(57))  +  960*x(50)*(1 - (x(9)-x(45))/x(45)/x(57))*(0.5*x(12)*x(57)*x(45) - x(9)  +  x(45))) - tol   ; 
	c(24) = -x(57)*(x(57)  +  200*x(50)/(1000*x(44)*x(45)))  +  1200*x(50)*(x(9)-x(45))/1000/x(44)/x(45)^2 - tol   ; 
	c(25) = -1000*x(58)  +  7*(7*6.5*(0.03*x(1)  +  5.7)  +  30*(x(9)/1000)^2*(3.5-x(1)/1000)) - tol   ; 
	c(26) = -x(59)  +  0.05*x(9)*x(58) - tol   ; 
	c(27) = x(22)/(2*x(2)*x(3)*x(4)*(x(1) - 41)) - 0.36   ; 
	c(28) = -x(22)  +  36/125*(x(2))^0.5*x(1)^2/(x(1) - 41)    ; 
	c(29) = x(23)/(2*x(2)*x(3)*x(4)*(x(1) - 41)) - 0.36     ; 
	c(30) = -1/2500*x(23)*(x(1) - 41)*(1 - x(23)/(4*x(2)*x(3)*(x(1) - 41)))  +  1/10*(0.03*x(1)  +  5.7)*(6.5/2 * +  x(9)/2000)*(7 - 0.7*x(9)/1000)^2/6.5     ; 
	c(31) = -x(23)  +  36/125*(x(2))^0.5*x(1)^2/(x(1) - 41)    ; 
	c(32) = x(23)/(x(1) - 41) - 4/5*x(2)*x(3)*x(4)    ; 
	c(33) = x(24)/(2*x(2)*x(3)*x(4)*(x(1) - 41)) - 0.36    ; 
	c(34) = -1/2500*x(24)*(x(1) - 41)*(1 - x(24)/(4*x(2)*x(3)*(x(1) - 41)))  +  9/64*(0.03*x(1)  +  5.7)*(7 - 0.7*x(9)/1000)^2    ; 
	c(35) = -x(24)  + 36/125*(x(2))^0.5*x(1)^2/(x(1) - 41)    ; 
	c(36) = x(24)/(x(1) - 41) - 4/5*x(2)*x(3)*x(4)    ; 
	c(37) = x(25)/(2*x(2)*x(3)*x(4)*(x(1) - 41)) - 0.36    ; 
	c(38) = -1/2500*x(25)*(x(1) - 41)*(1 - x(25)/(4*x(2)*x(3)*(x(1) - 41)))  +  1/20*(0.03*x(1)  +  5.7)*(7 - 0.7*x(9)/1000)^2    ; 
	c(39) = -x(25)  + 36/125*(x(2))^0.5*x(1)^2/(x(1) - 41)    ; 
	c(40) = x(25)/(x(1) - 41) - 4/5*x(2)*x(3)*x(4)    ; 
	c(41) = x(26)/(2*x(2)*x(3)*x(4)*(x(1) - 53)) - 0.36    ; 
	c(42) = -1/2500*x(26)*(x(1) - 53)*(1 - x(26)/(4*x(2)*x(3)*(x(1) - 53)))  +  9/128*(0.03*x(1)  +  5.7)*(7/2 * +  x(9)/2000)*(6.5 - 0.7*x(9)/1000)^2/(7/4 * +  x(9)/2000)     ; 
	c(43) = -x(26)  + 36/125*(x(2)^0.5)*x(1)^2/(x(1) - 53)    ; 
	c(44) = x(26)/(x(1) - 53) - 4/5*x(2)*x(3)*x(4)    ; 
	c(45) = x(27)/(2*x(2)*x(3)*x(4)*(x(1) - 53)) - 0.36    ; 
	c(46) = -1/2500*x(27)*(x(1) - 53)*(1 - x(27)/(4*x(2)*x(3)*(x(1) - 53)))  +  1/10*(0.03*x(1)  +  5.7)*(7/2 * +  x(9)/2000)*(6.5 - 0.7*x(9)/1000)^2/7   ; 
	c(47) = -x(27)  + 36/125*(x(2)^0.5)*x(1)^2/(x(1) - 53)    ; 
	c(48) = x(27)/(x(1) - 53) - 4/5*x(2)*x(3)*x(4)    ; 
	c(49) = -1/2500*x(28)*(x(1) - 53)*(1 - x(28)/(4*x(2)*x(3)*(x(1) - 53)))  +  9/64*7*(0.03*x(1)  +  5.7)*(6.5 - 0.7*x(9)/1000)^2/6.5     ; 
	c(50) = -x(28) + 36/125*(x(2))^0.5*x(1)^2/(x(1) - 41)    ; 
	c(51) = x(28)/(x(1) - 53) - 4/5*x(2)*x(3)*x(4)    ; 
	c(52) = x(29)/(2*x(2)*x(3)*x(4)*(x(1) - 53)) - 0.36    ; 
	c(53) = -1/2500*x(29)*(x(1) - 53)*(1 - x(29)/(4*x(2)*x(3)*(x(1) - 53)))  +  1/40*7*(0.03*x(1)  +  5.7)*(6.5 - 0.7*x(9)/1000)^2/(7-6.5/2)     ; 
	c(54) = -x(29)   +  36/125*(x(2)^0.5)*x(1)^2/(x(1) - 53)    ; 
	c(55) = x(29)/(x(1) - 53)  - 4/5*x(2)*x(3)*x(4)   ; 
	c(56) = 0.25*(0.03*x(1)  +  5.7)*(7  +  x(9)/1000)*(6.5  +  x(9)/1000) - 119/500000*(x(1) - 47)*(2*x(9)  +  x(1) - 47)*(x(2))^0.5/(1  +  125*(7   - 0.7*x(9)/1000)^2/8/(7  +  x(9)/1000)/(x(1) - 47))     ; 
	c(57) = 0.25*(0.03*x(1)  +  5.7)*(7  +  x(9)/1000)*(6.5  +  x(9)/1000) - 119/500000*(x(1) - 47)*(2*x(9)  +  x(1) - 47)*(x(2))^0.5/(1  +  125*(6.5 - 0.7*x(9)/1000)^2/8/(6.5  +  x(9)/1000)/(x(1) - 47))     ; 
	c(58) = 27/400*(6.5  +  x(9)/1000)*(7 - 0.7*x(9)/1000)^2 - 50    ; 
	c(59) = 1/160*(0.03*x(1)  +  5.7)*(6.5  +  x(9)/1000)*(7 - 0.7*x(9)/1000)^2 - 160     ; 
	c(60) = 27/400*(6.5  +  x(9)/1000)*(7 - 0.7*x(9)/1000)^2 - x(40)    ; 
	c(61) = 1/160*(0.03*x(1)  +  5.7)*(6.5  +  x(9)/1000)*(7 - 0.7*x(9)/1000)^2 - x(40)    ; 
	c(62) = x(40) - 27/400*(6.5  +  x(9)/1000)*(7 - 0.7*x(9)/1000)^2 - 160*(1-x(14))    ; 
	c(63) = x(40) - 1/160*(0.03*x(1)  +  5.7)*(6.5  +  x(9)/1000)*(7 - 0.7*x(9)/1000)^2 - 160*(1-x(15))    ; 
	c(64) = 0.5*7*(0.03*x(1)  +  5.7)*(6.5  +  x(9)/1000) - 119/500000*(x(1) - 47)*(3*x(9)  +  2*x(1) - 94)*(x(2))^0.5/(1  +  250*x(40)*(3*x(9)  +  2*x(1) - 94)/7/(0.03*x(1)  +  5.7)/(6.5  +  x(9)/1000)/(x(9)  +  x(1) - 47)/(x(1) - 47))     ; 
	c(65) = 0.5*7*(0.03*x(1)  +  5.7)*(6.5  +  x(9)/1000) - 119/500000*(x(1) - 47)*(3*x(9)  +  2*x(1) - 94)*(x(2))^0.5/(1  +  125/8*(6.5 - 0.7*x(9)/1000)^2*(3*x(9)  +  2*x(1) - 94)/(6.5  +  x(9)/1000)/(2*x(9)  +  x(1) - 47)/(x(1) - 47))     ; 
	c(66) = 27/400*(7  +  x(9)/1000)*(6.5 - 0.7*x(9)/1000)^2 - 50     ; 
	c(67) = 1/160*(0.03*x(1)  +  5.7)*(7  +  x(9)/1000)*(6.5 - 0.7*x(9)/1000)^2 - 160     ; 
	c(68) = 27/400*(7  +  x(9)/1000)*(6.5 - 0.7*x(9)/1000)^2 - x(41)    ; 
	c(69) = 1/160*(0.03*x(1)  +  5.7)*(7  +  x(9)/1000)*(6.5 - 0.7*x(9)/1000)^2 - x(41)    ; 
	c(70) = x(41) - 27/400*(7  +  x(9)/1000)*(6.5 - 0.7*x(9)/1000)^2 - 160*(1-x(16))    ; 
	c(71) = x(41) - 1/160*(0.03*x(1)  +  5.7)*(7  +  x(9)/1000)*(6.5 - 0.7*x(9)/1000)^2 - 160*(1-x(17))    ; 
	c(72) = 0.5*6.5*(0.03*x(1)  +  5.7)*(7  +  x(9)/1000) - 119/500000*(x(1) - 47)*(3*x(9)  +  2*x(1) - 94)*(x(2))^0.5/(1  +  125/8*(7 - 0.7*x(9)/1000)^2*(3*x(9)  +  2*x(1) - 94)/(7  +  x(9)/1000)/(2*x(9)  +  x(1) - 47)/(x(1) - 47))     ; 
	c(73) = 0.5*6.5*(0.03*x(1)  +  5.7)*(7  +  x(9)/1000) - 119/500000*(x(1) - 47)*(3*x(9)  +  2*x(1) - 94)*(x(2))^0.5/(1  +  250*(3*x(9)  +  2*x(1) - 94)*x(41)/6.5/(0.03*x(1)  +  5.7)/(7  +  x(9)/1000)/(x(9)  +  x(1) - 47)/(x(1) - 47))    ; 
	c(74) = 27/200*6.5*(7 - 0.7*x(9)/1000)^2 - 95     ; 
	c(75) = 1/80*6.5*(0.03*x(1)  +  5.7)*(7 - 0.7*x(9)/1000)^2 - 305     ; 
	c(76) = 27/200*6.5*(7 - 0.7*x(9)/1000)^2 - x(42)    ; 
	c(77) = 1/80*6.5*(0.03*x(1)  +  5.7)*(7 - 0.7*x(9)/1000)^2 - x(42)    ; 
	c(78) = x(42) - 27/200*6.5*(7 - 0.7*x(9)/1000)^2 - 305*(1-x(18))    ; 
	c(79) = x(42) - 1/80*6.5*(0.03*x(1)  +  5.7)*(7 - 0.7*x(9)/1000)^2 - 305*(1-x(19))    ; 
	c(80) = 27/200*7*(6.5 - 0.7*x(9)/1000)^2 - 95     ; 
	c(81) = 1/80*7*(0.03*x(1)  +  5.7)*(6.5 - 0.7*x(9)/1000)^2 - 305     ; 
	c(82) = 27/200*7*(6.5 - 0.7*x(9)/1000)^2 - x(43)    ; 
	c(83) = 1/80*7*(0.03*x(1)  +  5.7)*(6.5 - 0.7*x(9)/1000)^2 - x(43)    ; 
	c(84) = x(43) - 27/200*7*(6.5 - 0.7*x(9)/1000)^2 - 305*(1-x(20))    ; 
	c(85) = x(43) - 1/80*7*(0.03*x(1)  +  5.7)*(6.5 - 0.7*x(9)/1000)^2 - 305*(1-x(21))    ; 
	c(86) = 7*6.5*(0.03*x(1)  +  5.7) - 119/125000*(x(1) - 47)*(x(9)  +  x(1) - 47)*(x(2))^0.5/(1  +  500*x(42)/7/6.5/(0.03*x(1)  +  5.7)/(x(1) - 47))    ; 
	c(87) = 7*6.5*(0.03*x(1)  +  5.7) - 119/125000*(x(1) - 47)*(x(9)  +  x(1) - 47)*(x(2))^0.5/(1  +  500*x(43)/7/6.5/(0.03*x(1)  +  5.7)/(x(1) - 47))    ; 
	c(88) = -(0.025*x(1)  +  3.1)*(7 - 0.7*x(9)/1000)^2  +  1/750*x(1)^2*(x(2)^0.5 - 1/60*x(24)*x(33)/(20*x(1)  +  x(24) - 820))    ; 
	c(89) = log((1/6000*6.5*x(34)^3  +  0.1*x(24)*6.5*(x(1) - 41-x(34) )^2/x(5))/(1 - (1 - 4*x(34)^3/x(1)^3  - 2400*x(24)*(x(1) - 41-x(34))^2/x(5)/x(1)^3)*(1/750*x(1)^2*(x(2)^0.5 - (1/60*x(24)*x(33))/(20*x(1)  +  x(24) - 820))/(0.025*x(1)  +  3.1)/(7 - 0.7/1000*x(9))^2)^2)) - 50     ; 
	c(90) = log(1/24000*6.5*x(1)^3) - 50    ; 
	c(91) = x(35) - log((1/6000*6.5*x(34)^3  +  0.1*x(24)*6.5*(x(1) - 41-x(34) )^2/x(5))/(1 - (1 - 4*x(34)^3/x(1)^3  -2400*x(24)*(x(1) - 41-x(34))^2/x(5)/x(1)^3)*(1/750*x(1)^2*(x(2)^0.5 - (1/60*x(24)*x(33))/(20*x(1)  +  x(24) - 820))/(0.025*x(1)  +  3.1)/(7 - 0.7/1000*x(9))^2)^2))    ; 
	c(92) = x(35) - log(1/24000*6.5*x(1)^3)    ; 
	c(93) = -x(35)  +  log((1/6000*6.5*x(34)^3  +  0.1*x(24)*6.5*(x(1) - 41 - x(34))^2/x(5))/(1 - (1 - 4*x(34)^3/x(1)^3 - 2400*x(24)*(x(1) - 41 - x(34))^2/x(5)/x(1)^3)*(1/750*x(1)^2*(x(2)^0.5 - 1/60*x(24)*x(33)/(20*x(1)  +  x(24) - 820))/(0.025*x(1)  +  3.1)/(7 - 0.7/1000*x(9))^2)^2)) - 50*(1 - x(30))    ; 
	c(94) = -x(35)  +  log(1/24000*6.5*x(1)^3) - 50*(1-x(31))    ; 
	c(95) = -(0.025*x(1)  +  3.1)*(7 - 0.7/1000*x(9))^2  +  4/5625*x(1)^2*(x(2)^0.5 - (1/60*x(24)*x(33))/(20*x(1)  +  x(24) - 820))     ; 
	c(96) = log((1/6000*6.5*x(34)^3  +  0.1*x(24)*6.5*(x(1) - 41 - x(34))^2/x(5))/(1 - (1 - 4*x(34)^3/x(1)^3 - 2400*x(24)*(x(1) - 41- x(34))^2/x(5)/x(1)^3)*(4/5625*x(1)^2*(x(2)^0.5 - (1/60*x(24)*x(33))/(20*x(1)  +  x(24) - 820))/(0.025*x(1)  +  3.1)/(7 - 0.7/1000*x(9))^2)^2)) - 50     ; 
	c(97) = x(36) - log((1/6000*6.5*x(34)^3  +  0.1*x(24)*6.5*(x(1) - 41 - x(34))^2/x(5))/(1 - (1 - 4*x(34)^3/x(1)^3 - 2400*x(24)*(x(1) - 41- x(34))^2/x(5)/x(1)^3)*(4/5625*x(1)^2*(x(2)^0.5 - (1/60*x(24)*x(33))/(20*x(1)  +  x(24) - 820))/(0.025*x(1)  +  3.1)/(7 - 0.7/1000*x(9))^2)^2))    ; 
	c(98) = x(36) - log(1/24000*6.5*x(1)^3)    ; 
	c(99) = -x(36)  +  log((1/6000*6.5*x(34)^3  +  0.1*x(24)*6.5*(x(1) - 41 - x(34))^2/x(5))/(1 - (1 - 4*x(34)^3/x(1)^3 - 2400*x(24)*(x(1) - 41- x(34))^2/x(5)/x(1)^3)*(4/5625*x(1)^2*(x(2)^0.5 - (1/60*x(24)*x(33))/(20*x(1)  +  x(24) - 820))/(0.025*x(1)  +  3.1)/(7 - 0.7/1000*x(9))^2)^2)) - 50*(1 - x(37))    ; 
	c(100) = -x(36)  +  log(1/24000*6.5*x(1)^3) - 50*(1-x(38))     ; 
	c(101) = log(546875/96*6.5)  +  log(1  +  2*(0.025*x(1)  +  2.2)/(0.025*x(1)  +  3.1))  +  log(0.025*x(1)  +  3.1)  +  3*log(7 - 0.7*x(9)/1000) - log(x(5)) - log(exp(x(35))  +  exp(x(36))) - log(4)     ; 
	c(102) = log(546875/96*6.5)  +  log(1  +  2*(0.025*x(1)  +  2.2)/(0.025*x(1)  +  3.1))  +  log(0.025*x(1)  +  3.1)  +  4*log(7 - 0.7*x(9)/1000) - log(x(5)) - log(exp(x(35))  +  exp(x(36))) - log(25)     ; 
	c(103) = 1/80*7*(0.03*x(1)  +  5.7)*(6.5 - 0.7*x(9)/1000)^2 - x(59)    ; 
	c(104) = 1/80*6.5*(0.03*x(1)  +  5.7)*(7 - 0.7*x(9)/1000)^2 - x(59)    ; 
	c(105) = 1000*x(58) - x(59)*(x(52)-x(51))/x(53)  - x(51)    ; 
	c(106) = 1000*x(58) - x(59)*(x(54)-x(52))/(x(55)-x(53)) - (x(55)*x(52)-x(53)*x(54))/(x(55)-x(53))    ; 
	c(107) = -1000*x(58) - x(59)*x(54)/(x(56)-x(55))  +  x(56)*x(54)/(x(56)-x(55))    ; 
	c(108) = 0.01*x(9)^2 - 4*x(50)    ; 
	c(109) = -0.04*x(9)^2  +  4*x(50)    ; 
	c(110) = 3300000/x(10)/(x(9) - 78) - x(64)    ; 
	c(111) = 7*(3500 - x(1)) - 3300000*(x(63)  +  1)/x(10)/(x(9) - 78) ; 
	c(112) = x(28)/(2*x(2)*x(3)*x(4)*(x(1) - 53)) - 0.36 ;
	c(113) = x(22)/(x(1) - 41) - 4/5*x(2)*x(3)*x(4) ;
	c(114) = -1/2500*x(22)*(x(1) - 41)*(1 - x(22)/(4*x(2)*x(3)*(x(1) - 41))) + 9/128*(0.03*x(1) + 5.7)*(6.5/2 + x(9)/2000)*(7 - 0.7*x(9)/1000)^2/(6.5/4 + x(9)/2000) ;
	ceq = [];
	end

Could you please help me to tackle this error?

Really thank you so much,

[Walter Roberson]

You have problems if some of your variables such as x(5) or x(44) or x(45) can be 0, or your x(32) can be sufficiently negative, or if your x(2) can be negative, or your x(1) can be 53, or any of several combinations of values could just happen to cause a division by 0.

It would be easier to debug if we had the rest of your code.

[Hoang Trinh]

Dear Walter Roberson,

Thank you a lot for your response. Yes, I will copy all of my code here.

This is my main code:

% Main code for optimization
fun = @myFitness;
nvars = 82;
lb = [ 200 32 0.67 0.67 30100 348.6 0 0 450 32 0.67 0.67 348.6 0 0 0 0 0 0 0 0 366.7 366.7 366.7 366.7 366.7 366.7 366.7 366.7 0 0 100 100 10 5 5 0 0 0 2 2 2 2 2 50 0 0 0 16 200 5 5 5 5 5 5 0 5 5 20 20 20 2 100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ] ;
ub = [ 1100 65 0.85 0.85 37400 739.2 0 0 1000 65 0.85 0.85 739.2 1 1 1 1 1 1 1 1 1833.33 1833.33 1833.33 1833.33 1833.33 1833.33 1833.33 1833.33 1 1 1100 1200 1100 50 50 1 1 0 400 400 400 400 50 1000 1 1 0 40 1260 10000 10000 1000 10000 1000 1000 1 10000 1000 300 300 300 500 600 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ] ;


% Nonlinear constraints
nonlcon = @nlcon;
% Linear constraints
A = zeros([71 82]) ;
A(1,2) = -1;
A(2,3) = -1;
A(3,4) = -1;
A(4,5) = -1;
A(5,6) = -1;

A(8,2)  = 1 ; 
A(9,3)  = 1 ;
A(10,4) = 1 ;
A(11,5) = 1 ;
A(12,6) = 1 ;

A(13,10) = 1 ;
A(14,11) = 1 ;
A(15,12) = 1 ;
A(16,13) = 1 ;
A(17,10) = -1;
A(18,11) = -1;
A(19,12) = -1;
A(20,13) = -1;

A(45,9) = -1; 
A(46,9) = 1 ;
A(49,9) = 1 ;
A(50,9) = -1 ;
A(47,1) = 1;
A(48,1) = -1;

A(52,1) = 21/8 ;
A(53,1) = 21/8 ;
A(54,1) = 21/8 ;
A(55,1) = 21/8 ;
A(56,1) = 21/8 ;
A(57,1) = 21/8 ;
A(58,1) = 21/8 ;
A(59,1) = 21/8 ;
A(60,1) = 5 ;
A(61,2) = 1 ;
A(62,1) = -1 ;

A(61,10) = -1 ;
A(62,9) = -7.5;
A(66,9) = -1;
A(68,9) = -0.6;
A(71,9) = 0.6;

A(29,14) = 1 ; 
A(30,14) = -1 ;
A(29,15) = 1 ;
A(30,15) = -1 ;
A(31,16) = 1 ;
A(32,16) = -1 ;
A(31,17) = 1 ;
A(32,17) = -1 ;
A(33,18) = 1 ;
A(34,18) = -1 ;
A(33,19) = 1 ;
A(34,19) = -1 ;
A(35,20) = 1 ;
A(36,20) = -1 ;
A(35,21) = 1 ;
A(36,21) = -1 ;

A(52,22) = -1 ;
A(53,23) = -1 ;
A(54,24) = -1 ;
A(55,25) = -1 ;
A(56,26) = -1 ;
A(57,27) = -1 ;
A(58,28) = -1 ;
A(59,29) = -1 ;
A(60,24) = -1 ;

A(37,30) = 1 ;
A(38,30) = -1 ;
A(37,31) = 1 ;
A(38,31) = -1 ;

A(39,37) = 1 ;
A(40,37) = -1 ;
A(39,38) = 1 ;
A(40,38) = -1 ;

A(41,46) = 1 ;
A(42,46) = -1 ;
A(41,47) = 1 ;
A(42,47) = -1 ;

A(45,45) = 1 ;
A(46,45) = -1 ;
A(45,49) = 0.5;
A(46,49) = -0.5 ;

A(63,49) = 1.5 ;
A(65,49) = -1.5 ;
A(66,49) = 2 ;
A(67,49) = -15 ;
A(70,49) = 15 ;
A(64,46) = 20 ;
A(65,47) = 36 ;

A(23,49) = 1 ;
A(24,49) = -1 ;
A(25,50) = 1 ;
A(26,50) = -1 ;

A(1,65) = 32 ;
A(1,66) = 40 ;
A(1,67) = 50 ;
A(1,68) = 65 ;

A(2,65) = 0.85 ;
A(2,66) = 0.85 ;
A(2,67) = 0.85 ;
A(2,68) = 0.805 ;

A(3,65) = 0.826 ;
A(3,66) = 0.77 ;
A(3,67) = 0.7 ;
A(3,68) = 0.67 ;

A(4,65) = 30100 ;
A(4,66) = 32800 ;
A(4,67) = 34800 ;
A(4,68) = 37400 ;

A(5,65) = 348.6 ;
A(5,66) = 405 ;
A(5,67) = 513 ;
A(5,68) = 739.2 ;

A(6,65) = 1 ;
A(6,66) = 1 ;
A(6,67) = 1 ;
A(6,68) = 1 ;

A(7,65) = -1 ;
A(7,66) = -1 ;
A(7,67) = -1 ;
A(7,68) = -1 ;

A(8,65) = -32 ;
A(8,66) = -40 ;
A(8,67) = -50 ;
A(8,68) = -65 ;
		  
A(9,65) = -0.85 ;
A(9,66) = -0.85 ;
A(9,67) = -0.85 ;
A(9,68) = -0.805 ;

A(10,65) = -0.826 ;
A(10,66) = -0.77 ;
A(10,67) = -0.7 ;
A(10,68) = -0.67 ;
		   
A(11,65) = -30100 ;
A(11,66) = -32800 ;
A(11,67) = -34800 ;
A(11,68) = -37400 ;
		   
A(12,65) = -348.6 ;
A(12,66) = -405 ;
A(12,67) = -513 ;
A(12,68) = -739.2 ;

A(13,69) = -32 ;
A(13,70) = -40 ;
A(13,71) = -50 ;
A(13,72) = -65 ;
          
A(14,69) = -0.85 ;
A(14,70) = -0.85 ;
A(14,71) = -0.85 ;
A(14,72) = -0.805 ;  
         
A(15,69) =  -0.826 ;
A(15,70) =  -0.77 ;
A(15,71) =  -0.7 ;
A(15,72) =  -0.67 ; 
           
A(16,69) =  -348.6 ;
A(16,70) =  -405 ;
A(16,71) =  -513 ;
A(16,72) =  -739.2 ;
            
A(17,69) =  32 ;
A(17,70) =  40 ;
A(17,71) =  50 ;
A(17,72) =  65 ;  
         
A(18,69) =  0.85 ;
A(18,70) =  0.85 ;
A(18,71) =  0.85 ;
A(18,72) =  0.805 ; 
           
A(19,69) =  0.826 ;
A(19,70) =  0.77 ;
A(19,71) =  0.7 ;
A(19,72) =  0.67 ;

A(20,69) = 348.6 ;
A(20,70) = 405 ;
A(20,71) = 513 ;
A(20,72) = 739.2 ;

A(21,69) =  1;
A(21,70) =  1;
A(21,71) =  1;
A(21,72) =  1;

A(22,69) =  -1;
A(22,70) =  -1;
A(22,71) =  -1;
A(22,72) =  -1;


A(23,73) = -16 ;
A(23,74) = -20 ;
A(23,75) = -24 ;
A(23,76) = -28 ;
A(23,77) = -32 ;
A(23,78) = -36 ;
A(23,79) = -40 ;

A(24,73) = 16 ;
A(24,74) = 20 ;
A(24,75) = 24 ;
A(24,76) = 28 ;
A(24,77) = 32 ;
A(24,78) = 36 ;
A(24,79) = 40 ;

A(25,73) = -200 ;
A(25,74) = -310 ;
A(25,75) = -450 ;
A(25,76) = -620 ;
A(25,77) = -800 ;
A(25,78) = -1020 ;
A(25,79) = -1260 ;

A(26,73) = 200 ;
A(26,74) = 310 ;
A(26,75) = 450 ;
A(26,76) = 620 ;
A(26,77) = 800 ;
A(26,78) = 1020 ;
A(26,79) = 1260 ;

A(27,73) = 1;
A(27,74) = 1;
A(27,75) = 1;
A(27,76) = 1;
A(27,77) = 1;
A(27,78) = 1 ;
A(27,79) = 1 ;

A(28,73) = -1;
A(28,74) = -1;
A(28,75) = -1;
A(28,76) = -1;
A(28,77) = -1;
A(28,78) = -1 ;
A(28,79) = -1 ;

A(43,80) = 1 ;
A(43,81) = 1 ;
A(43,82) = 1 ;
A(44,80) = -1 ;
A(44,81) = -1 ;
A(44,82) = -1 ;

A(69,80) = 150 ;
A(70,81) = 450 ;
A(71,82) = 450 ;

A(67,64) = 1 ;
A(68,64) = 1 ;
A(69,64) = -1 ;
A(70,64) = -1 ;
A(71,64) = -1 ;

A(63,62) = -1 ;
A(64,62) = 1 ;
A(65,62) = 1 ;
A(66,62) = 1 ;

A(47,60) = -5 ;
A(48,60) = 5 ;
A(49,61) = -5 ;
A(50,61) = 5 ;



b = [ 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 -45 45 0 0 0 0 0 0 0 0 0 0 0 0 0 205 0 -3500 0 60 36 -90 0 0 -150 450 450 ]' ;


IntCon = [1 2 5 9 10 14 15 16 17 18 19 20 21 30 31 37 38 46 47 49 50 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82] ;


opts = optimoptions('ga', ...
                    'PopulationSize', 1000, ...
                    'MaxGenerations', 500, ...
                    'EliteCount', 10, ...
                    'FunctionTolerance', 1e-8, ...
                    'PlotFcn', @gaplotbestf);
                
[x fval] = ga(fun,nvars,A,b,[],[],lb,ub,nonlcon,IntCon);

And this is my Fitness function:

function y = myFitness(x) 
	y = 1/1000*7*(x(6)*x(1)*(7*3  +  x(9)/1000)*(6.5*3  +  x(9)/1000)/1000 + 40.251660/1000*((x(26)*(x(9)/1000 + 0.5*7) + 0.5*x(27)*7 + (3 - 1)*(0.5*6.5*x(28) + 7*x(29) - 0.5*6.5*x(29)))*(6.5*3 + x(9)/1000)+ (x(22)*(x9/1000 + 0.5*6.5) + 0.5*x(23)*6.5 + 0.5*6.5*(3 - 1)*(x(24) + x(25)))*(7*3 + x(9)/1000)) + x(13)*(3 + 1)*(3 + 1)*(3.5 - x(1)/1000)*(x(9)/1000)^2 + 161.006640/1000*(3 + 1)*(3 + 1)*x(50)) + 17.7107304/1000000*(3 + 1)*(3 + 1)*(x(63) + 1)*(x(9) - 51) ;
end

Thank you so much,

[Walter Roberson]

Your x(53), x(55), and x(56) all become 5. That gives you division by 0 in entries 106 and 107 of your nonlinear constraints, where you divide by the difference between some of those.

You need to add constraints to ensure relative order of those and that they are never equal.

[Hoang Trinh]

Dear Walter Roberson,

Thank you so much for your help,

I have added four linear constraints for x55, x53, and x56 as follows:

% Main code for optimization
fun = @myFitness;
nvars = 82;
lb = [ 200 32 0.67 0.67 30100 348.6 0 0 450 32 0.67 0.67 348.6 0 0 0 0 0 0 0 0 366.7 366.7 366.7 366.7 366.7 366.7 366.7 366.7 0 0 100 100 10 5 5 0 0 0 2 2 2 2 2 50 0 0 0 16 200 5 5 5 5 5 5 0 5 5 20 20 20 2 100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ] ;
ub = [ 1100 65 0.85 0.85 37400 739.2 0 0 1000 65 0.85 0.85 739.2 1 1 1 1 1 1 1 1 1833.33 1833.33 1833.33 1833.33 1833.33 1833.33 1833.33 1833.33 1 1 1100 1200 1100 50 50 1 1 0 400 400 400 400 50 1000 1 1 0 40 1260 10000 10000 1000 10000 1000 1000 1 10000 1000 300 300 300 500 600 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ] ;


% Nonlinear constraints
nonlcon = @nlcon;
% Linear constraints
A = zeros([74 82]) ;
A(1,2) = -1;
A(2,3) = -1;
A(3,4) = -1;
A(4,5) = -1;
A(5,6) = -1;

A(8,2)  = 1 ; 
A(9,3)  = 1 ;
A(10,4) = 1 ;
A(11,5) = 1 ;
A(12,6) = 1 ;

A(13,10) = 1 ;
A(14,11) = 1 ;
A(15,12) = 1 ;
A(16,13) = 1 ;
A(17,10) = -1;
A(18,11) = -1;
A(19,12) = -1;
A(20,13) = -1;

A(45,9) = -1; 
A(46,9) = 1 ;
A(49,9) = 1 ;
A(50,9) = -1 ;
A(47,1) = 1;
A(48,1) = -1;

A(52,1) = 21/8 ;
A(53,1) = 21/8 ;
A(54,1) = 21/8 ;
A(55,1) = 21/8 ;
A(56,1) = 21/8 ;
A(57,1) = 21/8 ;
A(58,1) = 21/8 ;
A(59,1) = 21/8 ;
A(60,1) = 5 ;
A(61,2) = 1 ;
A(62,1) = -1 ;

A(61,10) = -1 ;
A(62,9) = -7.5;
A(66,9) = -1;
A(68,9) = -0.6;
A(71,9) = 0.6;

A(29,14) = 1 ; 
A(30,14) = -1 ;
A(29,15) = 1 ;
A(30,15) = -1 ;
A(31,16) = 1 ;
A(32,16) = -1 ;
A(31,17) = 1 ;
A(32,17) = -1 ;
A(33,18) = 1 ;
A(34,18) = -1 ;
A(33,19) = 1 ;
A(34,19) = -1 ;
A(35,20) = 1 ;
A(36,20) = -1 ;
A(35,21) = 1 ;
A(36,21) = -1 ;

A(52,22) = -1 ;
A(53,23) = -1 ;
A(54,24) = -1 ;
A(55,25) = -1 ;
A(56,26) = -1 ;
A(57,27) = -1 ;
A(58,28) = -1 ;
A(59,29) = -1 ;
A(60,24) = -1 ;

A(37,30) = 1 ;
A(38,30) = -1 ;
A(37,31) = 1 ;
A(38,31) = -1 ;

A(39,37) = 1 ;
A(40,37) = -1 ;
A(39,38) = 1 ;
A(40,38) = -1 ;

A(41,46) = 1 ;
A(42,46) = -1 ;
A(41,47) = 1 ;
A(42,47) = -1 ;

A(45,45) = 1 ;
A(46,45) = -1 ;
A(45,49) = 0.5;
A(46,49) = -0.5 ;

A(63,49) = 1.5 ;
A(65,49) = -1.5 ;
A(66,49) = 2 ;
A(67,49) = -15 ;
A(70,49) = 15 ;
A(64,46) = 20 ;
A(65,47) = 36 ;

A(23,49) = 1 ;
A(24,49) = -1 ;
A(25,50) = 1 ;
A(26,50) = -1 ;

A(1,65) = 32 ;
A(1,66) = 40 ;
A(1,67) = 50 ;
A(1,68) = 65 ;

A(2,65) = 0.85 ;
A(2,66) = 0.85 ;
A(2,67) = 0.85 ;
A(2,68) = 0.805 ;

A(3,65) = 0.826 ;
A(3,66) = 0.77 ;
A(3,67) = 0.7 ;
A(3,68) = 0.67 ;

A(4,65) = 30100 ;
A(4,66) = 32800 ;
A(4,67) = 34800 ;
A(4,68) = 37400 ;

A(5,65) = 348.6 ;
A(5,66) = 405 ;
A(5,67) = 513 ;
A(5,68) = 739.2 ;

A(6,65) = 1 ;
A(6,66) = 1 ;
A(6,67) = 1 ;
A(6,68) = 1 ;

A(7,65) = -1 ;
A(7,66) = -1 ;
A(7,67) = -1 ;
A(7,68) = -1 ;

A(8,65) = -32 ;
A(8,66) = -40 ;
A(8,67) = -50 ;
A(8,68) = -65 ;
		  
A(9,65) = -0.85 ;
A(9,66) = -0.85 ;
A(9,67) = -0.85 ;
A(9,68) = -0.805 ;

A(10,65) = -0.826 ;
A(10,66) = -0.77 ;
A(10,67) = -0.7 ;
A(10,68) = -0.67 ;
		   
A(11,65) = -30100 ;
A(11,66) = -32800 ;
A(11,67) = -34800 ;
A(11,68) = -37400 ;
		   
A(12,65) = -348.6 ;
A(12,66) = -405 ;
A(12,67) = -513 ;
A(12,68) = -739.2 ;

A(13,69) = -32 ;
A(13,70) = -40 ;
A(13,71) = -50 ;
A(13,72) = -65 ;
          
A(14,69) = -0.85 ;
A(14,70) = -0.85 ;
A(14,71) = -0.85 ;
A(14,72) = -0.805 ;  
         
A(15,69) =  -0.826 ;
A(15,70) =  -0.77 ;
A(15,71) =  -0.7 ;
A(15,72) =  -0.67 ; 
           
A(16,69) =  -348.6 ;
A(16,70) =  -405 ;
A(16,71) =  -513 ;
A(16,72) =  -739.2 ;
            
A(17,69) =  32 ;
A(17,70) =  40 ;
A(17,71) =  50 ;
A(17,72) =  65 ;  
         
A(18,69) =  0.85 ;
A(18,70) =  0.85 ;
A(18,71) =  0.85 ;
A(18,72) =  0.805 ; 
           
A(19,69) =  0.826 ;
A(19,70) =  0.77 ;
A(19,71) =  0.7 ;
A(19,72) =  0.67 ;

A(20,69) = 348.6 ;
A(20,70) = 405 ;
A(20,71) = 513 ;
A(20,72) = 739.2 ;

A(21,69) =  1;
A(21,70) =  1;
A(21,71) =  1;
A(21,72) =  1;

A(22,69) =  -1;
A(22,70) =  -1;
A(22,71) =  -1;
A(22,72) =  -1;


A(23,73) = -16 ;
A(23,74) = -20 ;
A(23,75) = -24 ;
A(23,76) = -28 ;
A(23,77) = -32 ;
A(23,78) = -36 ;
A(23,79) = -40 ;

A(24,73) = 16 ;
A(24,74) = 20 ;
A(24,75) = 24 ;
A(24,76) = 28 ;
A(24,77) = 32 ;
A(24,78) = 36 ;
A(24,79) = 40 ;

A(25,73) = -200 ;
A(25,74) = -310 ;
A(25,75) = -450 ;
A(25,76) = -620 ;
A(25,77) = -800 ;
A(25,78) = -1020 ;
A(25,79) = -1260 ;

A(26,73) = 200 ;
A(26,74) = 310 ;
A(26,75) = 450 ;
A(26,76) = 620 ;
A(26,77) = 800 ;
A(26,78) = 1020 ;
A(26,79) = 1260 ;

A(27,73) = 1;
A(27,74) = 1;
A(27,75) = 1;
A(27,76) = 1;
A(27,77) = 1;
A(27,78) = 1 ;
A(27,79) = 1 ;

A(28,73) = -1;
A(28,74) = -1;
A(28,75) = -1;
A(28,76) = -1;
A(28,77) = -1;
A(28,78) = -1 ;
A(28,79) = -1 ;

A(43,80) = 1 ;
A(43,81) = 1 ;
A(43,82) = 1 ;
A(44,80) = -1 ;
A(44,81) = -1 ;
A(44,82) = -1 ;

A(69,80) = 150 ;
A(70,81) = 450 ;
A(71,82) = 450 ;

A(67,64) = 1 ;
A(68,64) = 1 ;
A(69,64) = -1 ;
A(70,64) = -1 ;
A(71,64) = -1 ;

A(63,62) = -1 ;
A(64,62) = 1 ;
A(65,62) = 1 ;
A(66,62) = 1 ;

A(47,60) = -5 ;
A(48,60) = 5 ;
A(49,61) = -5 ;
A(50,61) = 5 ;

A(51,55) = 1;

A(51,53) = -1;

A(72,55) = 1;

A(72,53) = -1;

A(73,55) = 1;

A(73,56) = -1;

A(74,55) = -1;

A(74,56) = 1;

b = [ 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 -45 45 0 0 0 0 0 0 0 0 0 0 0 0 0 205 0 -3500 0 60 36 -90 0 0 -150 450 450 0 0 0 ]' ;


IntCon = [1 2 5 9 10 14 15 16 17 18 19 20 21 30 31 37 38 46 47 49 50 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82] ;


opts = optimoptions('ga', ...
                    'PopulationSize', 1000, ...
                    'MaxGenerations', 500, ...
                    'EliteCount', 10, ...
                    'FunctionTolerance', 1e-8, ...
                    'PlotFcn', @gaplotbestf);
                
[x fval] = ga(fun,nvars,A,b,[],[],lb,ub,nonlcon,IntCon);

But it still resulted in an error message. :(

Kind Regards,

[Walter Roberson]

A(51,55) = 1;
A(51,53) = -1;

That expresses that (1) * x(55) + (-1) * x(53) <= b(51) . b(51) is 0, so you are expressing that x(55)-x(53) <= 0, which is to say that x(55) <= x(53) . But that still allows them to be equal, and when they are equal, you get the division by 0.

Linear constraints are A*x' <= b not A*x' < b.

If you want < then you need to make b(51) negative, even if it is only -realmin()

[Hoang Trinh]

Dear Walter Roberson,

I have made some changes like this:

A(51,55) = 1;

A(51,53) = -1;

A(72,56) = 1;

A(72,55) = -1;

with

b(51) = 0.1 ;

b(72) = 0.1 ;

So now, x(55) - x(53) <= 0.1 ; and x(56) - x(55) <= 0.1;

Still, the error has not been fixed. :(