Which solver would you recommend for multi(6) objective and multi(6) variable optimization with or without the toolbox. Is it even possible to put boundaries on these variables without optimization functions/toolbox?

ConstStr

N7 = 3.135E+00*N1*N2,

N8 = 4.100E-01*N2*N6,

N9 = 1.381E+01*N1*N4,

N10 = 7.610E+01*N2^2*N3,

N11 = 1.720E+05*N2*N3^2*N5^3,

N12 = 4.034E+04*N3*N5^2,

N13 = 2.615E+04*N2*N3^2*N5^2,

N14 = 3.826E+44*N1*N3*N5^2, //N14 = 3.826E+04*N1*N3*N5^2,

N15 = 1.458E+03*N2*N3*N5,

N16 = 2.435E+04*N1*N3^2*N5,

N17 = 1.186E+08*N3^2*N5^3,

N18 = 7.511E+02*N3*N5,

N19 = 6.874E+02*N3*N5;

Function

N1+N2+N3+N4+N5+N6+N7+N8+N9+N10+N11+N12+N13+N14+N15+N16+N17+N18+N19 = 1;

0.1962*(N2+N7+N8+2*N10+N11+N13+N15)-0.6575*(N1+N7+N9+N14+N16) = 0;

0.0557*(N3+N10+2*N11+N12+2*N13+N14+N15+2*N16+2*N17+N18+N19)-0.4698*(N4+N9) = 0;

0.0099*(N5+3*N11+2*N12+2*N13+2*N14+N15+N16+3*N17+N18+N19)-0.3525*(N6+N8) = 0;

0.0557*(N1+N7+N9+N14+N16)-0.1962*(N4+N9) = 0;

0.0099*(N2+N7+N8+2*N10+N11+N13+N15)-0.6575*(N6+N8) = 0;

Optimization

0< N1, N2, N3, N4, N5, N6 <1

Answer 1

[Shashank Gupta]

Hey Tasnim,

These equation seems non linear in nature, probably using solve function to optimise would make sense. Do setup the optimisation problem properly and check out the solve function. you will find hard time dealing such problem using fminsearch and fmincon functions, So I would not recommend this functions.

I hope this gives you a good headstart.

Cheers.

Answer 2

[Joe]

For multi-objective optimization with six objectives and six variables in MATLAB, I recommend using the MATLAB Optimization Toolbox, specifically the gamultiobj function, which is designed for multi-objective genetic algorithms. This function allows you to efficiently search for a set of Pareto-optimal solutions, which is essential when dealing with multiple objectives.

You can definitely impose boundaries on your variables without using optimization functions or toolboxes by simply defining constraints within your own optimization algorithm or using basic techniques like gradient descent, but this approach can be more complex and less efficient for multi-objective problems. Using built-in functions like gamultiobj simplifies this process by allowing you to set upper and lower bounds easily.

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