Dear Felipe,

Sum is not a good function as it leads to many answers which do not satisfy original functions . Sum of squared would be a better choice.

Best regards, 

BAN

.

@Mark

fsolve is a special function designed to Solve system of nonlinear equations in Matlab.

if your equations are not dependent, you may not find a solution that satisfies all the equations as you have e unknowns and 6 equations.

if you want to use GA, you have to define your objective function properly.

Hello,

First of all, a question:

What is your objective function?

If it's a criterion to find the best fitting x5, x6, so, you would have a code like this:

function optm

objective_function = @ objective;

% defineLB,UB and options

nvars = 2;

[x,fval] = ga(objective_function,nvars,[],[],[],[],LB,UB,[],options);

end

function M = objective(x5,x6)

PROBLEM = solv_ode(x5,x6);

M = PROBLEM - P;

end

function solv_ode(x5,x6)

% solve your ode using "fsolve"

end

Consider that since you have more equations (6) than unknowns (4) your problem might not have a solution. In order to investigate how far is your system of satisfying all the equations, I recommend you to add 6 variables (e1 to e6) to account for equality violation and to minimize the sum of those variables. In your notation:

z=[3 7 10 27 30 42];

p=[10.2 8.7 7.1 6.4 3.2 2];

e=[e1 e2 e3 e4 e5 e6];

minimize sum(e)

s.t.

((x1*x2)+x2-(x3*x4)+z)/((x1-x2)*z+(x3*x4))-p=e;

Furthermore, I recommend not using a genetic algorithm in this kind of problem (constrained optimization) but using a gradient based optimizer such as those in fmincon in MATLAB

Dear Felipe,

Sum is not a good function as it leads to many answers which do not satisfy original functions . Sum of squared would be a better choice.

Best regards, 

BAN

.

if one insists to solve this equation by GA. I could think of these two ways:

1-Define one equation as objective function and the rest of equations as equality constraint functions

2-Define sum(fi(x)^2) i=1:6 to be minimized as the objective function.

@ Felipe Scott

This is the command given for fmincon in MATLAB:

x = fmincon(fun,x0,A,b,Aeq,beq,lb,ub)

How to choose A,b,Aeq,beq according to my problem ?

@ Behrouz Ahmadi-Nedushan @ Arash Khassetarash

If I have more equations e.g 100 with 50 unknowns than How I will make objective function ?

As I read in Matlab help, we have to define a function and copy our problem in this function. But How will I define objective function with so long problem ?

@Mahak

The procedure for defining the objective function does not depend on number of variables.

from the command line

x = ga(fitnessfcn,nvars,A,b,Aeq,beq,LB,UB) defines a set of lower and upper bounds on the design variables, x, so that a solution is found in the range LB ≤ x ≤ UB. Use empty matrices for LB and UB if no bounds exist.

The input arguments are all defined in the help.

The Matlab help is very complete. I suggest that you print the corresponding pages and read it thoroughly (solving the examples as well) before solving your problem. You have to be patient in research. good luck:).

@Mark

Assuming that you want to solve the following 100 equations

fi(x)=0; i=1:100

You can define your objective function as F=f1(x)^2+f2(x)^2+....+f100(x)^2 (in a loop)

If you minimize the F(x), you will find the answer of your equations.

@Behrouz

I agree with you, sum of squares would be a better choice for objective function

@Mahak Chauhan

For fmincon:

x = fmincon(fun,x0,A,b,Aeq,beq,lb,ub,nonlcon,options)

Check the information in http://www.mathworks.com/help/optim/ug/fmincon.html.

You might have bounds on the value of your variables (lb,ub), fun corresponds to your objective function (a function handle in matlab), Aeq and Beq define linear equality constraints (as far as I know you don't have those in your problem) and nonlcon is a function handle with the vector of nonlinear constraints (the equations you show in your first post)

suppose you have N equations and rearrange them in |f(X)=0| and then select one of them as objective function and the others as equality constraints.

It is strongly recommended to write the GA algorithm yourself and solve the optimization problem.

also you can send me your equation and I will solve it

You can try the GA toolbox and write you own M-file, which I think is more flexible than some embedded functions.

You can also think about Multi-Objective GA. All of your equations are objectives.

Anyway, I haven't seen No-Objective GA yet.

All of your equations are constraints but no objective.

You can try both or any intermediate.

I think you should use GA tool of matlab. In which you can create and assign objective function file, constrain file and you can select range of variables along with wide range of parameter selection

Create the fitness function in M-file, in which P(1) you have the fitness function 1. So 6 fitness functions. And in the other M-file create multi-objectif function. and define the constraint of each function.

In the implementation. the set of nonlinear queations represents the objective function in the context of GA.