What solver for an integer minimization problem with linear objective and fractional constraints?

Hi,

I have to solve an integer problem with a linear objective and fractional constraint, and specifically of this type:

Can you suggest me a solver I can use?

Many thanks,

Elisabetta

Answer 1

[Matt J]

You can use ga(), if you havet Global Optimization Toolbox.

[Elisabetta Biondi]

Thank you Matt.

I have tried at first using ga() without the integer constraint. So I have built the function constraint.m:

function [c] = constraint(x)
global N aVec bVec T

c = -(ones(1,N)*((aVec.*transpose(x))./(bVec+transpose(x)))-T);

and then I have run the code

global N aVec bVec T
N=2;
aVec = [0.9; 0.9];
bVec = [2; 3];
T=1;

fun = @(x)(x*ones(N,1));
nonlcon = @constraint;
rng default
x = ga (fun, N, [], [], [], [], zeros(1,N), [], nonlcon)

However, it is returned to me an error:

Error using constraint

Too many output arguments.

Error in createAnonymousFcn>@(x)fcn(x,FcnArgs{:}) (line 11)

fcn_handle = @(x) fcn(x,FcnArgs{:});

Error in constrValidate (line 23)

[cineq,ceq] = nonlcon(Iterate.x');

Error in gacommon (line 132)

[LinearConstr, Iterate,nineqcstr,neqcstr,ncstr] = constrValidate(NonconFcn, ...

Error in ga (line 336)

NonconFcn,options,Iterate,type] = gacommon(nvars,fun,Aineq,bineq,Aeq,beq,lb,ub, ...

Error in optimization (line 22)

x = ga (fun, N, [], [], [], [], zeros(1,N), [], nonlcon)

Caused by:

Failure in initial user-supplied nonlinear constraint function evaluation.

In this case a solution exists, for example x=(10,10) satisfies the constraint. Can you tell me which is the problem? Thank you.