Using fmincon to find the best combination of x1,x2,x3

I would like to find the best combination of x1, x2, x3 that minimize my objective function.

Since the way to obtain the objective function is by using ODE, I write the separate M-file for this. Now, I have tried to use fmincon to find the best combination here, but it didn't work out.

x0=[2000,10000,1000];

A=[4.39 1.68 15.98];

b=[100000];

[x,fval]=fmincon(@allocation1,x0,A,b)

-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- For my M-file code:

function objective = allocation1 (x1,x2,x3)

%% compute r1,r2,r3 from the interrelationships

pop=1000;

% service coverage

DWS=0.1;

WST=0.1;

MSW=0.1;

% rate of convertion

rate_DWS=13.2;

rate_WST=50;

rate_MSW=4.38;

rate_DWS_MSW=0.05;

rate_WST_MSW=0.01;

rate_MSW_WST=0.10;

% total coverage

total_DWS=rate_DWS*pop;

total_WST=rate_WST*pop;

total_MSW=rate_MSW*pop;

% compute coverage

cov_DWS=DWS*pop*rate_DWS;

cov_WST=WST*pop*rate_WST;

cov_MSW=MSW*pop*rate_MSW;

% construct interrelationship matrix

I1 = [ 0 0 rate_DWS_MSW*cov_DWS; 0 0 rate_WST_MSW*cov_WST; 0 rate_MSW_WST*cov_MSW 0];

I2 = [ 0 0 rate_DWS_MSW*x1; 0 0 rate_WST_MSW*x2; 0 rate_MSW_WST*x3 0];

% compute the current state variables

r1_cur=(cov_DWS-sum(I1(:,1)))/total_DWS;

r2_cur=(cov_WST-sum(I1(:,2)))/total_WST;

r3_cur=(cov_MSW-sum(I1(:,3)))/total_MSW;

% compute the capacity expansion state variables

r1=r1_cur+((x1-sum(I2(:,1)))/total_DWS);

r2=r2_cur+((x2-sum(I2(:,2)))/total_WST);

r3=r3_cur+((x3-sum(I2(:,3)))/total_MSW);

%% function of nonlinear differential equation for disease incidents

function xprime = SIWDR2 (t,x)

% SIWDR model: the goal is the observe the behavior of system of % diferential equations

Lambda=0.05;

mu=0.04;

beta_i=0.005;

beta_w=0.001;

gamma=0.1;

alpha_1=1;

alpha_2=2;

theta_1=3;

theta_2=1;

psi=2;

xi_w=0.2; xi_d=0.2;

xprime=[Lambda-(1-r1)*beta_w*x(1)*x(3)-beta_i*x(1)*x(2)-mu*x(1);

    (1-r1)*beta_w*x(1)*x(3)+beta_i*x(1)*x(2)-gamma*x(2)-mu*x(2);

    (xi_w/alpha_1)*((1-r2)*alpha_1+theta_2)*x(2)+((xi_w*theta_2)/alpha_1)*x(1)+...

    ((xi_w*theta_2)/alpha_1)*x(5)+((1-r3)*psi*alpha_2*xi_w/(alpha_1*xi_d))*x(4)-...

    xi_w*x(3);

    (xi_d/alpha_2)*((1-r2)*alpha_2+theta_1)*x(2)+((xi_d*theta_1)/alpha_2)*x(1)+...

    ((xi_d*theta_1)/alpha_2)*x(5)-(xi_d*x(4));

    gamma*x(2)-mu*x(5)];

end

%% Output of the allocation model

tspan=0:1:364;

x0=[0.8 0.1 1 1 0.1];

[t,x]=ode45(@SIWDR2,tspan,x0);

objective = sum(x(:,2))

end

Error using @(x1,x2,x3)allocation1(x1,x2,x3)

Not enough input arguments.

Error in fmincon (line 564)

      initVals.f = feval(funfcn{3},X,varargin{:});

Caused by:

    Failure in initial user-supplied objective function evaluation. FMINCON cannot

continue.

Answer 1

[Alan Weiss]

Without reading your code in detail, it is clear that your main problem is that fmincon minimizes a SINGLE set of parameters. You simply have to rewrite allocation and your fmincon call to use a single variable x = [x1,x2,x3]:

 function objective = allocation(x)
 % Use x(1), x(2), and x(3) wherever you used x1, x2, or x3 before

Your objective for fmincon is @allocation or @(x)allocation(x).

Alan Weiss

MATLAB mathematical toolbox documentation