Why am I getting the error message "??? Assignment has more non-singleton rhs dimensions than non-singleton subscripts"?

Hi all,

Please help me to solve this problem.

clear all
clc
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % % %%%read data
% filename = 'D_test2.xlsx';
% sheet = 1;
% xlRange = 'A2:E60';
% 
% Mm = xlsread(filename, sheet, xlRange);
% % 
% % %Get the data
% % %X=(Mm(:,1:13));     %%% money ens  data
% HB=(Mm(:,2));   %%% hauteur brute 
% P=(Mm(:,3));     %%% puissance
% QTU=(Mm(:,1));%%débit turbiné
% Rg=(Mm(:,4));
% k=0.00981;
% m=(Mm(:,5));
% 
% x1=QTU(:);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % %%%read data
% % filename = 'D_final.xlsx';
% % sheet = 1;
% % xlRange = 'A2:AG8761';
% % 
% % Mm = xlsread(filename, sheet, xlRange);
% % % pause
% % % Get the data
% % % X=(Mm(:,1:13));     %%% money ens  data
% % HB=(Mm(:,17));   %%% hauteur brute 
% % P=(Mm(:,1));     %%% puissance
% % QTU=(Mm(:,11));%%débit turbiné
% % % hf=(Mm(:,22));%perte de charge dans la conduite
% % AMONT=(Mm(:,15));%hauteur amont
% % CdF=(Mm(:,16));%hauteur aval
% % % R=(Mm(:,23));%rendement
% %  m=(Mm(:,25));%durée
% % % rhf=(Mm(:,26));
% % Rg=(Mm(:,27));
% % k=0.00981;
% % % X=(Mm(:,31));
% % % hmin=36.5;
% % % hmax=41.5;
% % % qmin=130;
% % % qmax=152;
% % x1=QTU(:);
% % hfb=AMONT(:);
% % htr=CdF(:);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%P	QTU	AMONT	CdF	HB	R	Rg
GG=[
    296	845.7143	528.2500	488	40.2500	0.7475	0.8864
247	705.7143	528.2700	488	40.2700	0.6237	0.8860
246	702.8571	528.2400	488	40.2400	0.6212	0.8866
256	731.4286	528.2000	488	40.2000	0.6465	0.8875
265	757.1429	528.2600	488	40.2600	0.6692	0.8862
286	817.1429	528.2500	488	40.2500	0.7222	0.8864
273	780	528.2300	487.5000	40.7300	0.6894	0.8760
265	757.1429	528.3000	487.5000	40.8000	0.6692	0.8745
351	1.0029e+03	528.1000	487.6000	40.5000	0.8864	0.8809
349	997.1429	528.0600	487.7000	40.3600	0.8813	0.8840
365	1.0429e+03	528	487.7000	40.3000	0.9217	0.8853
359	1.0257e+03	528.1600	487.7000	40.4600	0.9066	0.8818
347	991.4286	528.3000	487.7000	40.6000	0.8763	0.8788
351	1.0029e+03	528.3000	487.7000	40.6000	0.8864	0.8788
368	1.0514e+03	528.2000	487.7000	40.5000	0.9293	0.8809
358	1.0229e+03	528.1400	487.7000	40.4400	0.9040	0.8822
359	1.0257e+03	528.0800	487.7000	40.3800	0.9066	0.8836
346	988.5714	528.1800	487.7000	40.4800	0.8737	0.8814
377	1.0771e+03	528.1500	488	40.1500	0.9520	0.8886
373	1.0657e+03	528.2100	488	40.2100	0.9419	0.8873
376	1.0743e+03	528.2400	488	40.2400	0.9495	0.8866
367	1.0486e+03	528.2000	488	40.2000	0.9268	0.8875
355	1.0143e+03	528.1800	488	40.1800	0.8965	0.8880
309	882.8571	528.2300	488	40.2300	0.7803	0.8868
276	788.5714	528.2500	488	40.2500	0.6970	0.8864
254	725.7143	528.2600	488	40.2600	0.6414	0.8862
253	722.8571	528.2600	488	40.2600	0.6389	0.8862
250	714.2857	528.2700	488	40.2700	0.6313	0.8860
258	737.1429	528.2400	488	40.2400	0.6515	0.8866
292	834.2857	528.1600	488	40.1600	0.7374	0.8884
280	800	528.1600	488.6000	39.5600	0.7071	0.9019
303	865.7143	528.2000	488.6000	39.6000	0.7652	0.9010
312	891.4286	528.1000	488.6000	39.5000	0.7879	0.9032
343	980.0000	528	488.6000	39.4000	0.8662	0.9055
345	985.7143	528.0600	488.6000	39.4600	0.8712	0.9042
333	951.4286	528.1800	488.6000	39.5800	0.8409	0.9014
329	940.0000	528.2400	488.6000	39.6400	0.8308	0.9000
315	900.0000	528.2800	488.6000	39.6800	0.7955	0.8991
338	965.7143	528.2000	488.6000	39.6000	0.8535	0.9010
328	937.1429	528.1000	488.6000	39.5000	0.8283	0.9032
315	900.0000	528.1000	488.6000	39.5000	0.7955	0.9032
317	905.7143	528.1000	488.6000	39.5000	0.8005	0.9032
358	1.0229e+03	528.0400	487.9000	40.1400	0.9040	0.8888
371	1060	528.1200	487.9000	40.2200	0.9369	0.8871
373	1.0657e+03	528.2200	487.9000	40.3200	0.9419	0.8849
364	1040	528.2500	487.9000	40.3500	0.9192	0.8842
348	994.2857	528.2100	487.9000	40.3100	0.8788	0.8851
296	845.7143	528.2400	487.9000	40.3400	0.7475	0.8844
267	762.8571	528.2200	487.9000	40.3200	0.6742	0.8849
242	691.4286	528.2800	487.9000	40.3800	0.6111	0.8836
243	694.2857	528.2800	487.9000	40.3800	0.6136	0.8836
238	680	528.2600	487.9000	40.3600	0.6010	0.8840
242	691.4286	528.2200	487.9000	40.3200	0.6111	0.8849
251	717.1429	528.2000	487.9000	40.3000	0.6338	0.8853
267	762.8571	528.2900	487.3000	40.9900	0.6742	0.8704
222	634.2857	528.1000	487.3000	40.8000	0.5606	0.8745
267	762.8571	527.9000	487.3000	40.6000	0.6742	0.8788
262	748.5714	527.9000	487.3000	40.6000	0.6616	0.8788
270	771.4286	528.1800	487.3000	40.8800	0.6818	0.8727
273	780	528.3000	487.3000	41.0000	0.6894	0.8702];
P=GG(:,1);
QTU=GG(:,2);
hfb=GG(:,3);
htr=GG(:,4);
HB=GG(:,5);
Rg=GG(:,7);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% options = optimset('PlotFcns',@optimplotfval);
%options = optimset('PlotFcns',@optimplotfval);
opts = optimset('fminsearch');
%opts = optimset('fminsearch',@optimplotfval);
opts.Display = 'iter';
opts.TolX = 1.e-12;
%opts.TolFun = 1.e-12;
opts.MaxFunEvals = 100;
sse =@(x)QTU-sum(x(1)+x(2)+x(3)+x(4)+x(5)+x(6)+x(7)+x(8));
x0=[ones(60,1),ones(60,1),ones(60,1),ones(60,1),ones(60,1),ones(60,1),ones(60,1),ones(60,1)];
 n=length(x0);
LB=[0*ones(n,1) zeros(n,1) zeros(n,1) zeros(n,1) zeros(n,1) zeros(n,1) zeros(n,1) zeros(n,1)];
UB=[152*ones(n,1) 152*ones(n,1) 152*ones(n,1) 152*ones(n,1) 152*ones(n,1) 152*ones(n,1) 152*ones(n,1) 152*ones(n,1)];
%sse = fminsearch(sse,x0,options)
%xsol = fminsearchbnd(sse,x0,LB,UB,opts)
[xsol,fval,exitflag,output] = fminsearchbnd(sse,x0,LB,UB)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

[Walter Roberson]

This appears to require John D'Errico's File Exchange contribution fminsearchbnd()

Answer 1

[Walter Roberson]

https://www.mathworks.com/help/matlab/ref/fminsearch.html#bvadxhn-1-fun

Function to minimize, specified as a function handle or function name. fun is a function that accepts a vector or array x and returns a real scalar f (the objective function evaluated at x).

QTU=GG(:,2);

That is 60 x 1

sse =@(x)QTU-sum(x(1)+x(2)+x(3)+x(4)+x(5)+x(6)+x(7)+x(8));

That is 60 x 1 minus the sum() of what is a scalar because x(1) each each name scalars and + operation between scalars gives a scalar. The sum() there is confusing. 60 x 1 minus a scalar is 60 x 1. However we see from the above that you must return a scalar.

fminsearchbnd() is not suitable for minimizing a multi-objective system: gamultiobj() is the best routine for that.

[Daniel Mbadjoun]

Thanks for your response. I also do a mistake when i express the objective function. The correct expression is:

sse =@(x)QTU-(x(1)+x(2)+x(3)+x(4)+x(5)+x(6)+x(7)+x(8));

[Daniel Mbadjoun]

In my script, i expect to have 60 values for each x as result of my optimization. Please how can i do?

[Walter Roberson]

By examination it becomes clear that the list of values will be minimized when the sum of the x is maximum. The sum is maximum when each of the x is set to its upper bound.

[Daniel Mbadjoun]

Thanks for this counsel. According your counsel, can i do this with inequality constraints:

for k=1:8
    sse =@(x)QTU-sum(x(k))
end

%sse =@(x)QTU-(x(1)+x(2)+x(3)+x(4)+x(5)+x(6)+x(7)+x(8));
x0=[ones(60,1),ones(60,1),ones(60,1),ones(60,1),ones(60,1),ones(60,1),ones(60,1),ones(60,1)];
 n=length(x0);
LB=[0*ones(n,1) zeros(n,1) zeros(n,1) zeros(n,1) zeros(n,1) zeros(n,1) zeros(n,1) zeros(n,1)];
UB=[152*ones(n,1) 152*ones(n,1) 152*ones(n,1) 152*ones(n,1) 152*ones(n,1) 152*ones(n,1) 152*ones(n,1) 152*ones(n,1)];
%sse = fminsearch(sse,x0,options)
%xsol = fminsearchbnd(sse,x0,LB,UB,opts)
%%%[xsol,fval,exitflag,output] = fminsearchbnd(sse,x0,LB,UB)

[x,fval]=fminsearchcon(sse,x0,LB,UB,[],[],@(x) x(1)+x(2)+x(3)+x(4)+x(5)+x(6)+x(7)+x(8)-QTU);

I want to use input vector for output vector. What can i do?

[Walter Roberson]

No. Each iteration of the loop you overwrite all of sse. Also x(k) is scalar there so sum() makes no difference.

Your sse returns a vector but only gamultiobj and fsolve can deal with vectors of results.

[Daniel Mbadjoun]

I already try with gamultiobj but i obtain a scalar not vector as i expect. Please how can i express my problem with this other constraint function @(x) x(1)+x(2)+x(3)+x(4)+x(5)+x(6)+x(7)+x(8)-QTU). How can i declare a vector as input. Can i express it as follows:

fitnessfcn = @(x)QTU-sum(x);
nvars = 8;
lb = 0;
ub = 152;
rng default % for reproducibility
x = gamultiobj(fitnessfcn,nvars,[],[],[],[],lb,ub, @(x) x(1)+x(2)+x(3)+x(4)+x(5)+x(6)+x(7)+x(8)-QTU)

[Walter Roberson]

Do I understand correctly that you want @(x) x(1)+x(2)+x(3)+x(4)+x(5)+x(6)+x(7)+x(8)-QTU) to be a non-linear inequality constraint? So x(1)+x(2)+x(3)+x(4)+x(5)+x(6)+x(7)+x(8)-QTU must be non-positive for all entries? x(1)+x(2)+x(3)+x(4)+x(5)+x(6)+x(7)+x(8)-QTU is sum(x(1:8))-QTU and in order for it to be non-positive for all QTU values, all(sum(x(1:8)) >= QTU) must hold, and in order for that to hold, sum(x(1:8)) >= min(QTU) must hold. In turn that is -sum(x(1:8)) <= -min(QTU). So this non-linear constraint can be expressed as a linear constraint:

A = -ones(1,8); b = -min(QTU);

However, I am unclear as to how your earlier problem with 480 variables suddenly become a problem in 8 variables.

[Daniel Mbadjoun]

I want to use non-linear inequality constraint x(1)+x(2)+x(3)+x(4)+x(5)+x(6)+x(7)+x(8)<=QTU. My problem is to determine all x (480 variables) for all the 60 equations with objective function:

f(x)=QTU-x(1)+x(2)+x(3)+x(4)+x(5)+x(6)+x(7)+x(8)

sub

0<=x(1:8)<=152

sum(x(1:8))<=QTU

can i express the objective function as follows:

f(x)=sum(QTU-sumx(1:8)).^2

sub

0<=x(1:8)<=152

sum(x(1:8))<=QTU

to obtain each x (all 480 variables) by using the adequate algorithm. Please help me with the adequate formulation of my problem of 480 variables.

[Walter Roberson]

I want to use non-linear inequality constraint x(1)+x(2)+x(3)+x(4)+x(5)+x(6)+x(7)+x(8)<=QTU

As I showed above this is really a linear inequality. It can be expressed by

A = [ones(1,8), ones(1,number_of_variables-8)];
b = min(QTU);

[Daniel Mbadjoun]

I also try your option counsel but the result is not seems at i mind it

fitnessfcn = @debit_optim;   % Function handle to the fitness function
nvars = 480;                      % Number of decision variables
% lb = [-5,-5];                   % Lower bound
% ub = [5,5];                     % Upper bound
lb=[0*ones(nvars,1),zeros(nvars,1),zeros(nvars,1),zeros(nvars,1),zeros(nvars,1),zeros(nvars,1),zeros(nvars,1),zeros(nvars,1)];
ub=[152*ones(nvars,1),152*ones(nvars,1),152*ones(nvars,1),152*ones(nvars,1),152*ones(nvars,1),152*ones(nvars,1),152*ones(nvars,1),152*ones(nvars,1)];
% A = []; b = [];                 % No linear inequality constraints
% Aeq = []; beq = [];             % No linear equality constraints

% A = [ones(1,8), ones(1,nvars-8)]; b = min(QTU);
% Aeq = [ones(1,8), ones(1,nvars-8)]; beq = min(QTU);

% A = [ones(1,nvars-8), ones(1,8)]; b = min(QTU);
% Aeq = [ ones(1,nvars-8), ones(1,8)]; beq = min(QTU);

% A = [ones(1,nvars-8), ones(1,8)]; b = QTU;
% Aeq = [ ones(1,nvars-8), ones(1,8)]; beq = QTU;

A = [ones(60,8)]; b = QTU;
Aeq = [ ones(60,8)]; beq = QTU;
options = gaoptimset('ParetoFraction',0.3,'PopulationSize',100,'Generations',200,'StallGenLimit',200,'TolFun',1e-100,'PlotFcns',@gaplotpareto);

[x,fval] = gamultiobj(fitnessfcn,nvars, A,b,Aeq,beq,lb,ub,options)

%%%% THE RESULT SIZE IS 1*480 WHILE I EXPECT TO HAVE 8*60 

[Walter Roberson]

A = [ones(1,8), zeros(1,nvars-8)];
b = miin(QTU);
Aeq = []; 
beq = [];

[Daniel Mbadjoun]

I used your proposal but I had a result of x with size 30*480, not 60*8 as i want

[Walter Roberson]

A result that size in which function?

[Daniel Mbadjoun]

I want to have equal x(1)+x(2)+x(3)+x(4)+x(5)+x(6)+x(7)+x(8)=QTU as a constraint. I want a solution for each equation. I expect in my formulation to obtain 60 equations which have 8 variables per equation plus non-linear equality and inequality constraints (x(1)+x(2)+x(3)+x(4)+x(5)+x(6)+x(7)+x(8)=QTU and x(1)+x(2)+x(3)+x(4)+x(5)+x(6)+x(7)+x(8)<=QTU) .