Can yalmip toolbox solve problems like this (my target function involves set operations)?thx!

[李汇熙]

As you guys can see in the above pic, my target function involves set operations(Vi and Cj here are sets). Hence I was wondering whether the yalmip could solve such type of problems.

sorry for this question if you guys thought it's stupid...cause I've worked with Matlab just a few days ago.

Thank you very much and best regards!

[Johan Löfberg]

You notation is very unclear. What are decision varaibles and what are constants. What does it mean to minimize a sum of sets?.What do your substractions and aditions mean? Minkowsky difference? Intersection? How does the set V relate to the (assumed) variable v. Is vc_j a variable, or the product of the variable v and c_j?...

[李汇熙]

Thank you very much for your reply.

Well, I mean I want to mimize the number of element of a set. So could I call functions of set operations, which are coded by myself, when I define the objective?

For instance, in the basic example you give for the beginner, you said:

% Define constraints and objective
Constraints = [sum(x) <= 1, x(1)==0, x(2) >= 0.5];
Objective = x'*x+norm(x);

and I want to modify the right side of the "Objective = x'*x+norm(x);" as "Objective = No_of_SET_Elm(X)", where X is a set and the No_of_SET_Elm() is a function of getting the element number of certain set. 

[Johan Löfberg]

Sounds like you say set when you simply mean a vector/matrix of variables.

One interpretation of what your description looks like is

% Decision variable
X = binvar(m,n,'full')
% Constants
vc = randn(1,m);
pc = randn(1,n);
v = randn(n,1)
c = randn(m,1)
Constraints = [sum(X,2) == 1, vc*X <= pc];
Objective = norm(X*v - c,1)

[李汇熙]

Thanks!

And yes I use a 0-1 matrix to describe the relationship between elements and sets. For example, if element a belongs to set A, the corrsponding value is 1 in the matrix；otherwise it's 0.

I've written several functions in Matlab to implement those basic set operations, and I wanna use them in Yalmip.

BTW, today is the Chinese New Years' Eve（除夕),  and happy Chinese Spring Festival (春节) to you!

[Johan Löfberg]

You are not going to be able to use those functions, unless they are simple linear operators

Give an example of what you are trying to do

[李汇熙]

Thanks!

The matrix M is below. For example, b belongs to set v2, hence m_22=1.

v1=[0 1 0 1 0 1 1]', v2, v3, v4, c1, c2 has property value vc1=3, vc2=4, vc3=2, vc4=4, pc1=6 and pc2=7 respectively.

My objective and constraints are shown in the figure below.

if X_ij=1, vi has certain type of relationship with cj. 

[李汇熙]

if X_ij=1, vi has certain type of relationship with cj; otherwise, X_ij=0.

[Johan Löfberg]

I don't see where the complication is. Sounds like you only have your own functions to define data , not to define any desired properties of the decision variable X. As I did before, the model you have is easily described as a simple MILP

[李汇熙]

yes, what I want to do is use my own defined functions in the objective, and I did not know whether this was feasible until I posted my question here and you answered it.  

Thank you very much for your help and time!

[Johan Löfberg]

You are not using any functions in your model. You are only using data created using your function, which of course is allowed (YALMIP does care how data was generated)

[李汇熙]

sorry sir, I don't understand precisely what do mean by "You are not using any functions in your model"... actually, I do make some operations of matrices in my objective (to obtain the unions and deferences of some sets), and I don't analyze whether these operations/functions are linear yet (but I think they are linear).

[Johan Löfberg]

What I am saying is that the YALMIP model I created based on your description, does not reference any of your strange functions. As long as your functions have created the data (c,v,pc,vc etc), everything is just standard MATLAB operations in the decision variable X.

Note, I interpret you U operation as a simple summation, i.e., the sum of all V(i) such that X(i,j)=1, which simplifies to a simple linear sum. If your U means something else, you have to clarify the notation (since if it is a set, i.e., a collection of something, it is really strange to take absolute value (if that is what | | means ) etc

[李汇熙]

Thx.

In my model, || is to obtain the number of element of a set (to count the number of 1 in an array) and U operation is to get the union of some sets.

For example, if x(1,2)=1 and x(2,2)=1, I will do (v1 U v2) - c2, and then obain the number of element of that set. There are many combinations of above operations, and I wish to find out which on could give me the smallest number of element.

[Johan Löfberg]

if v1 [0 1 0 1 0 1 1] and v2 is [1 1 0 1 0 0 0] and c1 = [1 0 0 1 1 0 0] , what is (v1 U v2)-c1?  The logic expression  v1 && v2 && (~c1)?

[李汇熙]

No sir, union operation is not && but ||(logic OR), and there is not logic expresssion for difference operation.

[Johan Löfberg]

Sorry, meant ||

So what is the result of (v1 U v2)-c1 with the given data

[李汇熙]

it's a set, and |v1| is the number of element of v1.

For instance, let the universal set = {a,b,c,d,e,f}, v1 = {a,b,c}, v2={b,c,d}, v3={d,e,f}, v4={a,c,e},c1={c}, c2={e,f}. so v1 U v2 ={a,b,c,d}, (v1 U v2)-c1={a,b,d}, and |(v1 U v2)-c1|=3.

In Matlab, I define the universal set = [1 1 1 1 1 1]', and v1= [1 1 1 0 0 0 ]', etc.

Actually, my trouble here is: in common, the objective of a MILP is like ∑c_i*x_i, it's a numerical plus operation (e.g.1+2=3), but my requirement here is more complicated. 

I  apply the 0-1 operators to choose which  sets could do the U operation, and then count the summation of total munber of all these union sets. 

In the example above, for |(v1 U v2)-c1|, I actually applied the 0-1 operator to remove v3 and v3 before I did the || operation(count the number of element).

Thx！

[Johan Löfberg]

So it is (v1 || v2 ) && (~c1) then, when everything simply is interpreted as binary vectors

[Johan Löfberg]

and the summary is simply that you have to write everything in terms of standard algebra on binary vectors (with a 1 representing that a particular item is in set, and picking out some element from e.g. the binary vector V would be X(i,j)*V(i,j) etc).

If you have a binary vector z, the cardinality is trivially given by sum(z)

If you have binaries a b c, and you want to compute d = a || b && ~c, you have

[d <= 1-c, d >= a-c, d >= b-c, d <= a + b]

or with auxilliary variable w  to hold the ||

[d <= 1-c, d >= w - c, d <= w, w >= a, w >= b, w <= a + b]

It is actually possible to let YALMIP do the binary modelling, but I would be careful, as I've seen a couple of bugs. I hope I've sorted them all out, but no promises

>> binvar a b c
>> true((a | b) & ~(c))

There are also high-level operators such as ismember  and nnz etc, but that will very likely give you overly complicated models. You model is naturally written as a simple 0/1 problem

[李汇熙]

Thank you very much for your help!

I'm gonna do some tests on my computer.

[李汇熙]

Sir, there are some errors after I run my test. I'm not sure whether these errors were caused by my source code or not because it said that there is an error of sdpvar.or.

Plz help me to fix them, thank you very much!

Error in sdpvar.or (line 22)

switch class(varargin{1})

Output argument "varargout" (and maybe others) not assigned during call to "D:\Program

Files\MATLAB\R2012a\toolbox\yalmip\@sdpvar\or.m>or".

Error in Sum_of_U (line 12)

        T = T | V;

Error in test1 (line 7)

Obj = Sum_of_U(X, M, C);

And here is my source code:

Sum_of_U.m

function [ s ] = Sum_of_U( X, M , C)

% matrix X is m*n, M is No_of_element*m, C is No_of_element*n 

%   m is the number of VM, n is the number of C 

[m, n] = size(X);

l = size(M, 1);

s1 = 0;

s2 = 0;

for j = 1:n

    T = zeros(l,1);

    for i = 1:m

        V = X(i, j) * M(:, i);

        T = T | V;

        if i == m

            T = T & (~C(:, n));

            s1 = sum(T);

        end        

    end

    s2 = s2 +s1; 

end

s = s2;

end

this Sum_of_U() function works well if I implemnt it independently.

then the test1.m script:

M=[1,0,0,1;1,1,1,1;1,1,0,0;0,1,1,0;0,0,0,1;0,0,1,0];

C=[0,0;0,0;1,0;0,1;0,0;0,0];

vc = [4 5 4 4];

pm = [10 10];

X = binvar(4,2);

F = [sum(X,2)==1, vc*X<=pm];

Obj = Sum_of_U(X, M, C);

optimize(F, Obj);

sol = value(X);

[Johan Löfberg]

As I said, there are likely bugs in the high-level framework (doesn't like constant T). You should implement them using standard low-level MILP logic

[李汇熙]

Thx for your advice!

Actually, what I want to minimize is this 

X_ij is the binvar, M= [v_1;v_2;...;v_m].

So as you can see, I don'y think my problem is exactly a LP.

[Johan Löfberg]

Not an LP but an MILP

All those operations can be written using standard MILP logic

z = x1 && x2 && .. xn is written as z <= x1, z <= x2,...,z<= xn, z >= x1+...+xn- (n-1)
z = x1 || x2 || ... ...xn  is written as    z <= x1+x2+..+xn, z >= x1, z >= x2,...

All your expressions can be unrolled to that, using a bunch of auxilliary variables. That is precisely what YALMIP (is supposed to do) does when you use high-level logics on binary variables (the code currently doesn't support vector arguments, and then you found that bug also)

[Johan Löfberg]

The next version of YALMIP will be fixed to support this vectorized logic code

[李汇熙]

Thank you very much!

Now, I'm using the method of exhaustion to solve this problem.

Although it's very very time-comsuming, obtaining an outcome is more importance for me.

I'm gonna improve my solution by applying your suggestion.

Thx again!

[Johan Löfberg]

What do you mean with exhaustion?

The MILP model is exhaustive search in the worst-case, but with the MILP model, cplex solves the problem in the root node in 0s, i.e., the model is trivial

[李汇熙]

I use "for" and "circshift" to list all possible X_ij matrix.

Take a 2*3 X_ij matrix for example, I begain with

1 0 0      

1 0 0  

to

0 1 0

1 0 0

to

0 0 1

1 0 0

to

1 0 0

0 1 0

.

.

.

finally to 

0 0 1

0 0 1

and there are 3^2 X_ij.

Someone has just told me that the implementation of "for" in matlab is inefficiency. 

And unfortunately, my problems are with large scale (the worst case could be 100^100 X_ij level).

[Johan Löfberg]

Ok, brute-forcing. No you don't want to do that. Use the YALMIP version I sent you per email and let me know if it works (via email correspondence to avoid any side-discussion here)

[李汇熙]

Hi Johan

There are two more questions.

1. As you can see below, why did it display so many "Maximum iterations or time limit exceeded "?

2. The 1st line of my code is "tic;" and the last line is "toc;" I spent nearly 20 hours to obtain an answer, but "Elapsed time is 136.338764 seconds." So how should I time the implementation precisely in Yalmip?

Thx1

* Starting YALMIP integer branch & bound.

* Lower solver   : LINPROG

* Upper solver   : rounder

* Max iterations : 300

 Node       Upper       Gap(%)      Lower    Open

    1 :          Inf      Inf      4.770E+02   2  Successfully solved 

    2 :          Inf      Inf      4.770E+02   3  Successfully solved 

    3 :          Inf      Inf      4.770E+02   4  Maximum iterations or time limit exceeded 

    4 :          Inf      Inf      4.770E+02   5  Maximum iterations or time limit exceeded 

    5 :          Inf      Inf      4.770E+02   6  Maximum iterations or time limit exceeded 

    6 :          Inf      Inf      4.770E+02   7  Maximum iterations or time limit exceeded 

    7 :          Inf      Inf      4.770E+02   8  Maximum iterations or time limit exceeded 

    8 :          Inf      Inf      4.770E+02   9  Successfully solved 

    9 :          Inf      Inf      4.770E+02  10  Maximum iterations or time limit exceeded 

   10 :          Inf      Inf      4.770E+02  11  Successfully solved 

   11 :          Inf      Inf      4.770E+02  12  Successfully solved 

   12 :          Inf      Inf      4.770E+02  13  Successfully solved 

   13 :          Inf      Inf      4.770E+02  14  Successfully solved 

   14 :          Inf      Inf      4.770E+02  15  Successfully solved 

   15 :          Inf      Inf      4.770E+02  16  Successfully solved 

   16 :          Inf      Inf      4.770E+02  17  Successfully solved 

   17 :          Inf      Inf      4.770E+02  18  Successfully solved 

   18 :          Inf      Inf      4.770E+02  19  Successfully solved 

   19 :          Inf      Inf      4.770E+02  20  Successfully solved 

   20 :          Inf      Inf      4.770E+02  21  Successfully solved 

   21 :    1.508E+03    51.94      4.770E+02  20  Successfully solved 

   22 :    1.508E+03    51.79      4.790E+02  21  Maximum iterations or time limit exceeded 

   23 :    1.508E+03    51.79      4.790E+02  22  Successfully solved 

   24 :    1.508E+03    51.79      4.790E+02  23  Successfully solved 

   25 :    1.508E+03    51.71      4.800E+02  24  Successfully solved 

   26 :    1.508E+03    51.71      4.800E+02  25  Successfully solved 

   27 :    1.508E+03    51.71      4.800E+02  26  Maximum iterations or time limit exceeded 

   28 :    1.508E+03    51.71      4.800E+02  27  Successfully solved 

   29 :    1.508E+03    51.71      4.800E+02  28  Maximum iterations or time limit exceeded 

   30 :    1.508E+03    51.71      4.800E+02  29  Successfully solved 

   31 :    1.508E+03    51.71      4.800E+02  30  Successfully solved 

   32 :    1.508E+03    51.71      4.800E+02  31  Successfully solved 

   33 :    1.508E+03    51.63      4.810E+02  32  Successfully solved 

   34 :    1.508E+03    51.63      4.810E+02  33  Successfully solved 

   35 :    1.508E+03    51.63      4.810E+02  34  Successfully solved 

   36 :    1.508E+03    51.63      4.810E+02  35  Successfully solved 

   37 :    1.508E+03    51.63      4.810E+02  36  Successfully solved 

   38 :    1.508E+03    51.63      4.810E+02  37  Successfully solved 

   39 :    1.508E+03    51.63      4.810E+02  38  Maximum iterations or time limit exceeded 

   40 :    1.508E+03    51.63      4.810E+02  39  Successfully solved 

   41 :    1.508E+03    51.56      4.820E+02  40  Successfully solved 

   42 :    1.508E+03    51.56      4.820E+02  41  Maximum iterations or time limit exceeded 

   43 :    1.508E+03    51.56      4.820E+02  42  Successfully solved 

   44 :    1.508E+03    51.56      4.820E+02  43  Maximum iterations or time limit exceeded 

   45 :    1.508E+03    51.48      4.830E+02  44  Successfully solved 

   46 :    1.508E+03    51.48      4.830E+02  45  Successfully solved 

   47 :    1.508E+03    51.48      4.830E+02  46  Successfully solved 

   48 :    1.508E+03    51.48      4.830E+02  47  Successfully solved 

   49 :    1.508E+03    51.48      4.830E+02  48  Successfully solved 

   50 :    1.508E+03    51.48      4.830E+02  49  Successfully solved 

   51 :    1.508E+03    51.48      4.830E+02  50  Successfully solved 

   52 :    1.508E+03    51.48      4.830E+02  51  Successfully solved 

   53 :    1.508E+03    51.48      4.830E+02  52  Successfully solved 

   54 :    1.508E+03    51.48      4.830E+02  53  Successfully solved 

   55 :    1.508E+03    51.48      4.830E+02  54  Successfully solved 

   56 :    1.508E+03    51.48      4.830E+02  55  Successfully solved 

   57 :    1.508E+03    51.48      4.830E+02  56  Successfully solved 

   58 :    1.508E+03    51.48      4.830E+02  57  Successfully solved 

   59 :    1.508E+03    51.48      4.830E+02  58  Successfully solved 

   60 :    1.508E+03    51.48      4.830E+02  59  Successfully solved 

   61 :    1.508E+03    51.41      4.840E+02  60  Maximum iterations or time limit exceeded 

   62 :    1.508E+03    51.41      4.840E+02  61  Maximum iterations or time limit exceeded 

   63 :    1.508E+03    51.41      4.840E+02  62  Maximum iterations or time limit exceeded 

   64 :    1.508E+03    51.41      4.840E+02  63  Successfully solved 

   65 :    1.508E+03    51.41      4.840E+02  64  Successfully solved 

   66 :    1.508E+03    51.41      4.840E+02  65  Successfully solved 

   67 :    1.508E+03    51.41      4.840E+02  66  Successfully solved 

   68 :    1.508E+03    51.41      4.840E+02  67  Maximum iterations or time limit exceeded 

   69 :    1.508E+03    51.41      4.840E+02  68  Successfully solved 

   70 :    1.508E+03    51.41      4.840E+02  69  Maximum iterations or time limit exceeded 

   71 :    1.508E+03    51.41      4.840E+02  70  Successfully solved 

   72 :    1.508E+03    51.41      4.840E+02  71  Successfully solved 

   73 :    1.508E+03    51.41      4.840E+02  72  Maximum iterations or time limit exceeded 

   74 :    1.508E+03    51.41      4.840E+02  73  Successfully solved 

   75 :    1.508E+03    51.41      4.840E+02  74  Successfully solved 

   76 :    1.508E+03    51.41      4.840E+02  75  Successfully solved 

   77 :    1.508E+03    51.41      4.840E+02  76  Successfully solved 

   78 :    1.508E+03    51.41      4.840E+02  77  Successfully solved 

   79 :    1.508E+03    51.33      4.850E+02  78  Maximum iterations or time limit exceeded 

   80 :    1.508E+03    51.33      4.850E+02  79  Successfully solved 

   81 :    1.508E+03    51.33      4.850E+02  80  Maximum iterations or time limit exceeded 

   82 :    1.508E+03    51.33      4.850E+02  81  Successfully solved 

   83 :    1.508E+03    51.33      4.850E+02  82  Successfully solved 

   84 :    1.508E+03    51.33      4.850E+02  83  Maximum iterations or time limit exceeded 

   85 :    1.508E+03    51.33      4.850E+02  84  Successfully solved 

   86 :    1.508E+03    51.33      4.850E+02  85  Successfully solved 

   87 :    1.508E+03    51.33      4.850E+02  86  Maximum iterations or time limit exceeded 

   88 :    1.508E+03    51.33      4.850E+02  87  Maximum iterations or time limit exceeded 

   89 :    1.508E+03    51.33      4.850E+02  88  Maximum iterations or time limit exceeded 

   90 :    1.508E+03    51.33      4.850E+02  89  Successfully solved 

   91 :    1.508E+03    51.25      4.860E+02  90  Successfully solved 

   92 :    1.508E+03    51.25      4.860E+02  91  Successfully solved 

   93 :    1.508E+03    51.25      4.860E+02  92  Successfully solved 

   94 :    1.508E+03    51.25      4.860E+02  93  Successfully solved 

   95 :    1.508E+03    51.25      4.860E+02  94  Successfully solved 

   96 :    1.508E+03    51.25      4.860E+02  95  Successfully solved 

   97 :    1.508E+03    51.25      4.860E+02  96  Maximum iterations or time limit exceeded 

   98 :    1.508E+03    51.25      4.860E+02  97  Successfully solved 

   99 :    1.508E+03    51.18      4.870E+02  98  Successfully solved 

  100 :    1.508E+03    51.18      4.870E+02  99  Successfully solved 

  101 :    1.508E+03    51.18      4.870E+02  100  Maximum iterations or time limit exceeded 

  102 :    1.508E+03    51.18      4.870E+02  101  Successfully solved 

  103 :    1.508E+03    51.18      4.870E+02  102  Successfully solved 

  104 :    1.508E+03    51.18      4.870E+02  103  Maximum iterations or time limit exceeded 

  105 :    1.508E+03    51.18      4.870E+02  104  Successfully solved 

  106 :    1.508E+03    51.18      4.870E+02  105  Maximum iterations or time limit exceeded 

  107 :    1.508E+03    51.10      4.880E+02  106  Successfully solved 

  108 :    1.508E+03    51.10      4.880E+02  107  Successfully solved 

  109 :    1.508E+03    51.10      4.880E+02  108  Successfully solved 

  110 :    1.508E+03    51.10      4.880E+02  109  Successfully solved 

  111 :    1.508E+03    51.10      4.880E+02  110  Successfully solved 

  112 :    1.508E+03    51.10      4.880E+02  111  Successfully solved 

  113 :    1.508E+03    51.10      4.880E+02  112  Successfully solved 

  114 :    1.508E+03    51.10      4.880E+02  113  Maximum iterations or time limit exceeded 

  115 :    1.508E+03    51.10      4.880E+02  114  Successfully solved 

  116 :    1.508E+03    51.10      4.880E+02  115  Maximum iterations or time limit exceeded 

  117 :    1.508E+03    51.03      4.890E+02  116  Successfully solved 

  118 :    1.508E+03    51.03      4.890E+02  117  Maximum iterations or time limit exceeded 

  119 :    1.508E+03    51.03      4.890E+02  118  Successfully solved 

  120 :    1.508E+03    51.03      4.890E+02  119  Maximum iterations or time limit exceeded 

  121 :    1.508E+03    51.03      4.890E+02  120  Successfully solved 

  122 :    1.508E+03    51.03      4.890E+02  121  Successfully solved 

  123 :    1.508E+03    51.03      4.890E+02  122  Successfully solved 

  124 :    1.508E+03    51.03      4.890E+02  123  Maximum iterations or time limit exceeded 

  125 :    1.508E+03    51.03      4.890E+02  124  Successfully solved 

  126 :    1.508E+03    51.03      4.890E+02  125  Successfully solved 

  127 :    1.508E+03    51.03      4.890E+02  126  Maximum iterations or time limit exceeded 

  128 :    1.508E+03    51.03      4.890E+02  127  Successfully solved 

  129 :    1.508E+03    50.95      4.900E+02  128  Maximum iterations or time limit exceeded 

  130 :    1.508E+03    50.95      4.900E+02  129  Maximum iterations or time limit exceeded 

  131 :    1.508E+03    50.95      4.900E+02  130  Successfully solved 

  132 :    1.508E+03    50.95      4.900E+02  131  Successfully solved 

  133 :    1.508E+03    50.95      4.900E+02  132  Maximum iterations or time limit exceeded 

  134 :    1.508E+03    50.95      4.900E+02  133  Maximum iterations or time limit exceeded 

  135 :    1.508E+03    50.95      4.900E+02  134  Successfully solved 

  136 :    1.508E+03    50.95      4.900E+02  135  Successfully solved 

  137 :    1.508E+03    50.95      4.900E+02  136  Successfully solved 

  138 :    1.508E+03    50.95      4.900E+02  137  Successfully solved 

  139 :    1.508E+03    50.88      4.910E+02  138  Successfully solved 

  140 :    1.508E+03    50.88      4.910E+02  139  Successfully solved 

  141 :    1.508E+03    50.88      4.910E+02  140  Successfully solved 

  142 :    1.508E+03    50.88      4.910E+02  141  Successfully solved 

  143 :    1.508E+03    50.88      4.910E+02  142  Successfully solved 

  144 :    1.508E+03    50.88      4.910E+02  143  Successfully solved 

  145 :    1.508E+03    50.88      4.910E+02  144  Successfully solved 

  146 :    1.508E+03    50.88      4.910E+02  145  Successfully solved 

  147 :    1.508E+03    50.88      4.910E+02  146  Successfully solved 

  148 :    1.508E+03    50.88      4.910E+02  147  Successfully solved 

  149 :    1.508E+03    50.88      4.910E+02  148  Successfully solved 

  150 :    1.508E+03    50.88      4.910E+02  149  Successfully solved 

  151 :    1.508E+03    50.88      4.910E+02  150  Successfully solved 

  152 :    1.508E+03    50.88      4.910E+02  151  Successfully solved 

  153 :    1.508E+03    50.88      4.910E+02  152  Successfully solved 

  154 :    1.508E+03    50.88      4.910E+02  153  Maximum iterations or time limit exceeded 

  155 :    1.508E+03    50.88      4.910E+02  154  Successfully solved 

  156 :    1.508E+03    50.88      4.910E+02  155  Maximum iterations or time limit exceeded 

  157 :    1.508E+03    50.80      4.920E+02  156  Maximum iterations or time limit exceeded 

  158 :    1.508E+03    50.80      4.920E+02  157  Maximum iterations or time limit exceeded 

  159 :    1.508E+03    50.80      4.920E+02  158  Successfully solved 

  160 :    1.508E+03    50.80      4.920E+02  159  Maximum iterations or time limit exceeded 

  161 :    1.508E+03    50.80      4.920E+02  160  Successfully solved 

  162 :    1.508E+03    50.80      4.920E+02  161  Successfully solved 

  163 :    1.508E+03    50.80      4.920E+02  162  Successfully solved 

  164 :    1.508E+03    50.80      4.920E+02  163  Successfully solved 

  165 :    1.508E+03    50.80      4.920E+02  164  Maximum iterations or time limit exceeded 

  166 :    1.508E+03    50.80      4.920E+02  165  Maximum iterations or time limit exceeded 

  167 :    1.508E+03    50.80      4.920E+02  166  Successfully solved 

  168 :    1.508E+03    50.80      4.920E+02  167  Maximum iterations or time limit exceeded 

  169 :    1.508E+03    50.80      4.920E+02  168  Maximum iterations or time limit exceeded 

  170 :    1.508E+03    50.80      4.920E+02  169  Successfully solved 

  171 :    1.508E+03    50.80      4.920E+02  170  Successfully solved 

  172 :    1.508E+03    50.80      4.920E+02  171  Maximum iterations or time limit exceeded 

  173 :    1.508E+03    50.72      4.930E+02  172  Successfully solved 

  174 :    1.508E+03    50.72      4.930E+02  173  Maximum iterations or time limit exceeded 

  175 :    1.508E+03    50.72      4.930E+02  174  Successfully solved 

  176 :    1.508E+03    50.72      4.930E+02  175  Successfully solved 

  177 :    1.508E+03    50.72      4.930E+02  176  Successfully solved 

  178 :    1.508E+03    50.72      4.930E+02  177  Successfully solved 

  179 :    1.508E+03    50.72      4.930E+02  178  Successfully solved 

  180 :    1.508E+03    50.72      4.930E+02  179  Successfully solved 

  181 :    1.508E+03    50.65      4.940E+02  180  Maximum iterations or time limit exceeded 

  182 :    1.508E+03    50.65      4.940E+02  181  Maximum iterations or time limit exceeded 

  183 :    1.508E+03    50.65      4.940E+02  182  Maximum iterations or time limit exceeded 

  184 :    1.508E+03    50.65      4.940E+02  183  Maximum iterations or time limit exceeded 

  185 :    1.508E+03    50.65      4.940E+02  184  Successfully solved 

  186 :    1.508E+03    50.65      4.940E+02  185  Successfully solved 

  187 :    1.508E+03    50.65      4.940E+02  186  Successfully solved 

  188 :    1.508E+03    50.65      4.940E+02  187  Successfully solved 

  189 :    1.508E+03    50.65      4.940E+02  188  Maximum iterations or time limit exceeded 

  190 :    1.508E+03    50.65      4.940E+02  189  Successfully solved 

  191 :    1.508E+03    50.65      4.940E+02  190  Successfully solved 

  192 :    1.508E+03    50.65      4.940E+02  191  Successfully solved 

  193 :    1.508E+03    50.57      4.950E+02  192  Successfully solved 

  194 :    1.508E+03    50.57      4.950E+02  193  Maximum iterations or time limit exceeded 

  195 :    1.508E+03    50.57      4.950E+02  194  Successfully solved 

  196 :    1.508E+03    50.57      4.950E+02  195  Successfully solved 

  197 :    1.508E+03    50.57      4.950E+02  196  Maximum iterations or time limit exceeded 

  198 :    1.508E+03    50.57      4.950E+02  197  Successfully solved 

  199 :    1.508E+03    50.57      4.950E+02  198  Successfully solved 

  200 :    1.508E+03    50.57      4.950E+02  199  Successfully solved 

  201 :    1.508E+03    50.57      4.950E+02  200  Successfully solved 

  202 :    1.508E+03    50.57      4.950E+02  201  Successfully solved 

  203 :    1.508E+03    50.57      4.950E+02  202  Successfully solved 

  204 :    1.508E+03    50.57      4.950E+02  203  Successfully solved 

  205 :    1.508E+03    50.57      4.950E+02  204  Successfully solved 

  206 :    1.508E+03    50.57      4.950E+02  205  Successfully solved 

  207 :    1.508E+03    50.57      4.950E+02  206  Successfully solved 

  208 :    1.508E+03    50.57      4.950E+02  207  Successfully solved 

  209 :    1.508E+03    50.57      4.950E+02  208  Successfully solved 

  210 :    1.508E+03    50.57      4.950E+02  209  Successfully solved 

  211 :    1.508E+03    50.57      4.950E+02  210  Successfully solved 

  212 :    1.508E+03    50.57      4.950E+02  211  Successfully solved 

  213 :    1.508E+03    50.57      4.950E+02  212  Maximum iterations or time limit exceeded 

  214 :    1.508E+03    50.57      4.950E+02  213  Successfully solved 

  215 :    1.508E+03    50.50      4.960E+02  214  Successfully solved 

  216 :    1.508E+03    50.50      4.960E+02  215  Maximum iterations or time limit exceeded 

  217 :    1.508E+03    50.50      4.960E+02  216  Maximum iterations or time limit exceeded 

  218 :    1.508E+03    50.50      4.960E+02  217  Successfully solved 

  219 :    1.508E+03    50.50      4.960E+02  218  Successfully solved 

  220 :    1.508E+03    50.50      4.960E+02  219  Maximum iterations or time limit exceeded 

  221 :    1.508E+03    50.50      4.960E+02  220  Successfully solved 

  222 :    1.508E+03    50.50      4.960E+02  221  Successfully solved 

  223 :    1.508E+03    50.50      4.960E+02  222  Successfully solved 

  224 :    1.508E+03    50.50      4.960E+02  223  Maximum iterations or time limit exceeded 

  225 :    1.508E+03    50.50      4.960E+02  224  Successfully solved 

  226 :    1.508E+03    50.50      4.960E+02  225  Successfully solved 

  227 :    1.508E+03    50.50      4.960E+02  226  Successfully solved 

  228 :    1.508E+03    50.50      4.960E+02  227  Maximum iterations or time limit exceeded 

  229 :    1.508E+03    50.50      4.960E+02  228  Successfully solved 

  230 :    1.508E+03    50.50      4.960E+02  229  Maximum iterations or time limit exceeded 

  231 :    1.508E+03    50.50      4.960E+02  230  Maximum iterations or time limit exceeded 

  232 :    1.508E+03    50.50      4.960E+02  231  Successfully solved 

  233 :    1.508E+03    50.50      4.960E+02  232  Successfully solved 

  234 :    1.508E+03    50.50      4.960E+02  233  Successfully solved 

  235 :    1.508E+03    50.42      4.970E+02  234  Maximum iterations or time limit exceeded 

  236 :    1.508E+03    50.42      4.970E+02  235  Maximum iterations or time limit exceeded 

  237 :    1.508E+03    50.42      4.970E+02  236  Successfully solved 

  238 :    1.508E+03    50.42      4.970E+02  237  Successfully solved 

  239 :    1.508E+03    50.42      4.970E+02  238  Successfully solved 

  240 :    1.508E+03    50.42      4.970E+02  239  Successfully solved 

  241 :    1.508E+03    50.42      4.970E+02  240  Maximum iterations or time limit exceeded 

  242 :    1.508E+03    50.42      4.970E+02  241  Successfully solved 

  243 :    1.508E+03    50.35      4.980E+02  242  Maximum iterations or time limit exceeded 

  244 :    1.508E+03    50.35      4.980E+02  243  Successfully solved 

  245 :    1.508E+03    50.35      4.980E+02  244  Maximum iterations or time limit exceeded 

  246 :    1.508E+03    50.35      4.980E+02  245  Successfully solved 

  247 :    1.508E+03    50.35      4.980E+02  246  Maximum iterations or time limit exceeded 

  248 :    1.508E+03    50.35      4.980E+02  247  Successfully solved 

  249 :    1.508E+03    50.35      4.980E+02  248  Successfully solved 

  250 :    1.508E+03    50.35      4.980E+02  249  Successfully solved 

  251 :    1.508E+03    50.35      4.980E+02  250  Successfully solved 

  252 :    1.508E+03    50.35      4.980E+02  251  Maximum iterations or time limit exceeded 

  253 :    1.508E+03    50.35      4.980E+02  252  Successfully solved 

  254 :    1.508E+03    50.35      4.980E+02  253  Maximum iterations or time limit exceeded 

  255 :    1.508E+03    50.27      4.990E+02  254  Successfully solved 

  256 :    1.508E+03    50.27      4.990E+02  255  Successfully solved 

  257 :    1.508E+03    50.27      4.990E+02  256  Successfully solved 

  258 :    1.508E+03    50.27      4.990E+02  257  Successfully solved 

  259 :    1.508E+03    50.27      4.990E+02  258  Successfully solved 

  260 :    1.508E+03    50.27      4.990E+02  259  Successfully solved 

  261 :    1.508E+03    50.27      4.990E+02  260  Successfully solved 

  262 :    1.508E+03    50.27      4.990E+02  261  Successfully solved 

  263 :    1.508E+03    50.27      4.990E+02  262  Successfully solved 

  264 :    1.508E+03    50.27      4.990E+02  263  Successfully solved 

  265 :    1.508E+03    50.20      5.000E+02  264  Successfully solved 

  266 :    1.508E+03    50.20      5.000E+02  265  Maximum iterations or time limit exceeded 

  267 :    1.508E+03    50.20      5.000E+02  266  Successfully solved 

  268 :    1.508E+03    50.20      5.000E+02  267  Successfully solved 

  269 :    1.508E+03    50.20      5.000E+02  268  Successfully solved 

  270 :    1.508E+03    50.20      5.000E+02  269  Successfully solved 

  271 :    1.508E+03    50.12      5.010E+02  270  Maximum iterations or time limit exceeded 

  272 :    1.508E+03    50.12      5.010E+02  271  Successfully solved 

  273 :    1.508E+03    50.12      5.010E+02  272  Successfully solved 

  274 :    1.508E+03    50.12      5.010E+02  273  Maximum iterations or time limit exceeded 

  275 :    1.508E+03    50.12      5.010E+02  274  Successfully solved 

  276 :    1.508E+03    50.12      5.010E+02  275  Successfully solved 

  277 :    1.508E+03    50.12      5.010E+02  276  Successfully solved 

  278 :    1.508E+03    50.12      5.010E+02  277  Successfully solved 

  279 :    1.508E+03    50.12      5.010E+02  278  Successfully solved 

  280 :    1.508E+03    50.12      5.010E+02  279  Successfully solved 

  281 :    1.508E+03    50.12      5.010E+02  280  Maximum iterations or time limit exceeded 

  282 :    1.508E+03    50.12      5.010E+02  281  Maximum iterations or time limit exceeded 

  283 :    1.508E+03    50.12      5.010E+02  282  Successfully solved 

  284 :    1.508E+03    50.12      5.010E+02  283  Successfully solved 

  285 :    1.508E+03    50.12      5.010E+02  284  Successfully solved 

  286 :    1.508E+03    50.12      5.010E+02  285  Maximum iterations or time limit exceeded 

  287 :    1.508E+03    50.12      5.010E+02  286  Successfully solved 

  288 :    1.508E+03    50.12      5.010E+02  287  Successfully solved 

  289 :    1.508E+03    50.12      5.010E+02  288  Successfully solved 

  290 :    1.508E+03    50.12      5.010E+02  289  Successfully solved 

  291 :    1.508E+03    50.05      5.020E+02  290  Successfully solved 

  292 :    1.508E+03    50.05      5.020E+02  291  Maximum iterations or time limit exceeded 

  293 :    1.508E+03    50.05      5.020E+02  292  Maximum iterations or time limit exceeded 

  294 :    1.508E+03    50.05      5.020E+02  293  Maximum iterations or time limit exceeded 

  295 :    1.508E+03    50.05      5.020E+02  294  Successfully solved 

  296 :    1.508E+03    50.05      5.020E+02  295  Successfully solved 

  297 :    1.508E+03    50.05      5.020E+02  296  Successfully solved 

  298 :    1.508E+03    50.05      5.020E+02  297  Successfully solved 

  299 :    1.508E+03    50.05      5.020E+02  298  Successfully solved 

  300 :    1.508E+03    50.05      5.020E+02  299  Successfully solved 

+ 300 Finishing.  Cost: 1508

ans =

        1508

ans =

  Columns 1 through 17

     0     1     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0

     0     1     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0

     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0

     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0

     0     1     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0

     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0

     0     1     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0

     0     0     0     0     0     0     0     0     0     0     0     0     0     1     0     0     0

     0     1     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0

     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0

  Columns 18 through 20

     0     0     0

     0     0     0

     0     0     1

     0     0     1

     0     0     0

     0     1     0

     0     0     0

     0     0     0

     0     0     0

     0     1     0

Elapsed time is 136.338764 seconds.

[李汇熙]

now I know "Maximum iterations or time limit exceeded " is caused by the solver...

[Johan Löfberg]

As I said, you have to install a MILP solver. I will not answer any MILP-relaed questions until you have done so.

Regarding tic-toc, YALMIP currently destroys tic-toc, known bug. Use clock/etime instead until fixed (hopefully that works

[Johan Löfberg]

Another way to code around tictoc bug

s=tic;
blabla
toc(s);

[李汇熙]

hi Johan

I wrote z=x1&&x2||x3 as constraints:

z1 <= x1,  z1 <= x2, z1 >= x1 + x2 - 1,  z <= z1 + x3,  z >= z1, z >= x3 (z1 had been initialized before)

And yalmip showed "Error using lmi/horzcat (line 21), One of the constraints evaluates to a FALSE LOGICAL variable" for "z <= z1 + x3,  z >= z1, z >= x3".

Does this mean that I cannot create z1 to help me to express these constraints?

[Johan Löfberg]

No, it means you are defining a trivially infeasible model. Some of those constraints evaluates to something like 0 >= 1. Similar to

sdpvar z1 x3
z = z1+x3+1
[z <= z1+x3, z >= z1, z >= x3]

[Johan Löfberg]

and I doubt your code actually runs as you have stated it. Short-circuit logic is not allowed on variables

>> binvar x1 x2 x3 z1
>> z=x1&&x2||x3
The following error occurred converting from sdpvar to logical:
Error using logical
Conversion to logical from sdpvar is not possible.

You must mean

z=x1&x2|x3
Nonlinear scalar (real, models 'or', binary, 1 variable, current value : 1)

[Johan Löfberg]

unless x1,x2,x3 aren't sdpvars of course

[李汇熙]

no, x_1,x_2,x_3 are not completely sdpars. x_i = X(i)*M(i), in which M(i) are known array and X(i) is the sdpvars(binvar).

So what I attempt to do here is convert z=x_1&x_2|x_3, which sum(z) is my object, into constraints. Hence this could be a standard MILP model as you told me before.

[Johan Löfberg]

So they are sdpvars, and you should thus not use short-circuit logics

[李汇熙]

So the reason is that I made a short-circuit logics...BTW, is it feasible to use z1 to describe the relationship between x1 and x2 (x1&x2) as a constraint?

[Johan Löfberg]

Yes, short-circuit makes no sense when the variables are decision variables, as they don't have any values and there is thus no way to terminate anything early

You are free to write and as z=x1&x2, z=and(x1,x2), or manually z<=x1,z<=x2,z>=x1+x2-1,. it is entirely up to you. They will all generate precisely the same model in the end

[李汇熙]

I tried two pieces of code.

the first one is :

X = binvar(1);
M=round(rand(400,1));
z11=X*M;
z_11= sdpvar(400,1);
C=round(rand(400,1));
constraint = [z_11<=z11+C,z_11>=z11,z_11>=C];

It's OK.

Then the 2nd one:

X = binvar(1);
z11=X*M(:,1);
z_11= sdpvar(400,1);
constraint = [z_11<=z11+(~C1(1 ,:)'),z_11>=z11,z_11>=(~C1(1 ,:)')];

matlab showed:

Error using sdpvar/plus (line 35)
Cannot add SDPVAR object and LOGICAL object

Error in exp_test1 (line 4)
constraint = [z_11<=z11+(~C1(1 ,:)'),z_11>=z11,z_11>=(~C1(1 ,:)')];

I've no idea why this happen...

M and C1 are also randomly created.

[Johan Löfberg]

>> x1 + (1~=0)

Error using sdpvar/plus (line 35)
Cannot add SDPVAR object and LOGICAL object

Hence, you have to cast as a double

>> x1 + double(1~=0)

[李汇熙]

yes, it works.Thx!

But there is another problem.

I changed the scale of my problem, it always said:

Attempted to access internal_sdpvarstate.extVariables(5573); index out of bounds because

numel(internal_sdpvarstate.extVariables)=5572.

Error in yalmip (line 1103)

                logicextvariables = [logicextvariables internal_sdpvarstate.extVariables(i)];

Error in convertlogics (line 6)

    extvariables = yalmip('logicextvariables');

Error in compileinterfacedata (line 71)

[F,changed] = convertlogics(F);

Error in solvesdp (line 251)

[interfacedata,recoverdata,solver,diagnostic,F,Fremoved,ForiginalQuadratics] =

compileinterfacedata(F,[],logdetStruct,h,options,0,solving_parametric);

Error in optimize (line 31)

varargout{:} = solvesdp(varargin{:});

Error in test5 (line 50)

optimize([constraints,vc*X <= pm, vm*X <= pc,sum(X,2)==1], obj);

[Johan Löfberg]

Reproducible example needed

[李汇熙]

I was wondering what and why is 5572...

[李汇熙]

Plz take a look at this, Johan.

Thx!

[Johan Löfberg]

Runs fine here.

Try yalmip('clear') in case there is some bad internals after crashes etc

[李汇熙]

oh, it's ok now.

so the error means the cache is full...that's why it keeps saying 5572.

Thank you!

[Johan Löfberg]

No, it has nothing to do with any cache, and the number 5572 has no particular meaning. The internal database for YALMIP got messed up somehow. It is adviced that you have a yalmip('clear') in the beginning of YALMIP scipts, to setup a clean start.

[李汇熙]

ok, thanks for your advice!