how can I get all optimal solutions using Yalmip linked with CPLEX

[yezhifneg]

I was using yalmip toolbox linked with CPLEX to solve optimization problem.

a example can be shown like 

MIQP Presolve eliminated 121 rows and 0 columns.

Aggregator did 24 substitutions.

Reduced MIQP has 728 rows, 936 columns, and 3768 nonzeros.

Reduced MIQP has 936 binaries, 0 generals, 0 SOSs, and 0 indicators.

Presolve time = 0.01 sec. (3.03 ticks)

Probing fixed 24 vars, tightened 0 bounds.

Probing time = 0.02 sec. (2.28 ticks)

Clique table members: 4432.

MIP emphasis: balance optimality and feasibility.

MIP search method: dynamic search.

Parallel mode: deterministic, using up to 2 threads.

Root relaxation solution time = 0.06 sec. (24.60 ticks)

        Nodes                                         Cuts/

   Node  Left     Objective  IInf  Best Integer    Best Bound    ItCnt     Gap

      0     0       -9.2000   269                     -9.2000      725         

      0     0       -9.2000   139                     Cuts: 4      786         

      0     0       -9.2000   203                    Cuts: 41      967         

      0     0       -9.2000    94                 ZeroHalf: 1      970         

      0     0       -9.2000   200                ZeroHalf: 20     1129         

*     0+    0                           -7.8500       -9.2000     1129   17.20%

*     0+    0                           -8.4500       -9.2000     1129    8.88%

*     0+    0                           -8.8500       -9.2000     1129    3.95%

      0     2       -9.2000   130       -8.8500       -9.2000     1129    3.95%

Elapsed time = 0.86 sec. (279.74 ticks, tree = 0.01 MB, solutions = 3)

*    79+   75                           -9.0000       -9.2000     9841    2.22%

*    85    77      integral     0       -9.1000       -9.2000    10188    1.10%

*   116    79      integral     0       -9.1000       -9.2000    10965    1.10%

*   153    48      integral     0       -9.2000       -9.2000    12312    0.00%

Implied bound cuts applied:  2

Zero-half cuts applied:  10

Root node processing (before b&c):

  Real time             =    0.83 sec. (276.23 ticks)

Parallel b&c, 2 threads:

  Real time             =    0.65 sec. (261.08 ticks)

  Sync time (average)   =    0.00 sec.

  Wait time (average)   =    0.00 sec.

                          ------------

Total (root+branch&cut) =    1.48 sec. (537.31 ticks)

 Suppose in my codes, the decision variable is X, then I can use ' double(X)' get final solution 

 my question is how can I know how much optimal solutions I got at last, and how can matlab display all optimal solutions, Because it always only give 1 solution. What codes should I use?

 And in command window, CPLEX shows solution=3, is this means at that time, they find 3 solutions have the same objective value? 

[Johan Löfberg]

Solution pools currently not supported. Under development though, but there were some strange crashes in cplex so it is not released.

If x is binary, you can resolve the problem, and add a cut to avoid the known solution. For instance

allX = [];

sol = solvesdp(con,obj)

while sol.problem == 0

allX = [allX double(x)];

con = [con, exclude(x,double(x)];

 sol = solvesdp(con,obj);

end

[Johan Löfberg]

related documentation

http://users.isy.liu.se/johanl/yalmip/pmwiki.php?n=Commands.Exclude

[yezhifneg]

Thank you John, variable in my problem is binary. Your suggestion really saved my work!

[yezhifneg]

John, I followed your method and rewrite my code, 

However, when I run my codes, the result is:

Undefined function 'exclude' for input arguments of type 'ndsdpvar'.

Error in trainee_S111 (line 133)

    F=[F,exclude(X,double(X))];

is there anything missing?

[Johan Löfberg]

Use  F=[F,exclude(X(:),double(X(:)))]; instead and it will work