elaborate solution

[waqas ikhtiar]

Mr johan here are some results optimization problem of unit commitment. i cant find where are total number of nodes in solution. what does this  'H' means in nodes column. what do i need to study to understand this result completely

where is total solution time. 

Optimize a model with 12870 rows, 6478 columns and 145635 nonzeros

Presolve removed 4497 rows and 1247 columns

Presolve time: 0.57s

Presolved: 8373 rows, 5231 columns, 46027 nonzeros

Variable types: 2107 continuous, 3124 integer (3124 binary)

Found heuristic solution: objective 4205046.4000

Root relaxation: objective 4.137131e+06, 2888 iterations, 0.58 seconds

    Nodes    |    Current Node    |     Objective Bounds      |     Work

 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

     0     0 4137131.49    0  203 4205046.40 4137131.49  1.62%     -    2s

H    0     0                    4160128.5000 4137131.49  0.55%     -    2s

H    0     0                    4156578.6000 4137131.49  0.47%     -    2s

     0     0 4139449.82    0  153 4156578.60 4139449.82  0.41%     -    2s

     0     0 4141135.71    0  180 4156578.60 4141135.71  0.37%     -    3s

H    0     0                    4155082.6000 4141135.71  0.34%     -    3s

     0     0 4141709.43    0  244 4155082.60 4141709.43  0.32%     -    3s

H    0     0                    4153073.5000 4141709.43  0.27%     -    3s

     0     0 4142116.31    0  186 4153073.50 4142116.31  0.26%     -    4s

H    0     0                    4151205.4000 4142116.31  0.22%     -    4s

     0     0 4142167.31    0  167 4151205.40 4142167.31  0.22%     -    4s

H    0     0                    4149876.4000 4142167.31  0.19%     -    4s

H    0     0                    4143301.4000 4142167.31  0.03%     -    4s

     0     0 4142167.31    0  111 4143301.40 4142167.31  0.03%     -    4s

H    0     0                    4142926.4000 4142167.31  0.02%     -    5s

     0     0 4142210.14    0  147 4142926.40 4142210.14  0.02%     -    5s

H    0     0                    4142801.4000 4142210.14  0.01%     -    5s

     0     0 4142214.18    0  110 4142801.40 4142214.18  0.01%     -    5s

     0     0 4142214.18    0  160 4142801.40 4142214.18  0.01%     -    5s

     0     0 4142214.18    0   50 4142801.40 4142214.18  0.01%     -    6s

     0     0 4142214.18    0   80 4142801.40 4142214.18  0.01%     -    7s

     0     0 4142235.85    0  183 4142801.40 4142235.85  0.01%     -    7s

     0     0 4142253.35    0  225 4142801.40 4142253.35  0.01%     -    8s

     0     0 4142365.84    0  224 4142801.40 4142365.84  0.01%     -    8s

     0     0 4142388.14    0  198 4142801.40 4142388.14  0.01%     -    9s

Cutting planes:

  Gomory: 6

  Cover: 107

  Implied bound: 163

  Clique: 62

  MIR: 15

  Flow cover: 25

  GUB cover: 1

  Zero half: 18

Explored 0 nodes (16028 simplex iterations) in 9.26 seconds

Thread count was 2 (of 2 available processors)

Optimal solution found (tolerance 1.00e-04)

Best objective 4.142801400000e+06, best bound 4.142388138371e+06, gap 0.0100%

thanks

[Johan Löfberg]

It explicitly says "Explored 0 nodes". Hence, the problem was solved in the root-node during presolve (i.e., a pretty simple problem). H means that heuristics was applied to find integer feasible solutions


[waqas ikhtiar]

how can be it is possible that it is solved at root-node. as these results are are reproduced by me of paper here

see table I (computational results) of the paper. There are 531 nodes for original formulation in problem number one and solution time is 1485 sec. similarly for problem num 4 nodes:528, time:5340

above results which i had posted were of problem number 4 size 45 (table I of paper which is linked) of orginal formulation but there are 0 nodes. is there any prblem with my simulations?

[Johan Löfberg]

That is an impossible question to answer. The problem you have posed is trivially solved using essentially any solver (mosek, gurobi, cplex, even bnb finds a solution with 0.27% duality gap in 30 seconds, meaning it is extremely easy)

Either the problem is simply solved easily using moderns solvers, or you have implemented the wrong model, used the wrong data, or the authors have reported the wrong data or the wrong model, etc etc

You would have to check if the solution satisfies all the constraints you want it to satisfy, and you should also find a known value on the optimal objective (which doesn't seem to be reported in the paper)

[Johan Löfberg]

Note that the paper [4] which is used for comparison replicates the units 10 times (and load) when solving the problem, i.e., the 10 generator case is actually a 100 generator case. Most likely, the data in this paper does the same thing. That puts the production cost in the right ball-park. You get 477e3 for 8 generators, while in the paper [4], the cost for the 10x10 case is 5.6e6., i.e. roughly a factor 10 hihger

[waqas ikhtiar]

can you guide me how to handle symetry in an optimization problem. for unit commitment problem

[Johan Löfberg]

no

[waqas ikhtiar]

thanks

[waqas ikhtiar]

hi sir, i've simulated a paper and i want to discuss my code with you as my results are very different from paper, for that matter may i send you my code 

i've attatched paper with this message

thanks

[Johan Löfberg]

Well, discuss then?