Originally posted by: Jayyo

Hi, I am a cplex user and am running a mip model through java.

I got a solution but it shows the gap to be quite large to be considered as a optimal value,

but if I print out the relative mip gap and absolute mip gap, it shows 0, and almost 0 consecutively.

I want to know how should I interpret this result,

whether this problem is already in optimum or there should be something wrong.
Here is the result I have.

as shown below, last gap shows around 10%
but I expected it to be close to 0, meaning the optimal place.
I could't know if this is wrong or not.

(I tried printing all the nodes to see the problems, but maybe this is not a solution)

---

Tried aggregator 2 times.
MIP Presolve eliminated 100 rows and 4970992 columns.
MIP Presolve modified 80 coefficients.
Aggregator did 9496 substitutions.
Reduced MIP has 40754 rows, 222088 columns, and 820752 nonzeros.
Reduced MIP has 16 binaries, 0 generals, 0 SOSs, and 0 indicators.
Presolve time = 3.52 sec.
MIP emphasis: balance optimality and feasibility.
MIP search method: dynamic search.
Parallel mode: deterministic, using up to 4 threads.
Root relaxation solution time = 48.81 sec.

Nodes Cuts/
Node Left Objective IInf Best Integer Best Node ItCnt Gap

0 0 149055.3166 16 149055.3166 25445

• 0+ 0 206887.8812 149055.3166 25445 27.95%

0 0 153090.4661 15 206887.8812 Fract: 6 25485 26.00%

• 0+ 0 199737.3585 153090.4661 25485 23.35%
• 0+ 0 193593.4062 153090.4661 25485 20.92%

Heuristic still looking.
0 2 153090.4661 15 193593.4062 153090.4661 25485 20.92%
Elapsed real time = 142.09 sec. (tree size = 0.01 MB, solutions = 3)
1 3 154453.3101 14 193593.4062 153090.4661 25601 20.92%
2 4 172369.3433 8 193593.4062 153090.4661 26589 20.92%
3 5 156112.8121 13 193593.4062 153090.4661 26639 20.92%
4 6 184570.9678 6 193593.4062 153090.4661 27422 20.92%
5 7 158370.9764 12 193593.4062 153090.4661 27489 20.92%
6 8 181862.7354 7 193593.4062 153090.4661 28403 20.92%
7 9 161779.2526 11 193593.4062 158783.5937 28807 17.98%

• 8+ 8 192929.5430 158783.5937 28818 17.70%
• 8+ 8 192929.5393 158783.5937 28818 17.70%

8 10 174547.2053 7 192929.5393 158783.5937 28818 17.70%

• 9 9 integral 0 191731.7250 158783.5937 29028 17.18%

10 10 183946.3386 6 191731.7250 158783.5937 29082 17.18%
11 11 182226.2871 7 191731.7250 158783.5937 29872 17.18%
12 12 176851.9210 6 191731.7250 158783.5937 29892 17.18%
13 13 185923.6447 5 191731.7250 158783.5937 29951 17.18%
14 14 167571.5754 10 191731.7250 158783.5937 30520 17.18%
15 15 178919.4573 5 191731.7250 158783.5937 30570 17.18%
16 16 187742.2163 4 191731.7250 158783.5937 30608 17.18%
17 17 174657.8644 7 191731.7250 158783.5937 31531 17.18%
18 18 182117.0101 4 191731.7250 158783.5937 31592 17.18%
19 18 191336.6525 3 191731.7250 158783.5937 31666 17.18%
20 17 192388.2180 0 191731.7250 158783.5937 31881 17.18%
Elapsed real time = 191.62 sec. (tree size = 0.41 MB, solutions = 4)
21 16 cutoff 191731.7250 158783.5937 31890 17.18%
22 17 188424.0124 3 191731.7250 158783.5937 31982 17.18%
23 16 cutoff 191731.7250 158783.5937 31984 17.18%
24 15 cutoff 191731.7250 158783.5937 31995 17.18%
25 14 cutoff 191731.7250 158783.5937 32073 17.18%
26 13 cutoff 191731.7250 158783.5937 32179 17.18%
27 12 cutoff 191731.7250 158783.5937 32200 17.18%
28 11 cutoff 191731.7250 158783.5937 32233 17.18%
29 10 cutoff 191731.7250 158783.5937 32621 17.18%
30 9 cutoff 191731.7250 158783.5937 32806 17.18%
31 10 176786.8091 6 191731.7250 167583.9510 32886 12.59%
32 11 171616.2462 9 191731.7250 167583.9510 33925 12.59%
33 12 174667.6551 7 191731.7250 167583.9510 34228 12.59%
34 11 cutoff 191731.7250 167583.9510 34250 12.59%
35 12 179235.0272 5 191731.7250 167583.9510 34307 12.59%
36 13 173804.4946 9 191731.7250 167583.9510 34498 12.59%
37 14 176754.4697 6 191731.7250 167583.9510 34706 12.59%
38 15 183452.8394 4 191731.7250 167583.9510 34972 12.59%
39 16 175122.8190 7 191731.7250 167583.9510 35057 12.59%
40 17 179995.9127 5 191731.7250 167583.9510 35447 12.59%
Elapsed real time = 211.85 sec. (tree size = 0.30 MB, solutions = 7)
41 16 cutoff 191731.7250 167583.9510 35855 12.59%
42 17 177083.2016 6 191731.7250 167583.9510 35878 12.59%
43 16 cutoff 191731.7250 167583.9510 36397 12.59%
44 17 187134.1354 3 191731.7250 167583.9510 36624 12.59%
45 18 179834.4632 5 191731.7250 167583.9510 36968 12.59%
46 19 184831.4267 4 191731.7250 167583.9510 37247 12.59%
47 18 cutoff 191731.7250 167583.9510 37501 12.59%
48 19 185154.2347 4 191731.7250 167583.9510 37920 12.59%
49 18 cutoff 191731.7250 167583.9510 38383 12.59%
50 17 cutoff 191731.7250 167583.9510 38434 12.59%
51 18 188071.3434 3 191731.7250 167583.9510 38685 12.59%
52 17 cutoff 191731.7250 167583.9510 39269 12.59%
53 16 cutoff 191731.7250 167583.9510 39339 12.59%
54 15 cutoff 191731.7250 167583.9510 40173 12.59%
55 15 189960.8358 2 191731.7250 167583.9510 40205 12.59%
56 16 184259.5843 6 191731.7250 167583.9510 40274 12.59%
57 15 cutoff 191731.7250 167583.9510 40306 12.59%
58 16 186127.5548 5 191731.7250 167583.9510 40425 12.59%
59 15 cutoff 191731.7250 167583.9510 41412 12.59%
60 16 188985.5824 4 191731.7250 167583.9510 41579 12.59%
Elapsed real time = 229.84 sec. (tree size = 0.18 MB, solutions = 8)
61 15 cutoff 191731.7250 167583.9510 41579 12.59%
62 14 191638.0186 3 191731.7250 167583.9510 41618 12.59%
63 13 cutoff 191731.7250 167583.9510 41661 12.59%
64 12 cutoff 191731.7250 167583.9510 42100 12.59%
65 11 cutoff 191731.7250 167583.9510 42193 12.59%
66 10 cutoff 191731.7250 167583.9510 42196 12.59%
67 9 cutoff 191731.7250 171616.2462 42552 10.49%
68 9 188594.6750 3 191731.7250 171616.2462 42725 10.49%
69 10 183839.4411 7 191731.7250 171616.2462 43205 10.49%
70 9 cutoff 191731.7250 171616.2462 43982 10.49%
71 8 cutoff 191731.7250 171616.2462 44586 10.49%
72 7 cutoff 191731.7250 171616.2462 44603 10.49%
73 8 186116.2794 6 191731.7250 171616.2462 44971 10.49%
74 9 186761.0754 5 191731.7250 171616.2462 45017 10.49%
75 10 183004.8488 7 191731.7250 171616.2462 45743 10.49%
76 11 188270.9736 5 191731.7250 171616.2462 45779 10.49%
77 11 188943.6814 4 191731.7250 171616.2462 46020 10.49%
78 12 185768.1593 6 191731.7250 171616.2462 46109 10.49%
79 11 cutoff 191731.7250 171616.2462 46131 10.49%
80 11 190825.4247 3 191731.7250 171616.2462 46206 10.49%
Elapsed real time = 250.79 sec. (tree size = 0.07 MB, solutions = 8)
81 11 188856.2639 5 191731.7250 171616.2462 46244 10.49%
82 10 cutoff 191731.7250 171616.2462 46318 10.49%
83 9 cutoff 191731.7250 171616.2462 46318 10.49%
84 8 cutoff 191731.7250 171616.2462 46321 10.49%
85 7 cutoff 191731.7250 171616.2462 46397 10.49%
86 6 cutoff 191731.7250 171616.2462 46400 10.49%
87 5 cutoff 191731.7250 171616.2462 46481 10.49%
88 4 cutoff 191731.7250 171616.2462 46583 10.49%
89 3 cutoff 191731.7250 171616.2462 46618 10.49%
90 2 cutoff 191731.7250 171616.2462 46867 10.49%
91 1 cutoff 191731.7250 171616.2462 47065 10.49%
92 0 cutoff 191731.7250 171616.2462 47261 10.49%

Gomory fractional cuts applied: 3

Root node processing (before b&c):
Real time = 148.22
Parallel b&c, 4 threads:
Real time = 136.53
Sync time (average) = 44.10
Wait time (average) = 47.24

---

Total (root+branch&cut) = 284.75 sec.
Warning: Output names have been modified to conform to LP format.

---

obj val: 191731.725002806
rel gap: 0.0
dual bd: 191731.725002806
nnodes: 93
left: 0
gap lim: 1.0E-4

this last rows are by below codes.

System.out.println("obj val: " + cplex.getObjValue());
System.out.println("rel gap: " + cplex.getMIPRelativeGap());
System.out.println("dual bd: " + cplex.getBestObjValue());
System.out.println("nnodes: " + cplex.getNnodes());
System.out.println("left: " + cplex.getNnodesLeft());
System.out.println("gap lim: " + cplex.getParam(IloCplex.DoubleParam.EpGap));
#CPLEXOptimizers
#DecisionOptimization

Originally posted by: SystemAdmin

I think your results are good.
The log file shows that CPLEX has enumerated all search tree nodes. When CPLEX started to work on the last open node that node had a gap of 10%. Then CPLEX managed to prove that this node can be cut off. After that no open nodes remain: the problem is solved to optimality.
The important gap values are not the last ones displayed in the log but the ones returned by the functions you call. The last gap displayed in the log is not necessarily the gap between final primal and dual bound (like in your example).
#CPLEXOptimizers
#DecisionOptimization

Originally posted by: Jayyo

Thank you for your reply.
Yes, maybe I am not familiar with the result interpretation, so I was confused with the function result and the log file result about the gap.
So, now I understand the difference between those two.

Thank you!!
#CPLEXOptimizers
#DecisionOptimization