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Department of Mathematics
Computational Results for Map Matching by
Optimization
Kaj Holmberg
Department of Mathematics Link¨oping University S-581 83 Link¨oping, Sweden.
Computational Results for Map Matching by
Optimization
Kaj Holmberg
Department of Mathematics Linköping Institute of Technology
SE-581 83 Linköping, Sweden
LiTH-MAT-R–2015/02–SE January 29, 2015
Abstract: The problem of map matching appears when evaluating GPS-tracks recorded by service vehicles, and is used to associate the sequences of GPS-points to links in a graph. Difficulties are errors in the GPS-coordinates and possible lack of GPS-points on short street segments. This paper reports computational tests on integer program-ming models for the problem, and on several heuristic methods, based on shortest paths and rural postman problems. We present extensive computational results for several methods and for both artificial and real life test cases.
1
Introduction
A short definition of map matching is as follows. Given a set of GPS-positions and a digital map, the question is which streets (links) were used when recording the GPS-positions.
We have a (city street) network, with n nodes and m links. We also have a set of q GPS points. The GPS points are supposed to lie on the links, but due to various errors, that is not the case. Our goal is to find a path that has the best consistency with the positions, i.e. the most likely path that generated the GPS points. The task is simply to find the set of links that were used by the vehicle.
This paper contains the computational results from tests described in the paper Holm-berg (2015). The problem and various Mixed Integer Programming models are described in Holmberg (2015), as well as several heuristic methods.
2
Computational tests
We have constructed several test problems: First 6 small artificial networks (called p1) and between 3 and 11 GPS-tracks for each network, yielding 31 different instances. Secondly 9 more realistic networks, p2, (with proper coordinates) and between 4 and 7 GPS-tracks for each network, yielding 41 instances. Finally we extracted 12 real life networks from OpenStreetMap, and created between 4 and 28 different real life GPS-tracks for each network, by traveling around with a mobile phone and the app GPS-logger. GPS-positions were recorded every minute or every 30 seconds. That gave 118 different instances. In total we have 190 test instances.
We have 22 basic methods (24 - 29, 30 - 33, 34 - 39, 54 - 59) and 8 different improvement heuristics with 3 different reductions schemes, yielding in total 504 different methods. If each method should be tested on each instance, we would get 95,760 tests. For this reason, some test were only performed on the initial test sets, and only the best and least time consuming ones were used on the real life instances. Simply solving the MIP-models (with or without splitting), methods 24 - 29, is not a complete method, since the solution may be infeasible (not connected or in the wrong order).
2.1 Computational details
The computer used is an Acer Aspire X3 X3995, Intel Core i7-3770, 3.4GHz, running Linux, Fedora Core 19. The machine has four CPUs, but only one was used in the testing.
The code is written in Python. Tools from Numpy, and some graph routines, especially shortest path calculations, from Scipy are used. The rural postman code used is our own creation, Holmberg (2010).
CPU-time was limited to 60 seconds for the MIP-models. Preliminary tests indicate that if the problem is not solved by then, one may expect several hours of solution time. The increase of solution time for the heuristics is not that abrupt, so we did not use a maximal time limit for those.
Below we give values for some parameters in the methods. For descriptions of these parameters, see Holmberg (2015).
We used δ = 0.2, i.e. if the projected point lies more than 0.2 times the link length outside the link, we don’t allow allocation.
We also used DA = 500, i.e. if a point lies more than 500 meters outside the limits of the map, it is removed, and all links with both end points more than 500 meters outside (on the same side) the maximal and minimal limits of the points, are removed. The
When the instance name includes ’-s’, selective two-degree elimination with q = 0.98 has been used on the network.
Furthermore, we used ν = 0.1 as the weight of the distance on the links in the objective function, and a value of 100 of the weight of intralink traveling in the heuristics based in distances in the network. In heuristic 31, we did not use parts of the length of a link, but the whole link length.
We used LM AX = 2 in model 14. In the improvement heuristics, we did at most 10 iterations.
When using splitting, we decided to split on a node if the distance to the closest point was less or equal to 10 m, and the distance to the next closest was greater or equal to 100 m, or if the distance to the closest point was less or equal to 1 m. We decided to split on a link if the distance to the closest point was less or equal to 10 m, and the distance to the next closest was greater or equal to 100 m. All the distances between points and links (or nodes) were calculated once, and if the distance between a point and a link is more then 500 m, we don’t allow that allocation.
2.2 Possible outcomes of the tests
When solving MIP-models, a maximal time of 60 seconds was enforced. Unfortunately, when using GLPK for a MIP-problem, this time limit does not seem to affect the LP-solver, but only the branching procedure. Furthermore, at some occasions, the LP-solver got into a seemingly infinite loop.
This means that we have the following possible outcomes of a run with a MIP-model: • The optimal solutions was found in a time less than 60 s, which is indicated by a
solution time less than 60 s.
• The branch-and-bound procedure was terminated at maxtime, 60 s, and an integer solution was found.
• The branch-and-bound procedure was terminated at maxtime, 60 s, and no integer solution was found.
• The first LP-problem takes more than 60 s to solve. This leads to a solution time that can be higher than 60.
• The code gets into an infinite loop at the first (or later) LP-problem. Then a manual break is needed, and no result at all is obtained.
• The modeler (GMPL) breaks down. Then no result is obtained, not even the number of variables and constraints are obtained. (This happens if model 25 is used for the mini-09-instances.)
methods 34 - 39 and 54 - 59, the heuristic may overcome failures by the MIP-model and give a solution in several of the cases above (in the worst case based on no good MIP-solution at all). Therefore a solution time of more than 60 s for these methods does not indicate a complete failure.
3
The tables
The following tables are given. Table 1 gives results for trying all methods on three very small problems with three GPS-tracks. Here C denotes the number of connected components (preferably equal to 1) and U denotes the number of points out of sequence (preferably equal to 0). Results for the MIP-models on the first group of test problems are presented in tables 2 and 3, where instances not solved by any method in the table are removed. For many instances, splitting never occured, and results for the instances where splitting had effect are given in the lower part of the table.
The sizes of all MIP-models (including those not solved) are shown in tables 4, 5 and 6, together with the number of simplex iterations and branch-and-bound nodes, if the problem was solved within 60 seconds. (Solution data for instances present in the other tables with solution time more than 60 seconds are here removed, as the number of iterations and nodes are only what 60 seconds allowed.)
Table 7 shows the results of the heuristics 30 - 34 on the first problem set, while the table 8 shows the results of the MIP-based heuristics 34 - 39, and table 9 shows the results of the heuristics 54 - 39, i.e. using a heuristic before the MIP-model. The lower parts of these tables show the results when using splitting.
The results for the improvement heuristics on the first problem set are shown in tables 10, 11, 12, 13, 14, 15, 16 and 17. There are columns for the different forbidding strate-gies (column 0 means no forbidding), and rows for each basic method and link choice variation. Tables for problems where no improvement was obtained are omitted. Table 18 shows the results of the heuristics 30 - 34 on the first problem set without limit reduction, which can be compared to table 7, where limit reduction is made. Tables 19 and 20 show the results of the heuristics 30 - 34 on the second problem set. The tables 21, 22 and 24 show the results for the MIP-models on the second problem group, without splitting, while tables 23 and 25 show the results with splitting. Tables 26, 27, 28 and 29 give the sizes of the MIP-models for problem set two. Tables 30, 31 and 32 give the results of the MIP-based heuristics 34 - 39 for the second problem set. The results of the improvement heuristics for problem set two are reported in the tables 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, and 61. Again tables for problems where no improvement was obtained are omitted.
Tables 67, 68, 69 and 70 give the results of the heuristics 30 - 33 on the third problem set, without splitting. Tables 71, 72, 73 and 74 give the sizes of MIP-model 14, used in method 34, and some solution data for problem set three. The results of a preliminary selection of the improvement heuristics, without splitting, are reported in tables 75, 76, 77, 78, 79 and 81, while the results with splitting are reported in table 80. Here the objective function values and times are given below each other, in separate rows, and not beside each other, as previously done.
In the tables 82 - 88 and 89 - 95 the 13 improvement heuristics that performed best on problem set two are used on problem set three. The methods are listed in the order they performed on problem set two, the best first (3013). In these tables, each instance occupies two rows, since there is not room for 13 columns in one row, so the first 7 methods are given in the first of these rows and the 6 remaining methods are given in the second. The tables 82 - 88 give the objective function values and tables 89 - 95 give the solution times.
Finally, in tables 96, 97, 98 and 99 the results for methods 30 - 33 without limit reduction are reported.
GPS-track g0a g0b g0c
Method Obj Time C U Obj Time C U Obj Time C U mini-0a 24 66.80 0.05 1 0 53.93 0.07 1 0 71.99 0.58 1 0 26 188.67 0.05 1 1 187.30 0.05 1 1 230.95 0.05 1 1 27 188.67 0.05 1 1 187.30 0.05 1 1 230.95 0.05 1 1 28 94.30 0.05 1 0 93.17 0.05 1 0 99.49 0.05 1 0 29 94.30 0.05 1 0 93.17 0.05 1 0 99.49 0.05 1 0 30 94.30 0.03 1 0 93.17 0.03 1 0 99.49 0.03 1 0 31 94.30 0.03 1 0 93.17 0.03 1 0 99.49 0.03 1 0 32 94.30 0.03 1 0 93.17 0.03 1 0 99.49 0.03 1 0 33 94.30 0.03 1 0 93.17 0.03 1 0 99.49 0.03 1 0 34 94.30 0.05 1 0 93.17 0.05 1 0 99.49 0.06 1 0 36 94.30 0.05 1 0 93.17 0.06 1 0 99.49 0.05 1 0 37 94.30 0.05 1 0 93.17 0.06 1 0 99.49 0.05 1 0 38 94.30 0.06 1 0 93.17 0.06 1 0 99.49 0.05 1 0 39 94.30 0.05 1 0 93.17 0.05 1 0 99.49 0.06 1 0 mini-0b 24 53.93 0.07 1 0 52.98 0.05 1 0 55.41 0.04 1 0 26 186.13 0.05 1 1 183.78 0.05 1 1 224.51 0.05 1 1 27 186.13 0.05 1 1 183.78 0.05 1 1 224.51 0.05 1 1 28 81.43 0.05 1 0 80.48 0.05 1 0 82.91 0.05 1 0 29 81.43 0.05 1 0 80.48 0.05 1 0 82.91 0.05 1 0 30 81.43 0.03 1 0 80.48 0.05 1 0 82.91 0.03 1 0 31 81.43 0.03 1 0 80.48 0.03 1 0 82.91 0.03 1 0 32 81.43 0.03 1 0 80.48 0.03 1 0 82.91 0.03 1 0 33 81.43 0.03 1 0 80.48 0.03 1 0 82.91 0.02 1 0 34 81.43 0.06 1 0 80.48 0.06 1 0 82.91 0.06 1 0 36 81.43 0.05 1 0 80.48 0.05 1 0 82.91 0.05 1 0 37 81.43 0.05 1 0 80.48 0.06 1 0 82.91 0.06 1 0 38 81.43 0.05 1 0 80.48 0.06 1 0 82.91 0.05 1 0 39 81.43 0.06 1 0 80.48 0.05 1 0 82.91 0.06 1 0 mini-0c 24 75.57 0.06 1 0 89.13 0.05 1 0 100.33 0.05 1 0 26 205.69 0.05 1 1 218.31 0.05 1 1 270.60 0.05 1 1 27 205.69 0.05 1 1 218.31 0.05 1 1 270.60 0.05 1 1 28 103.07 0.05 1 0 116.63 0.05 1 0 127.83 0.05 1 0 29 103.07 0.05 1 0 116.63 0.05 1 0 127.83 0.05 1 0 30 103.07 0.04 1 0 116.63 0.03 1 0 127.83 0.03 1 0 31 103.07 0.03 1 0 116.63 0.03 1 0 127.83 0.03 1 0 32 103.07 0.03 1 0 116.63 0.03 1 0 127.83 0.03 1 0 33 103.07 0.03 1 0 116.63 0.03 1 0 127.83 0.03 1 0 34 103.07 0.05 1 0 116.63 0.06 1 0 127.83 0.06 1 0 36 103.07 0.05 1 0 116.63 0.05 1 0 127.83 0.05 1 0
Method 24 26
Problem n m q Obj Time C Obj Time C U p1-3-g1a 5 5 4 83.98 0.05 1 83.98 0.07 1 0 p1-3-g1b 5 5 8 118.25 0.05 1 118.25 0.07 1 0 p1-3-g1c 5 5 3 62.10 0.05 1 62.10 0.05 1 0 p1-3-g1d 5 5 8 124.98 0.05 1 110.68 0.06 2 0 p1-3-g1e 5 5 3 64.08 0.05 1 48.58 0.05 1 0 p1-3-g1f 5 5 4 122.10 0.05 1 156.70 0.06 2 1 p1-3-g1g 5 5 8 110.44 0.06 1 551.87 0.06 1 3 p1-3-g1 5 5 8 138.15 0.06 1 138.15 0.07 1 0 p1-3-g2 5 5 8 189.86 0.06 1 264.02 0.06 1 2 p1-3-g3 5 5 8 131.50 0.05 1 165.35 0.06 1 1 p1-3-g4 5 5 3 111.87 0.05 1 111.87 0.06 1 0 p1-4-g1 8 9 8 172.91 0.05 1 263.89 0.12 1 2 p1-4-g2 8 9 8 198.78 0.05 1 283.99 0.15 2 2 p1-4-g3 8 9 8 216.00 0.05 1 210.23 0.17 2 0 p1-4-g4 8 9 8 230.86 0.06 2 228.39 1.21 2 0 p1-5-g1 5 5 13 196.50 0.06 1 428.49 0.06 1 5 p1-5-g2 5 5 8 144.19 0.05 1 426.23 0.05 1 3 p1-5-g3 5 5 7 164.03 0.06 1 427.28 0.06 1 3 p1-5-g4 5 5 8 184.67 0.05 1 764.51 0.12 1 4 p1-5-g5 5 5 8 272.63 0.05 1 921.12 0.06 1 6 p1-6-g1 9 11 8 142.64 0.06 1 151.84 0.11 1 0 p1-6-g2 9 11 9 276.66 0.06 1 276.66 0.12 1 0 p1-6-g3 9 11 21 361.52 0.07 1 1026.88 0.51 1 9 p1-8-g1 9 15 20 317.41 0.08 1 317.93 0.66 1 0 p1-8-g2 9 15 21 355.01 0.15 1 839.08 0.50 1 9 p1-8-g3 9 15 4 150.90 0.06 2 142.28 7.06 2 0 p1-9-g1 18 26 23 217.23 1.26 2 332.11 60.69 2 11 p1-9-g2 18 26 46 343.30 22.86 1 1025.97 60.85 1 34 p1-9-g3 18 26 7 88.89 0.08 2 275.86 60.23 1 4 p1-9-g4 18 26 7 103.29 0.08 1 204.57 60.47 2 3 p1-9-g5 18 26 10 151.84 0.33 2 199.91 60.49 2 2 p1-5-g1 5 5 13 141.10 1.04 1 220.10 0.18 1 0 p1-5-g2 5 5 8 88.79 0.11 1 144.19 0.14 1 0 p1-6-g3 9 11 21 298.42 0.13 1 831.68 1.28 1 7 p1-8-g1 9 15 20 166.71 0.17 1 318.93 0.95 1 0
Table 2: Problem set 1, MIP-models 24 and 26. At the top without split, at the bottom with split.
Method 27 28 29
Problem Obj Time C U Obj Time C U Obj Time C U p1-3-g1a 83.98 0.06 1 0 83.98 0.10 1 0 83.98 0.10 1 0 p1-3-g1b 118.25 0.31 1 0 118.25 0.17 1 0 118.25 0.10 1 0 p1-3-g1c 62.10 0.06 1 0 62.10 0.06 1 0 62.10 0.07 1 0 p1-3-g1d 124.98 0.07 1 0 124.98 0.17 1 0 110.68 0.25 2 0 p1-3-g1e 48.58 0.08 1 0 48.58 0.09 1 0 48.58 0.07 1 0 p1-3-g1f 124.60 0.09 1 0 124.60 0.45 1 0 97.86 0.15 2 0 p1-3-g1g 551.87 0.07 1 3 211.94 3.51 1 0 184.44 2.55 1 0 p1-3-g1 138.15 0.07 1 0 138.15 0.17 1 0 138.15 0.13 1 0 p1-3-g2 389.35 0.16 1 2 191.39 1.37 1 0 191.39 1.42 1 0 p1-3-g3 131.50 0.10 1 0 131.50 0.16 1 0 131.50 0.41 1 0 p1-3-g4 111.87 0.09 1 0 111.87 0.36 1 0 111.87 0.13 1 0 p1-4-g1 172.91 0.31 1 0 172.91 1.33 1 0 172.91 1.59 1 0 p1-4-g2 198.78 5.22 1 0 198.78 8.16 1 0 193.01 0.93 2 0 p1-4-g3 216.00 3.64 1 0 216.00 6.03 1 0 210.23 1.22 2 0 p1-4-g4 234.16 1.33 1 0 234.16 2.78 1 0 228.39 3.69 2 0 p1-5-g1 196.50 0.07 1 0 196.50 0.27 1 0 196.50 0.24 1 0 p1-5-g2 144.19 0.07 1 0 144.19 0.19 1 0 144.19 0.13 1 0 p1-5-g3 164.03 0.09 1 0 164.03 0.15 1 0 164.03 0.17 1 0 p1-5-g4 523.08 0.16 1 2 237.33 9.09 1 0 222.03 2.51 1 0 p1-5-g5 604.76 0.43 1 2 325.83 13.54 1 0 310.53 3.18 1 0 p1-6-g1 151.84 0.17 1 0 151.84 1.72 1 0 151.84 1.87 1 0 p1-6-g2 276.66 0.23 1 0 276.66 3.06 1 0 276.66 1.94 1 0 p1-6-g3 831.68 0.26 1 7 370.01 62.95 1 0 548.22 69.23 1 0 p1-8-g1 540.69 2.78 1 6 - - - -p1-8-g2 1268.12 19.59 1 13 367.62 128.23 1 0 - - - -p1-8-g3 151.40 23.43 1 0 151.40 66.54 1 0 142.28 18.64 2 0 p1-5-g1 196.50 0.18 1 0 196.50 0.38 1 0 196.50 0.30 1 0 p1-5-g2 144.19 0.15 1 0 144.19 0.20 1 0 144.19 0.20 1 0 p1-6-g3 831.68 0.64 1 7 370.01 30.91 1 0 370.01 34.79 1 0 p1-8-g1 318.93 4.19 1 0 - - - - 317.93 40.78 1 0 Table 3: Problem set 1, MIP-models 27, 28 and 29. Above without split, below with.
Model Rows Cols Iter Nodes Model Rows Cols Iter Nodes p1-3-g1a p1-3-g1b 24 25 32 18 3 24 47 60 33 7 26 107 96 19 3 26 240 215 300 35 27 279 128 126 1 27 652 275 288 1 28 528 256 464 9 28 1529 719 1025 1 29 356 224 201 1 29 1117 659 635 3 p1-3-g1c p1-3-g1d 24 21 29 10 3 24 42 56 23 9 26 100 93 15 1 26 233 211 48 1 27 272 125 75 1 27 645 271 230 3 28 457 221 177 1 28 1402 655 1345 15 29 285 189 118 1 29 990 595 1107 23 p1-3-g1e p1-3-g1f 24 21 29 9 3 24 28 40 28 7 26 101 93 38 5 26 160 149 54 11 27 273 125 462 59 27 444 199 360 47 28 458 221 240 1 28 795 379 1118 45 29 286 189 315 7 29 511 329 543 13 p1-3-g1g p1-3-g1 24 53 65 59 31 24 52 64 32 9 26 253 222 114 1 26 249 219 433 39 27 665 282 264 1 27 661 279 298 3 28 1686 798 27474 443 28 1658 783 1303 1 29 1274 738 24498 493 29 1246 723 993 5 p1-3-g2 p1-3-g3 24 51 63 75 31 24 52 64 35 1 26 248 218 246 9 26 252 220 164 3 27 660 278 1891 33 27 664 280 718 19 28 1633 770 11909 141 28 1661 784 1147 3 29 1221 710 13634 263 29 1249 724 3924 43 p1-3-g4 p1-4-g1 24 25 42 31 1 24 57 88 46 5 26 205 198 17 3 26 589 567 1155 17 27 617 258 739 33 27 1813 727 2107 25 28 966 438 3960 61 28 3554 1607 5686 43 29 554 378 1471 27 29 2330 1447 9287 75
Table 4: Problem set 1: Sizes of MIP-models, simplex iterations and branch-and-bound nodes.
Model Rows Cols Iter Nodes Model Rows Cols Iter Nodes p1-4-g2 p1-4-g3 24 58 89 58 9 24 53 80 39 1 26 589 568 1399 63 26 496 477 1210 17 27 1813 728 37850 467 27 1490 621 15046 239 28 3594 1628 27070 241 28 2913 1341 12847 111 29 2370 1468 5255 13 29 1919 1197 18204 173 p1-4-g4 p1-5-g1 24 56 87 43 5 24 75 82 40 1 26 589 571 22744 247 26 287 237 120 1 27 1813 731 9073 161 27 699 297 270 1 28 3514 1591 10011 75 28 2248 1077 1771 1 29 2290 1431 17078 197 29 1836 1017 1653 1 p1-5-g2 p1-5-g3 24 51 63 28 1 24 45 58 27 1 26 247 218 111 1 26 239 213 293 17 27 659 278 245 1 27 651 273 277 1 28 1632 770 1435 1 28 1480 693 1219 1 29 1220 710 968 5 29 1068 633 1542 15 p1-5-g4 p1-5-g5 24 51 63 53 7 24 44 52 44 21 26 248 218 1149 101 26 187 161 473 55 27 660 278 1806 55 27 471 211 1668 91 28 1633 770 59394 1199 28 1142 551 31832 747 29 1221 710 20955 443 29 858 501 11967 351 p1-6-g1 p1-6-g2 24 77 112 44 9 24 81 120 53 13 26 721 683 1521 13 26 856 816 932 7 27 2199 859 847 1 27 2636 1032 1302 3 28 4994 2267 5123 1 28 5829 2640 9600 13 29 3516 2091 6618 3 29 4049 2424 8039 3 p1-6-g3 p1-8-g1 24 188 215 123 7 24 197 241 120 3 26 1038 911 4856 65 26 1564 1434 4285 29 27 2818 1127 1251 3 27 4704 1722 9378 29 28 11147 5303 - - 28 16385 7578 - -29 9367 5087 - - 29 13245 7290 - -Table 5: Problem set 1: Sizes of MIP-models, simplex iterations and branch-and-bound nodes.
Model Rows Cols Iter Nodes Model Rows Cols Iter Nodes p1-8-g2 p1-8-g3 24 219 262 1746 397 24 50 106 85 15 26 1606 1457 3199 19 26 1167 1156 30175 607 27 4746 1745 61886 185 27 3931 1426 146320 2209 28 17835 8305 - - 28 6062 2506 - -29 14695 8017 - - 29 3298 2236 162386 1107 p1-9-g1 p1-9-g2 24 255 349 24619 2601 24 550 621 263420 24281 26 4173 4040 188663 11 26 4683 4334 134758 1 27 13519 5012 - - 27 14029 5306 - -28 38522 17540 - - 28 70892 33764 - -29 29176 16568 - - 29 61546 32792 - -p1-9-g3 p1-9-g4 24 95 205 450 133 24 89 199 493 93 26 3891 3888 224825 41 26 3878 3877 235971 249 27 13237 4860 - - 27 13224 4849 - -28 20960 8748 - - 28 20299 8413 - -29 11614 7776 - - 29 10953 7441 - -p1-9-g5 24 125 232 8002 1035 26 3947 3917 180198 288 27 13293 4889 - -28 24256 10397 - -29 14910 9425 -
-Table 6: Problem set 1: Sizes of MIP-models, simplex iterations and branch-and-bound nodes.
Method 30 31 32 33 34 Problem Obj Time Obj Time Obj Time Obj Time Obj Time p1-3-g1a 83.98 0.04 83.98 0.04 83.98 0.03 83.98 0.03 83.98 0.05 p1-3-g1b 118.25 0.08 118.25 0.04 118.25 0.04 118.25 0.04 118.25 0.06 p1-3-g1c 62.10 0.04 62.10 0.03 62.10 0.03 62.10 0.03 62.10 0.07 p1-3-g1d 124.98 0.04 124.98 0.03 124.98 0.04 124.98 0.04 124.98 0.06 p1-3-g1e 48.58 0.04 48.58 0.03 48.58 0.03 48.58 0.03 48.58 0.08 p1-3-g1f 148.06 0.03 148.06 0.03 148.06 0.03 148.06 0.03 124.60 0.06 p1-3-g1g 221.44 0.08 221.44 0.04 221.44 0.04 221.44 0.04 221.44 0.06 p1-3-g1 138.15 0.04 138.15 0.04 138.15 0.04 138.15 0.03 138.15 0.05 p1-3-g2 214.86 0.03 214.86 0.04 214.86 0.04 214.86 0.03 214.86 0.06 p1-3-g3 131.50 0.04 131.50 0.04 131.50 0.03 131.50 0.04 131.50 0.06 p1-3-g4 111.87 0.03 111.87 0.03 111.87 0.03 111.87 0.03 111.87 0.06 p1-4-g1 172.91 0.03 172.91 0.04 172.91 0.04 172.91 0.03 172.91 0.06 p1-4-g2 198.78 0.04 198.78 0.03 198.78 0.04 198.78 0.04 198.78 0.06 p1-4-g3 216.00 0.03 216.00 0.04 216.00 0.04 216.00 0.04 216.00 0.05 p1-4-g4 240.06 0.04 240.06 0.04 240.06 0.04 240.06 0.04 240.06 0.06 p1-5-g1 196.50 0.04 196.50 0.04 196.50 0.04 196.50 0.04 196.50 0.06 p1-5-g2 144.19 0.04 144.19 0.04 144.19 0.04 144.19 0.03 144.19 0.06 p1-5-g3 164.03 0.04 164.03 0.04 164.03 0.04 164.03 0.03 164.03 0.06 p1-5-g4 241.57 0.03 241.57 0.04 241.57 0.03 241.57 0.03 241.57 0.06 p1-5-g5 325.83 0.03 325.83 0.04 325.83 0.04 325.83 0.03 325.83 0.06 p1-6-g1 175.36 0.04 151.84 0.04 151.84 0.04 151.84 0.04 151.84 0.06 p1-6-g2 276.66 0.04 276.66 0.05 276.66 0.05 276.66 0.04 276.66 0.07 p1-6-g3 417.22 0.04 401.92 0.07 401.92 0.07 401.92 0.05 401.92 0.07 p1-8-g1 366.41 0.04 347.99 0.08 366.41 0.08 348.90 0.05 336.61 0.07 p1-8-g2 383.00 0.04 371.25 0.08 371.25 0.08 371.25 0.05 393.31 0.16 p1-8-g3 181.81 0.03 181.81 0.04 181.81 0.04 181.81 0.03 151.40 0.06 p1-9-g1 293.98 0.04 278.74 0.11 293.98 0.11 279.49 0.06 323.03 1.25 p1-9-g2 572.32 0.07 572.39 0.18 591.72 0.20 552.42 0.08 789.90 22.71 p1-9-g3 119.02 0.04 119.02 0.05 119.02 0.58 119.02 0.04 164.99 0.09 p1-9-g4 210.08 0.04 123.44 0.04 210.08 0.05 123.44 0.04 182.19 0.08 p1-9-g5 311.39 0.04 206.59 0.06 206.59 0.06 185.11 0.04 251.24 0.34 p1-5-g1 196.50 0.05 1427.49 0.06 196.50 0.05 1427.49 0.04 196.50 0.11 p1-5-g2 144.19 0.04 144.19 0.03 144.19 0.04 144.19 0.04 144.19 0.08 p1-6-g3 437.42 0.05 401.92 0.07 401.92 0.07 401.92 0.05 422.12 0.09 p1-8-g1 366.41 0.05 347.99 0.07 366.41 0.08 347.72 0.05 336.61 0.10 Table 7: Problem set 1, methods 30, 31, 32, 33 and 34, above without split, below with
Method 34 36 37 38 39 Problem Obj Time Obj Time Obj Time Obj Time Obj Time p1-3-g1a 83.98 0.16 83.98 0.06 83.98 0.07 83.98 0.10 83.98 0.11 p1-3-g1b 118.25 0.09 118.25 0.07 118.25 0.11 118.25 0.15 118.25 0.11 p1-3-g1c 62.10 0.06 62.10 0.06 62.10 0.06 62.10 0.07 62.10 0.06 p1-3-g1d 124.98 0.06 124.98 0.06 124.98 0.08 124.98 0.18 124.98 0.15 p1-3-g1e 48.58 0.06 48.58 0.06 48.58 0.07 48.58 0.08 48.58 0.07 p1-3-g1f 124.60 0.06 148.06 0.06 124.60 0.10 124.60 0.45 148.06 0.16 p1-3-g1g 221.44 0.11 221.44 0.06 221.44 0.08 221.44 3.55 221.44 2.54 p1-3-g1 138.15 0.11 138.15 0.07 138.15 0.08 138.15 0.18 138.15 0.13 p1-3-g2 214.86 0.06 191.39 0.07 214.86 0.17 191.39 1.38 191.39 1.42 p1-3-g3 131.50 0.06 131.50 0.07 131.50 0.10 131.50 0.16 131.50 0.40 p1-3-g4 111.87 0.06 111.87 0.06 111.87 0.12 111.87 0.35 111.87 0.13 p1-4-g1 172.91 0.06 172.91 0.12 172.91 0.31 172.91 1.24 172.91 1.55 p1-4-g2 198.78 0.06 214.11 0.15 198.78 5.10 198.78 8.08 214.11 0.86 p1-4-g3 216.00 0.06 231.33 0.18 216.00 3.64 216.00 5.94 231.33 1.23 p1-4-g4 240.06 0.06 255.39 1.20 240.06 1.30 240.06 2.73 255.39 3.70 p1-5-g1 196.50 0.06 196.50 0.06 196.50 0.34 196.50 0.29 196.50 0.25 p1-5-g2 144.19 0.06 144.19 0.06 144.19 0.07 144.19 0.20 144.19 0.14 p1-5-g3 164.03 0.06 164.03 0.08 164.03 0.07 164.03 0.18 164.03 0.17 p1-5-g4 241.57 0.06 271.29 0.11 241.57 0.17 237.33 9.07 237.33 2.49 p1-5-g5 325.83 0.06 325.83 0.07 325.83 0.43 325.83 13.49 325.83 3.19 p1-6-g1 151.84 0.08 151.84 0.12 151.84 0.17 151.84 1.70 151.84 1.87 p1-6-g2 276.66 0.16 276.66 0.13 276.66 0.23 276.66 2.98 276.66 1.95 p1-6-g3 401.92 0.07 401.92 0.50 401.92 0.26 370.01 62.43 401.92 69.16 p1-8-g1 336.61 0.07 317.93 0.67 317.93 2.77 - - - -p1-8-g2 393.31 0.16 416.58 0.51 371.25 19.31 358.62 126.39 - -p1-8-g3 151.40 0.07 161.88 7.06 151.40 23.32 151.40 66.40 161.88 18.63 p1-9-g1 323.03 1.26 428.46 60.80 - - - -p1-9-g2 789.90 22.68 987.46 60.92 - - - -p1-9-g3 164.99 0.09 156.58 60.21 182.47 63.95 - - - -p1-9-g4 182.19 0.08 144.52 60.39 175.07 66.64 - - - -p1-9-g5 251.24 0.34 283.02 60.50 274.15 94.53 - - - -p1-5-g1 196.50 0.11 196.50 0.12 196.50 0.13 196.50 0.37 196.50 0.25 p1-5-g2 144.19 0.08 144.19 0.09 144.19 0.10 144.19 0.20 144.19 0.16 p1-6-g3 422.12 0.10 422.12 0.20 422.12 0.59 370.01 30.87 370.01 35.12 p1-8-g1 336.61 0.10 317.93 0.89 317.93 4.17 - - 317.93 41.22
Method 54 56 57 58 59 Problem Obj Time Obj Time Obj Time Obj Time Obj Time p1-3-g1a 83.98 0.06 83.98 0.06 83.98 0.06 83.98 0.06 83.98 0.06 p1-3-g1b 118.25 0.06 118.25 0.06 118.25 0.08 118.25 0.08 118.25 0.08 p1-3-g1c 62.10 0.06 62.10 0.06 62.10 0.05 62.10 0.06 62.10 0.06 p1-3-g1d 124.98 0.06 124.98 0.07 124.98 0.06 124.98 0.08 124.98 0.08 p1-3-g1e 48.58 0.06 48.58 0.06 48.58 0.06 48.58 0.06 48.58 0.06 p1-3-g1f 124.60 0.06 148.06 0.06 124.60 0.06 124.60 0.08 148.06 0.07 p1-3-g1g 221.44 0.06 221.44 0.07 221.44 0.08 221.44 3.38 221.44 0.90 p1-3-g1 138.15 0.06 138.15 0.06 138.15 0.06 138.15 0.08 138.15 0.09 p1-3-g2 214.86 0.07 191.39 0.08 214.86 0.10 191.39 0.33 191.39 0.42 p1-3-g3 131.50 0.26 131.50 0.07 131.50 0.07 131.50 0.08 131.50 0.09 p1-3-g4 111.87 0.06 111.87 0.06 111.87 0.07 111.87 0.07 111.87 0.06 p1-4-g1 172.91 0.07 172.91 0.07 172.91 0.08 172.91 0.15 172.91 0.13 p1-4-g2 198.78 0.07 214.11 0.08 198.78 0.11 198.78 0.30 214.11 0.28 p1-4-g3 216.00 0.07 231.33 0.08 216.00 0.12 216.00 0.20 231.33 0.34 p1-4-g4 240.06 0.07 255.39 0.21 240.06 0.16 240.06 0.68 255.39 0.56 p1-5-g1 196.50 0.07 196.50 0.06 196.50 0.07 196.50 0.11 196.50 0.14 p1-5-g2 144.19 0.07 144.19 0.07 144.19 0.07 144.19 0.08 144.19 0.09 p1-5-g3 164.03 0.06 164.03 0.06 164.03 0.07 164.03 0.08 164.03 0.08 p1-5-g4 241.57 0.06 271.29 0.09 241.57 0.13 237.33 2.56 237.33 1.06 p1-5-g5 325.83 0.07 325.83 0.08 355.56 0.15 325.83 1.98 325.83 0.60 p1-6-g1 151.84 0.07 151.84 0.08 151.84 0.08 151.84 0.17 151.84 0.13 p1-6-g2 276.66 0.07 276.66 0.08 276.66 0.09 276.66 0.22 276.66 0.18 p1-6-g3 401.92 0.08 401.92 0.12 401.92 0.18 370.01 12.51 370.01 4.34 p1-8-g1 336.61 0.09 317.93 0.16 317.93 0.52 317.93 4.68 317.93 2.88 p1-8-g2 393.31 0.17 416.58 0.15 371.25 3.18 358.62 27.23 - -p1-8-g3 151.40 0.06 161.88 0.08 151.40 0.24 151.40 0.44 161.88 0.41 p1-9-g1 323.03 1.26 369.46 60.24 366.95 61.63 - - - -p1-9-g2 789.90 22.73 971.17 60.62 - - - -p1-9-g3 164.99 0.10 164.99 3.03 156.58 60.18 147.82 60.82 156.63 28.53 p1-9-g4 182.19 0.10 137.07 3.60 182.19 18.08 124.09 61.53 168.84 39.72 p1-9-g5 251.24 0.34 258.84 60.18 332.95 60.98 183.41 83.56 229.22 66.98 p1-5-g1 267.30 0.20 267.30 0.16 267.30 0.17 267.30 0.27 267.30 0.26 p1-5-g2 167.79 0.10 167.79 0.15 167.79 0.14 167.79 0.15 167.79 0.15 p1-6-g3 646.52 0.13 646.52 0.60 646.52 0.42 617.11 33.29 606.81 21.64 p1-8-g1 337.61 0.16 318.93 0.70 318.93 0.37 317.93 12.45 317.93 3.31 Table 9: Problem set 1, methods 54, 56, 57, 58 and 59, without split above the line and with split below.
0 1 2 3 Problem Method Obj Time Obj Time Obj Time Obj Time p1-3-g1f 301 148.06 0.04 124.60 0.06 124.60 0.05 124.60 0.04 p1-3-g1f 302 124.60 0.06 124.60 0.06 124.60 0.06 p1-3-g1f 303 124.60 0.06 124.60 0.06 148.06 0.04 p1-3-g1f 304 124.60 0.06 124.60 0.05 148.06 0.04 p1-3-g1f 305 124.60 0.04 124.60 0.05 124.60 0.04 p1-3-g1f 306 124.60 0.05 124.60 0.06 124.60 0.06 p1-3-g1f 307 124.60 0.05 124.60 0.04 142.85 0.04 p1-3-g1f 308 124.60 0.06 124.60 0.06 148.06 0.04 p1-3-g1f 311 148.06 0.03 124.60 0.04 124.60 0.07 124.60 0.59 p1-3-g1f 312 124.60 0.05 124.60 0.08 124.60 0.05 p1-3-g1f 313 124.60 0.05 124.60 0.07 148.06 0.04 p1-3-g1f 314 124.60 0.04 124.60 0.07 148.06 0.04 p1-3-g1f 315 124.60 0.04 124.60 0.04 124.60 0.04 p1-3-g1f 316 124.60 0.04 124.60 0.07 124.60 0.05 p1-3-g1f 317 124.60 0.04 124.60 0.04 142.85 0.04 p1-3-g1f 318 124.60 0.05 124.60 0.07 148.06 0.04 p1-3-g1f 321 148.06 0.04 124.60 0.05 124.60 0.06 124.60 0.04 p1-3-g1f 322 124.60 0.05 124.60 0.06 124.60 0.04 p1-3-g1f 323 124.60 0.05 124.60 0.06 148.06 0.04 p1-3-g1f 324 124.60 0.05 124.60 0.06 148.06 0.04 p1-3-g1f 325 124.60 0.04 124.60 0.04 124.60 0.03 p1-3-g1f 326 124.60 0.05 124.60 0.06 124.60 0.04 p1-3-g1f 327 124.60 0.04 124.60 0.05 142.85 0.04 p1-3-g1f 328 124.60 0.05 124.60 0.06 148.06 0.04 p1-3-g1f 331 148.06 0.03 124.60 0.04 124.60 0.07 124.60 0.04 p1-3-g1f 332 124.60 0.05 124.60 0.07 124.60 0.05 p1-3-g1f 333 124.60 0.05 124.60 0.06 148.06 0.04 p1-3-g1f 334 124.60 0.05 124.60 0.07 148.06 0.04 p1-3-g1f 335 124.60 0.04 124.60 0.04 124.60 0.04 p1-3-g1f 336 124.60 0.05 124.60 0.07 124.60 0.04 p1-3-g1f 337 124.60 0.04 124.60 0.04 142.85 0.04 p1-3-g1f 338 124.60 0.05 124.60 0.07 148.06 0.03 Table 10: Problem p1-3-g1f, n = 5, m = 5, q = 8, no split, improvement heuristics.
0 1 2 3 Problem Method Obj Time Obj Time Obj Time Obj Time p1-3-g2 301 214.86 0.04 214.86 0.05 214.86 0.05 214.86 0.04 p1-3-g2 302 191.39 0.06 191.39 0.06 191.39 0.06 p1-3-g2 303 214.86 0.05 214.86 0.05 214.86 0.04 p1-3-g2 304 191.39 0.06 191.39 0.06 214.86 0.04 p1-3-g2 305 191.39 0.05 191.39 0.05 191.39 0.05 p1-3-g2 306 191.39 0.06 191.39 0.06 191.39 0.06 p1-3-g2 307 191.39 0.05 191.39 0.05 209.64 0.05 p1-3-g2 308 191.39 0.06 191.39 0.06 214.86 0.04 p1-3-g2 311 214.86 0.04 214.86 0.05 214.86 0.11 214.86 0.04 p1-3-g2 312 191.39 0.06 191.39 0.11 191.39 0.06 p1-3-g2 313 214.86 0.05 214.86 0.11 214.86 0.05 p1-3-g2 314 191.39 0.06 191.39 0.10 214.86 0.04 p1-3-g2 315 191.39 0.05 191.39 0.05 191.39 0.05 p1-3-g2 316 191.39 0.06 191.39 0.11 191.39 0.06 p1-3-g2 317 191.39 0.05 191.39 0.05 209.64 0.04 p1-3-g2 318 191.39 0.06 191.39 0.10 214.86 0.04 p1-3-g2 321 214.86 0.04 214.86 0.06 214.86 0.06 214.86 0.04 p1-3-g2 322 191.39 0.07 191.39 0.08 191.39 0.07 p1-3-g2 323 214.86 0.06 214.86 0.06 214.86 0.05 p1-3-g2 324 191.39 0.07 191.39 0.08 214.86 0.04 p1-3-g2 325 191.39 0.05 191.39 0.06 191.39 0.05 p1-3-g2 326 191.39 0.07 191.39 0.08 191.39 0.06 p1-3-g2 327 191.39 0.05 191.39 0.06 209.64 0.04 p1-3-g2 328 191.39 0.07 191.39 0.08 214.86 0.04 p1-3-g2 331 214.86 0.03 214.86 0.05 214.86 0.09 214.86 0.03 p1-3-g2 332 191.39 0.06 191.39 0.09 191.39 0.05 p1-3-g2 333 214.86 0.05 214.86 0.09 214.86 0.04 p1-3-g2 334 191.39 0.05 191.39 0.09 214.86 0.04 p1-3-g2 335 191.39 0.05 191.39 0.05 191.39 0.04 p1-3-g2 336 191.39 0.06 191.39 0.09 191.39 0.05 p1-3-g2 337 191.39 0.05 191.39 0.05 209.64 0.04 p1-3-g2 338 191.39 0.06 191.39 0.10 214.86 0.04
0 1 2 3 Problem Method Obj Time Obj Time Obj Time Obj Time p1-6-g1 301 175.36 0.04 166.14 0.07 166.14 0.07 166.14 0.05 p1-6-g1 302 151.84 0.10 151.84 0.10 175.36 0.08 p1-6-g1 303 166.14 0.07 166.14 0.07 175.36 0.05 p1-6-g1 304 175.36 0.11 175.36 0.11 175.36 0.05 p1-6-g1 305 175.36 0.05 175.36 0.04 175.36 0.05 p1-6-g1 306 151.84 0.10 151.84 0.10 175.36 0.08 p1-6-g1 307 175.36 0.04 175.36 0.05 175.36 0.04 p1-6-g1 308 175.36 0.13 175.36 0.11 175.36 0.05 p1-6-g1 311 151.84 0.04 151.84 0.07 151.84 0.15 151.84 0.05 p1-6-g1 312 151.84 0.11 151.84 0.15 151.84 0.08 p1-6-g1 313 151.84 0.08 151.84 0.14 151.84 0.06 p1-6-g1 314 151.84 0.12 151.84 0.15 151.84 0.05 p1-6-g1 315 151.84 0.04 151.84 0.04 151.84 0.05 p1-6-g1 316 151.84 0.11 151.84 0.14 151.84 0.08 p1-6-g1 317 151.84 0.05 151.84 0.05 151.84 0.04 p1-6-g1 318 151.84 0.11 151.84 0.15 151.84 0.04 p1-6-g1 321 151.84 0.05 151.84 0.09 151.84 0.15 151.84 0.05 p1-6-g1 322 151.84 0.13 151.84 0.12 151.84 0.10 p1-6-g1 323 151.84 0.12 151.84 0.15 151.84 0.09 p1-6-g1 324 151.84 0.14 151.84 0.15 151.84 0.05 p1-6-g1 325 151.84 0.04 151.84 0.04 151.84 0.04 p1-6-g1 326 151.84 0.14 151.84 0.13 151.84 0.12 p1-6-g1 327 151.84 0.05 151.84 0.04 151.84 0.04 p1-6-g1 328 151.84 0.15 151.84 0.14 151.84 0.15 p1-6-g1 331 151.84 0.04 151.84 0.18 151.84 0.10 151.84 0.05 p1-6-g1 332 151.84 0.09 151.84 0.10 151.84 0.07 p1-6-g1 333 151.84 0.06 151.84 0.10 151.84 0.05 p1-6-g1 334 151.84 0.10 151.84 0.10 151.84 0.05 p1-6-g1 335 151.84 0.04 151.84 0.04 151.84 0.04 p1-6-g1 336 151.84 0.10 151.84 0.11 151.84 0.07 p1-6-g1 337 151.84 0.04 151.84 0.04 151.84 0.04 p1-6-g1 338 151.84 0.09 151.84 0.11 151.84 0.04 Table 12: Problem p1-6-g1, n = 9, m = 11, q = 8, no split, improvement heuristics.
0 1 2 3 Problem Method Obj Time Obj Time Obj Time Obj Time p1-8-g2 301 383.00 0.05 383.00 0.04 383.00 0.05 383.00 0.06 p1-8-g2 302 371.25 0.18 371.25 0.18 383.00 0.10 p1-8-g2 303 383.00 0.04 383.00 0.04 383.00 0.04 p1-8-g2 304 383.00 0.17 383.00 0.17 383.00 0.05 p1-8-g2 305 383.00 0.04 383.00 0.04 383.00 0.04 p1-8-g2 306 371.25 0.17 371.25 0.18 383.00 0.10 p1-8-g2 307 383.00 0.05 383.00 0.05 383.00 0.05 p1-8-g2 308 383.00 0.17 383.00 0.17 383.00 0.05 p1-8-g2 311 371.25 0.08 371.25 0.12 371.25 0.11 371.25 0.08 p1-8-g2 312 371.25 0.35 371.25 0.48 371.25 0.13 p1-8-g2 313 371.25 0.12 371.25 0.12 371.25 0.12 p1-8-g2 314 371.25 0.31 371.25 0.43 371.25 0.10 p1-8-g2 315 371.25 0.08 371.25 0.08 371.25 0.08 p1-8-g2 316 371.25 0.33 371.25 0.50 371.25 0.13 p1-8-g2 317 371.25 0.08 371.25 0.08 371.25 0.10 p1-8-g2 318 371.25 0.32 371.25 0.44 371.25 0.10 p1-8-g2 321 371.25 0.08 371.25 0.23 371.25 0.91 371.25 0.08 p1-8-g2 322 371.25 0.40 371.25 0.52 371.25 0.16 p1-8-g2 323 371.25 0.24 371.25 0.17 371.25 0.22 p1-8-g2 324 371.25 0.38 371.25 0.52 371.25 0.09 p1-8-g2 325 371.25 0.08 371.25 0.08 371.25 0.08 p1-8-g2 326 371.25 0.40 371.25 0.54 371.25 0.17 p1-8-g2 327 371.25 0.08 371.25 0.10 371.25 0.08 p1-8-g2 328 371.25 0.40 371.25 0.52 371.25 0.10 p1-8-g2 331 371.25 0.05 371.25 0.07 371.25 0.07 371.25 0.05 p1-8-g2 332 371.25 0.17 371.25 0.23 371.25 0.09 p1-8-g2 333 371.25 0.07 371.25 0.07 371.25 0.07 p1-8-g2 334 371.25 0.20 371.25 0.22 371.25 0.06 p1-8-g2 335 371.25 0.05 371.25 0.05 371.25 0.05 p1-8-g2 336 371.25 0.16 371.25 0.23 371.25 0.10 p1-8-g2 337 371.25 0.05 371.25 0.05 371.25 0.05 p1-8-g2 338 371.25 0.20 371.25 0.23 371.25 0.06 Table 13: Problem p1-8-g2, n = 9, m = 15, q = 21, no split, improvement heuristics.
0 1 2 3 Problem Method Obj Time Obj Time Obj Time Obj Time p1-8-g3 301 181.81 0.04 151.40 0.10 151.40 0.09 161.88 0.09 p1-8-g3 302 151.40 0.08 151.40 0.08 173.02 0.09 p1-8-g3 303 181.81 0.10 181.81 0.12 181.81 0.05 p1-8-g3 304 181.81 0.10 181.81 0.10 181.81 0.04 p1-8-g3 305 172.27 0.06 172.27 0.05 172.27 0.06 p1-8-g3 306 151.40 0.08 151.40 0.08 173.02 0.10 p1-8-g3 307 172.27 0.05 172.27 0.06 181.81 0.04 p1-8-g3 308 181.81 0.10 181.81 0.10 181.81 0.04 p1-8-g3 311 181.81 0.04 151.40 0.09 151.40 0.12 181.81 0.07 p1-8-g3 312 151.40 0.09 151.40 0.13 181.81 0.06 p1-8-g3 313 181.81 0.09 151.40 0.12 181.81 0.05 p1-8-g3 314 181.81 0.10 181.81 0.12 181.81 0.05 p1-8-g3 315 161.88 0.05 161.88 0.06 161.88 0.05 p1-8-g3 316 151.40 0.10 151.40 0.13 181.81 0.06 p1-8-g3 317 161.88 0.05 161.88 0.06 161.88 0.05 p1-8-g3 318 181.81 0.10 181.81 0.12 181.81 0.05 p1-8-g3 321 181.81 0.04 151.40 0.11 151.40 0.08 181.81 0.12 p1-8-g3 322 151.40 0.10 151.40 0.08 181.81 1.01 p1-8-g3 323 181.81 0.10 181.81 0.14 181.81 0.05 p1-8-g3 324 181.81 0.11 181.81 0.10 181.81 0.04 p1-8-g3 325 161.88 0.05 161.88 0.06 161.88 0.06 p1-8-g3 326 151.40 0.10 151.40 0.08 181.81 0.11 p1-8-g3 327 161.88 0.06 161.88 0.06 161.88 0.05 p1-8-g3 328 181.81 0.11 181.81 0.10 181.81 0.04 p1-8-g3 331 181.81 0.04 151.40 0.07 151.40 0.08 181.81 0.07 p1-8-g3 332 151.40 0.07 151.40 0.09 181.81 0.05 p1-8-g3 333 181.81 0.08 151.40 0.09 181.81 0.05 p1-8-g3 334 181.81 0.08 181.81 0.09 181.81 0.04 p1-8-g3 335 161.88 0.05 161.88 0.05 161.88 0.04 p1-8-g3 336 151.40 0.07 151.40 0.08 181.81 0.06 p1-8-g3 337 161.88 0.04 161.88 0.04 161.88 0.04 p1-8-g3 338 181.81 0.08 181.81 0.09 181.81 0.04 Table 14: Problem p1-8-g3, n = 9, m = 15, q = 4, no split, improvement heuristics.
0 1 2 3 Problem Method Obj Time Obj Time Obj Time Obj Time p1-9-g1 301 293.98 0.05 282.19 0.07 282.19 0.07 293.98 0.08 p1-9-g1 302 258.71 0.23 258.71 0.22 293.98 0.08 p1-9-g1 303 282.19 0.07 282.19 0.07 293.98 0.07 p1-9-g1 304 293.98 0.23 293.98 0.22 293.98 0.07 p1-9-g1 305 282.19 0.07 282.19 0.07 293.98 0.06 p1-9-g1 306 258.71 0.22 258.71 0.23 293.98 0.08 p1-9-g1 307 282.19 0.07 282.19 0.07 293.98 0.07 p1-9-g1 308 293.98 0.21 293.98 0.21 293.98 0.07 p1-9-g1 311 278.74 0.09 278.74 0.25 278.74 0.56 278.74 0.15 p1-9-g1 312 278.74 0.45 278.74 0.56 278.74 0.15 p1-9-g1 313 278.74 0.29 278.74 0.50 278.74 0.15 p1-9-g1 314 278.74 0.36 278.74 0.42 278.74 0.13 p1-9-g1 315 278.74 0.30 278.74 0.53 278.74 0.12 p1-9-g1 316 278.74 0.44 278.74 0.55 278.74 0.25 p1-9-g1 317 278.74 0.20 278.74 0.50 278.74 0.12 p1-9-g1 318 278.74 0.36 278.74 0.44 278.74 0.13 p1-9-g1 321 293.98 0.10 293.98 0.47 281.45 0.59 293.98 0.28 p1-9-g1 322 293.98 0.33 283.30 0.66 293.98 0.15 p1-9-g1 323 287.49 0.48 272.12 0.41 293.98 0.30 p1-9-g1 324 293.98 0.46 293.98 0.61 293.98 0.15 p1-9-g1 325 293.98 0.31 281.45 0.19 293.98 0.22 p1-9-g1 326 293.98 0.33 283.30 0.62 293.98 0.15 p1-9-g1 327 293.98 0.25 281.45 0.19 293.98 0.21 p1-9-g1 328 293.98 0.47 293.98 0.65 293.98 0.15 p1-9-g1 331 279.49 0.06 279.49 0.25 279.49 0.26 279.49 0.11 p1-9-g1 332 279.49 0.26 279.49 0.27 279.49 0.11 p1-9-g1 333 279.49 0.22 279.49 0.25 279.49 0.11 p1-9-g1 334 279.49 0.25 279.49 0.26 279.49 0.08 p1-9-g1 335 279.49 0.16 279.49 0.28 279.49 0.12 p1-9-g1 336 279.49 0.25 279.49 0.28 279.49 0.12 p1-9-g1 337 279.49 0.19 279.49 0.27 279.49 0.11 p1-9-g1 338 279.49 0.24 279.49 0.26 279.49 0.08 Table 15: Problem p1-9-g1, n = 18, m = 26, q = 23, no split, improvement heuristics.
0 1 2 3 Problem Method Obj Time Obj Time Obj Time Obj Time p1-9-g4 301 210.08 0.07 209.08 0.13 209.08 0.13 210.08 0.10 p1-9-g4 302 209.08 0.14 209.08 0.14 210.08 0.08 p1-9-g4 303 130.33 0.07 130.33 0.06 210.08 0.09 p1-9-g4 304 201.88 1.15 201.88 0.14 210.08 0.07 p1-9-g4 305 174.08 0.12 174.08 0.11 188.54 0.08 p1-9-g4 306 209.08 0.14 209.08 0.14 210.08 0.08 p1-9-g4 307 130.33 0.07 130.33 0.07 210.08 0.06 p1-9-g4 308 201.88 0.13 201.88 0.14 210.08 0.07 p1-9-g4 311 123.44 0.05 123.44 0.05 123.44 0.05 123.44 0.05 p1-9-g4 312 123.44 0.13 123.44 0.17 123.44 0.07 p1-9-g4 313 123.44 0.05 123.44 0.05 123.44 0.05 p1-9-g4 314 123.44 0.14 123.44 0.16 123.44 0.07 p1-9-g4 315 123.44 0.04 123.44 0.05 123.44 0.05 p1-9-g4 316 123.44 0.13 123.44 0.17 123.44 0.07 p1-9-g4 317 123.44 0.05 123.44 0.05 123.44 0.05 p1-9-g4 318 123.44 0.14 123.44 0.16 123.44 0.08 p1-9-g4 321 210.08 0.05 193.97 0.19 210.08 0.12 174.08 0.15 p1-9-g4 322 176.84 0.20 202.74 0.16 194.98 0.11 p1-9-g4 323 130.33 0.07 130.33 0.08 174.08 0.11 p1-9-g4 324 187.55 0.20 181.53 0.22 194.98 0.12 p1-9-g4 325 174.08 0.12 186.55 0.12 174.08 0.08 p1-9-g4 326 176.84 0.19 202.74 0.16 194.98 0.11 p1-9-g4 327 130.33 0.07 130.33 0.07 174.08 0.08 p1-9-g4 328 187.55 0.20 181.53 0.22 194.98 0.11 p1-9-g4 331 123.44 0.04 123.44 0.04 123.44 0.04 123.44 0.04 p1-9-g4 332 123.44 0.11 123.44 0.13 123.44 0.07 p1-9-g4 333 123.44 0.04 123.44 0.04 123.44 0.04 p1-9-g4 334 123.44 0.11 123.44 0.12 123.44 0.07 p1-9-g4 335 123.44 0.04 123.44 0.04 123.44 0.04 p1-9-g4 336 123.44 0.12 123.44 0.13 123.44 0.07 p1-9-g4 337 123.44 0.04 123.44 0.04 123.44 0.04 p1-9-g4 338 123.44 0.12 123.44 0.12 123.44 0.07 Table 16: Problem p1-9-g4, n = 18, m = 26, q = 7, no split, improvement heuristics.
0 1 2 3 Problem Method Obj Time Obj Time Obj Time Obj Time p1-9-g5 301 311.39 0.04 184.52 0.20 184.52 0.14 194.47 0.10 p1-9-g5 302 234.64 0.16 234.64 0.16 311.39 0.06 p1-9-g5 303 211.38 0.22 211.38 0.16 194.47 0.10 p1-9-g5 304 293.36 0.15 293.36 0.15 311.39 0.06 p1-9-g5 305 186.12 0.11 186.12 0.11 213.47 0.06 p1-9-g5 306 234.64 0.17 234.64 0.16 311.39 0.06 p1-9-g5 307 211.38 0.12 211.38 0.12 213.47 1.11 p1-9-g5 308 293.36 0.15 293.36 0.16 311.39 0.06 p1-9-g5 311 206.59 0.06 206.59 0.18 206.59 0.23 206.59 0.09 p1-9-g5 312 206.59 0.22 206.59 0.25 206.59 0.10 p1-9-g5 313 206.59 0.10 206.59 0.24 206.59 0.09 p1-9-g5 314 206.59 0.20 206.59 0.21 206.59 0.09 p1-9-g5 315 206.59 0.15 206.59 0.23 206.59 0.12 p1-9-g5 316 206.59 0.22 206.59 0.25 206.59 0.10 p1-9-g5 317 206.59 0.15 206.59 0.21 206.59 0.11 p1-9-g5 318 206.59 0.19 206.59 0.21 206.59 0.09 p1-9-g5 321 206.59 0.06 206.59 0.25 206.59 0.30 206.59 0.13 p1-9-g5 322 206.59 0.27 206.59 0.30 206.59 0.10 p1-9-g5 323 206.59 0.26 206.59 0.30 206.59 0.13 p1-9-g5 324 206.59 0.27 206.59 0.29 206.59 0.13 p1-9-g5 325 206.59 0.26 206.59 0.20 206.59 0.16 p1-9-g5 326 206.59 0.27 206.59 0.31 206.59 0.11 p1-9-g5 327 206.59 0.20 206.59 0.12 206.59 0.15 p1-9-g5 328 206.59 0.27 206.59 0.32 206.59 0.13 p1-9-g5 331 185.11 0.04 185.11 0.10 185.11 0.07 185.11 0.13 p1-9-g5 332 185.11 0.12 185.11 0.15 185.11 0.08 p1-9-g5 333 185.11 0.08 185.11 0.14 185.11 0.06 p1-9-g5 334 185.11 0.14 185.11 0.14 185.11 0.07 p1-9-g5 335 185.11 0.10 185.11 0.14 185.11 0.09 p1-9-g5 336 185.11 0.11 185.11 0.15 185.11 0.07 p1-9-g5 337 185.11 0.11 185.11 0.14 185.11 0.09 p1-9-g5 338 185.11 0.14 185.11 0.14 185.11 0.07 Table 17: Problem p1-9-g5, n = 18, m = 26, q = 10, no split, improvement heuristics.
Method 30 31 32 33 Problem Obj Time Obj Time Obj Time Obj Time p1-3-g1a 83.98 0.04 83.98 0.03 83.98 0.04 83.98 0.03 p1-3-g1b 1120.46 0.21 1120.46 0.04 1120.46 0.04 1120.46 0.03 p1-3-g1c 62.10 0.04 62.10 0.03 62.10 0.03 62.10 0.04 p1-3-g1d 1620.25 0.04 1589.15 0.04 1603.45 0.05 1603.45 0.03 p1-3-g1e 48.58 0.04 48.58 0.03 48.58 0.03 48.58 0.03 p1-3-g1f 112.16 0.03 112.16 0.04 112.16 0.04 112.16 0.03 p1-3-g1g 221.44 0.04 221.44 0.04 221.44 0.04 221.44 0.04 p1-3-g1 138.15 0.04 138.15 0.04 138.15 0.04 138.15 0.04 p1-3-g2 214.86 0.04 214.86 0.04 214.86 0.04 214.86 0.04 p1-3-g3 131.50 0.03 131.50 0.04 131.50 0.04 131.50 0.05 p1-3-g4 111.87 0.03 111.87 0.03 111.87 0.03 111.87 0.03 p1-4-g1 172.91 0.04 172.91 0.05 172.91 0.05 172.91 0.04 p1-4-g2 198.78 0.04 198.78 0.05 198.78 0.05 198.78 0.04 p1-4-g3 216.00 0.04 216.00 0.05 216.00 0.06 216.00 0.04 p1-4-g4 240.06 0.04 240.06 0.05 240.06 0.05 240.06 0.04 p1-5-g1 196.50 0.03 196.50 0.05 196.50 0.05 196.50 0.04 p1-5-g2 144.19 0.04 144.19 0.04 144.19 0.04 144.19 0.03 p1-5-g3 164.03 0.04 164.03 0.04 164.03 0.04 164.03 0.04 p1-5-g4 241.57 0.04 241.57 0.04 241.57 0.04 241.57 0.03 p1-5-g5 325.83 0.04 325.83 0.04 325.83 0.04 325.83 0.04 p1-6-g1 175.36 0.03 151.84 0.06 151.84 0.06 151.84 0.05 p1-6-g2 276.66 0.04 276.66 0.06 276.66 0.06 276.66 0.05 p1-6-g3 417.22 0.04 401.92 0.11 401.92 0.12 401.92 0.06 p1-8-g1 366.41 0.05 347.99 0.15 366.41 0.17 348.90 0.06 p1-8-g2 383.00 0.05 371.25 0.33 371.25 0.17 371.25 0.06 p1-8-g3 181.81 0.04 181.81 0.05 181.81 0.06 181.81 0.04 p1-9-g1 293.98 0.06 278.74 0.42 293.98 0.43 279.49 0.09 p1-9-g2 572.32 0.08 572.39 0.88 591.72 0.91 552.42 0.14 p1-9-g3 119.02 0.04 119.02 0.14 119.02 0.15 119.02 0.06 p1-9-g4 210.08 0.06 123.44 0.14 210.08 0.15 123.44 0.06 p1-9-g5 311.39 0.05 206.59 0.20 206.59 0.25 185.11 0.07
Method 30 31 32 33 34 Problem Obj Time Obj Time Obj Time Obj Time Obj Time p2-1-g11 161.55 0.09 161.55 0.04 161.55 0.04 161.55 0.04 161.55 0.07 p2-1-g12 370.75 0.04 370.75 0.05 370.75 0.05 370.75 0.05 370.75 0.07 p2-1-g13 634.62 0.05 614.42 0.06 614.42 0.06 614.42 0.05 634.62 0.07 p2-1-g14 869.31 0.05 828.91 0.07 828.91 0.08 828.91 0.06 869.31 0.08 p2-2-g21 192.12 0.04 192.12 0.04 192.12 0.04 192.12 0.04 192.12 0.06 p2-2-g22 375.47 0.04 375.47 0.05 375.47 0.05 375.47 0.05 375.47 0.06 p2-2-g23 302.89 0.03 302.89 0.05 302.89 0.05 302.89 0.04 264.61 0.06 p2-2-g24 228.41 0.03 228.41 0.03 228.41 0.04 228.41 0.04 177.17 0.06 p2-2-g25 236.47 0.04 236.47 0.04 236.47 0.03 236.47 0.03 199.88 0.06 p2-2-g26 173.20 0.03 173.20 0.04 173.20 0.04 173.20 0.03 173.20 0.06 p2-3-g31 411.56 0.04 414.99 0.05 411.56 0.06 411.56 0.04 411.56 0.08 p2-3-g32 880.67 0.04 880.67 0.06 880.67 0.06 880.67 0.05 808.90 0.10 p2-3-g33 1150.81 0.05 1123.38 0.08 1121.21 0.09 1121.21 0.05 1150.81 0.15 p2-3-g34 263.97 0.04 263.97 0.04 263.97 0.04 264.29 0.04 263.97 0.07 p2-4-g41 375.46 0.04 349.67 0.05 349.64 0.06 349.99 0.04 314.38 0.08 p2-4-g42 726.27 0.05 728.79 0.10 726.27 0.11 728.29 0.06 726.27 0.20 p2-4-g43 297.45 0.04 297.45 0.04 297.45 0.04 297.45 0.04 297.45 0.08 p2-4-g44 894.24 0.05 894.24 0.08 894.24 0.10 894.24 0.06 894.24 0.19 p2-4-g45 131.55 0.04 113.93 0.04 113.93 0.04 115.70 0.04 113.93 0.06 p2-4-g46 608.85 0.04 609.19 0.05 608.85 0.06 608.85 0.04 911.46 0.12 p2-5-g41 419.82 0.04 349.67 0.06 349.64 0.07 349.99 0.05 314.38 0.06 p2-5-g42 830.08 0.05 739.96 0.12 739.93 0.13 741.95 0.06 739.93 0.23 p2-5-g43 248.52 0.04 248.52 0.04 248.52 0.04 248.52 0.04 231.13 0.07 p2-5-g44 953.86 0.04 894.24 0.11 894.24 0.12 894.24 0.06 894.24 0.45 p2-5-g45 131.55 0.04 113.93 0.04 113.93 0.04 115.70 0.04 113.93 0.06 p2-5-g46 459.96 0.04 459.96 0.06 459.96 0.06 459.96 0.05 513.85 0.21 p2-6-g61 136.36 0.04 136.36 0.05 136.36 0.06 136.36 0.04 131.14 0.07 p2-6-g62 353.72 0.04 338.72 0.10 353.72 0.11 353.72 0.06 301.51 0.08 p2-6-g63 790.43 0.06 790.43 0.18 790.43 0.20 792.45 0.09 790.43 3.06 p2-6-g64 489.26 0.04 489.26 0.06 489.26 0.06 490.64 0.05 465.93 0.08 p2-6-g65 157.24 0.04 157.24 0.07 157.24 0.07 157.24 0.05 157.73 0.07 p2-7-g61 285.19 0.04 285.19 0.05 285.19 0.06 285.19 0.05 256.84 0.07 p2-7-g62 456.03 0.05 456.03 0.10 456.03 0.10 457.01 0.06 432.35 0.09 p2-7-g63 1022.50 0.06 1022.50 0.19 1022.50 0.20 1022.73 0.09 1052.56 1.27 p2-7-g64 467.60 0.04 443.00 0.24 443.00 0.40 444.39 0.05 427.60 0.11 p2-7-g65 157.24 0.04 157.24 0.07 157.24 0.07 157.24 0.05 157.73 0.09
Method 30 31 32 33 34 Problem Obj Time Obj Time Obj Time Obj Time Obj Time p2-8-g81 530.46 0.04 427.86 0.05 530.46 0.06 460.36 0.04 525.64 0.15 p2-8-g82 775.39 0.05 654.19 0.08 775.39 0.09 666.99 0.05 717.44 0.78 p2-8-g83 1729.58 0.08 1655.77 0.21 1718.58 0.23 1710.04 0.11 1734.25 13.57 p2-8-g84 1541.88 0.11 1478.42 0.38 1556.08 0.41 1534.23 0.16 1593.38 60.25 p2-8-g85 105.70 0.03 105.70 0.03 105.70 0.04 105.70 0.04 108.11 0.07 p2-8-g86 340.14 0.04 297.74 0.06 297.74 0.06 297.75 0.05 361.32 0.31 p2-8-g87 68.65 0.05 68.65 0.08 68.65 0.08 68.65 0.05 104.63 0.08 p2-9-g81 481.31 0.04 365.73 0.06 481.31 0.07 365.01 0.04 454.94 0.20 p2-9-g82 840.17 0.05 569.27 0.10 840.17 0.11 572.07 0.06 658.87 0.21 p2-9-g83 1128.46 0.08 1118.53 0.27 1128.46 0.28 1173.62 0.11 983.52 1.28 p2-9-g84 679.53 0.12 679.94 0.52 679.53 0.50 679.84 0.18 805.80 60.26 p2-9-g85 151.01 0.04 136.13 0.04 136.13 0.04 136.13 0.03 108.11 0.08 p2-9-g86 352.58 0.05 293.18 0.08 293.18 0.08 293.18 0.05 435.95 0.21 p2-9-g87 68.65 0.05 68.65 0.09 68.65 0.09 68.65 0.05 104.63 0.08
Method 24 26
Problem n m q Obj Time C Obj Time C U p2-1-g11 5 5 11 161.55 0.87 1 161.55 0.11 1 0 p2-1-g12 5 5 24 347.15 0.06 1 570.97 0.07 1 5 p2-1-g13 5 5 32 552.92 0.13 1 1374.61 0.14 1 24 p2-1-g14 5 5 43 642.91 0.07 1 1734.21 0.15 1 31 p2-2-g21 5 5 12 192.12 0.08 1 192.12 0.09 1 0 p2-2-g22 5 5 27 351.87 0.06 1 495.42 0.08 1 4 p2-2-g23 5 5 18 241.01 0.06 1 445.36 0.07 1 5 p2-2-g24 5 5 9 153.57 0.06 1 177.17 0.07 1 0 p2-2-g25 5 5 8 199.88 0.05 1 309.61 0.06 1 2 p2-2-g26 5 5 4 150.50 0.05 1 142.31 0.06 2 0 p2-3-g31 8 11 16 408.26 0.07 1 1398.48 1.66 1 15 p2-3-g32 8 11 22 715.00 0.10 1 1782.93 1.87 1 18 p2-3-g33 8 11 34 851.41 0.20 1 1905.26 1.72 1 19 p2-3-g34 8 11 8 234.87 0.07 1 411.94 6.76 2 1 p2-4-g41 9 11 16 314.38 0.10 1 1031.81 0.12 1 12 p2-4-g42 9 11 40 623.77 0.17 1 1729.86 0.68 1 25 p2-4-g43 9 11 6 273.45 0.10 1 428.82 17.06 1 1 p2-4-g44 9 11 35 641.64 0.20 1 3261.48 2.42 1 31 p2-4-g45 9 11 7 93.73 0.06 1 113.93 0.14 1 0 p2-4-g46 9 11 12 463.86 0.11 1 1475.15 47.83 1 7 p2-5-g41 9 13 16 314.38 0.07 1 1031.81 0.16 1 12 p2-5-g42 9 13 40 623.13 0.22 1 2405.80 1.64 1 35 p2-5-g43 9 13 6 231.13 0.06 1 1043.15 34.99 1 4 p2-5-g44 9 13 35 641.64 0.42 1 3261.48 7.92 1 31 p2-5-g45 9 13 7 93.73 0.05 1 264.97 0.08 1 2 p2-5-g46 9 13 12 383.65 0.08 1 1593.59 60.13 1 9 p2-6-g61 9 15 13 131.14 0.08 1 131.14 0.18 1 0 p2-6-g62 9 15 31 301.51 0.09 1 301.51 0.90 1 0 p2-6-g63 9 15 63 653.13 3.11 1 2585.42 3.50 1 53 p2-6-g64 9 15 15 447.93 0.08 1 1305.52 2.28 1 12 p2-6-g65 9 15 14 132.43 0.07 1 442.27 0.30 1 10 p2-7-g61 12 18 13 256.84 0.07 1 256.84 0.87 1 0 p2-7-g62 12 18 31 432.35 0.08 1 472.71 1.27 1 1 p2-7-g63 12 18 63 934.36 1.29 1 2736.93 60.40 1 54 p2-7-g64 12 18 15 418.60 0.10 1 1396.48 35.33 1 13 p2-7-g65 12 18 14 129.43 0.07 1 574.61 1.07 1 13 Table 21: Problem set 1, MIP-models 24 and 26, no split.
Method 24 26
Problem n m q Obj Time C Obj Time C U p2-8-g81 15 21 11 396.14 0.17 4 623.63 60.35 1 6 p2-8-g82 15 21 24 471.74 0.76 3 1126.55 60.32 1 22 p2-8-g83 15 21 78 1341.85 13.64 1 1673.27 58.32 1 72 p2-8-g84 15 21 138 1139.38 60.24 1 1734.22 61.42 1 94 p2-8-g85 15 21 4 102.51 0.08 2 93.05 7.78 2 0 p2-8-g86 15 21 15 240.72 0.30 3 423.12 60.63 2 6 p2-8-g87 15 21 12 64.23 0.07 1 64.23 0.24 1 0 p2-9-g81 18 26 11 332.44 0.21 1 603.54 60.69 1 9 p2-9-g82 18 26 24 411.67 0.20 1 989.62 60.57 1 18 p2-9-g83 18 26 78 875.72 1.26 1 1458.94 61.95 1 59 p2-9-g85 18 26 4 102.51 0.07 2 112.03 60.17 2 0 p2-9-g86 18 26 15 223.65 0.18 2 502.52 60.62 1 10 p2-9-g87 18 26 12 64.23 0.08 1 64.23 2.03 1 0 Table 22: Problem set 1, MIP-models 24 and 26. Without split.
Method 24 26
Problem n m q Obj Time C Obj Time C U p2-1-g11 5 5 11 161.55 0.08 1 185.15 0.12 1 0 p2-1-g12 5 5 24 347.15 0.08 1 394.35 0.10 1 0 p2-1-g13 5 5 32 561.65 0.11 1 672.75 0.13 1 1 p2-1-g14 5 5 43 637.01 0.09 1 1808.43 0.13 1 1 p2-4-g41 9 11 16 235.72 0.15 1 314.42 0.16 1 0 p2-4-g42 9 11 40 455.41 0.16 1 1771.62 0.55 1 1 p2-4-g45 9 11 7 73.53 0.07 1 113.93 0.10 1 0 p2-4-g46 9 11 12 411.65 0.08 2 1755.11 8 11.92 1 1 p2-5-g41 9 13 16 235.72 0.14 1 314.42 0.19 1 0 p2-5-g42 9 13 40 455.41 0.17 1 1771.62 3.99 1 1 p2-5-g45 9 13 7 73.53 0.08 1 113.93 0.10 1 0 p2-5-g46 9 13 12 365.01 0.08 1 1629.59 2 15.35 1 1 p2-6-g61 9 15 13 87.34 0.09 1 131.14 0.23 1 0 p2-6-g62 9 15 31 205.86 0.12 1 307.76 0.30 1 0 p2-6-g63 9 15 63 566.75 0.12 1 1543.52 1.65 1 1 p2-7-g61 12 18 13 207.84 0.08 1 256.84 0.73 1 0 p2-7-g62 12 18 31 396.17 0.10 1 1249.09 2.33 1 1 p2-7-g63 12 18 63 843.24 0.16 1 1748.28 5.13 1 1 Table 23: Problem set 1, MIP-models 24 and 26. With split.
Method 27 28 29
Problem Obj Time C U Obj Time C U Obj Time C U p2-1-g11 161.55 0.09 1 0 161.55 0.19 1 0 161.55 0.16 1 0 p2-1-g12 570.97 0.12 1 5 370.75 1.07 1 0 370.75 1.01 1 0 p2-1-g13 1374.61 0.16 1 24 614.42 7.87 1 0 614.42 7.91 1 0 p2-1-g14 1732.67 0.15 1 31 1153.06 61.38 1 5 2195.39 61.08 1 31 p2-2-g21 192.12 0.07 1 0 192.12 0.21 1 0 192.12 0.22 1 0 p2-2-g22 495.42 0.08 1 4 375.47 1.58 1 0 375.47 0.90 1 0 p2-2-g23 445.36 0.09 1 5 264.61 0.98 1 0 264.61 0.30 1 0 p2-2-g24 177.17 0.06 1 0 177.17 0.08 1 0 177.17 0.07 1 0 p2-2-g25 199.88 0.07 1 0 199.88 0.20 1 0 199.88 0.14 1 0 p2-2-g26 156.61 0.07 1 0 156.61 0.14 1 0 142.31 0.07 2 0 p2-3-g31 1398.48 13.78 1 15 408.26 51.77 1 0 408.26 9.90 1 0 p2-3-g32 1098.18 39.32 1 8 - - - - 966.20 66.18 1 0 p2-3-g34 433.04 3.10 1 1 290.47 62.04 1 0 239.57 49.77 2 0 p2-4-g41 314.38 0.39 1 0 314.38 14.29 1 0 314.38 3.45 1 0 p2-4-g42 1747.86 2.85 1 25 - - - -p2-4-g43 273.45 24.82 1 0 273.45 47.95 1 0 271.97 52.44 2 0 p2-4-g45 113.93 0.18 1 0 113.93 1.72 1 0 264.97 6.27 1 2 p2-5-g41 314.38 0.37 1 0 314.38 128.66 1 0 314.38 9.67 1 0 p2-5-g42 2278.33 26.99 1 34 - - - -p2-5-g45 113.93 0.17 1 0 113.93 12.93 1 0 264.97 1.42 1 2 p2-6-g61 131.14 0.71 1 0 131.14 41.29 1 0 131.14 100.59 1 0 p2-6-g62 301.51 0.98 1 0 - - - -p2-6-g65 574.61 1.91 1 13 - - - - 499.66 74.08 1 3 p2-7-g61 256.84 1.88 1 0 256.84 84.31 1 0 - - - -p2-7-g62 432.35 3.77 1 0 - - - -p2-8-g87 116.45 0.95 1 8 - - - -p2-9-g87 116.45 2.63 1 8 - - -
Method 27 28 29
Problem Obj Time C U Obj Time C U Obj Time C U p2-1-g11 185.15 0.09 1 0 185.15 0.19 1 0 185.15 0.15 1 0 p2-1-g12 394.35 0.12 1 0 394.35 1.26 1 0 394.35 0.84 1 0 p2-1-g13 658.22 0.16 1 0 673.95 1.27 1 0 658.22 0.82 1 0 p2-1-g14 1808.43 0.15 1 1 759.25 1.90 1 0 759.25 2.21 1 0 p2-4-g41 314.42 0.28 1 0 314.42 3.55 1 0 314.42 1.84 1 0 p2-4-g42 1771.62 5.18 1 1 708.73 85.98 1 0 904.99 69.81 1 0 p2-4-g45 113.93 0.19 1 0 113.93 0.91 1 0 113.93 0.69 1 0 p2-4-g46 1658.17 63.98 1 1 610.76 122.53 1 0 525.14 48.71 1 0 p2-5-g41 314.42 0.41 1 0 314.42 6.05 1 0 314.42 2.98 1 0 p2-5-g42 1771.62 42.53 1 1 - - - -p2-5-g45 113.93 0.19 1 0 113.93 1.30 1 0 113.93 0.84 1 0 p2-5-g46 1553.53 120.46 1 1 442.34 99.01 1 0 419.44 53.52 1 0 p2-6-g61 131.14 1.04 1 0 131.14 50.04 1 0 131.14 4.82 1 0 p2-6-g62 307.76 1.55 1 0 307.76 49.84 1 0 307.76 51.71 1 0 p2-6-g63 1867.98 19.85 1 1 - - - -p2-7-g61 256.84 1.39 1 0 256.84 42.40 1 0 256.84 14.89 1 0 p2-7-g62 1249.09 5.68 1 1 - - - -p2-7-g63 1566.17 23.53 1 1 - - -
Model Rows Cols Iter Nodes Model Rows Cols Iter Nodes p2-1-g11 p2-1-g12 24 64 73 40 1 24 125 121 64 3 26 268 229 80 3 26 376 278 320 9 27 680 289 168 1 27 788 338 880 17 28 1965 937 1164 1 28 3537 1718 4994 19 29 1553 877 1138 1 29 3125 1658 5324 33 p2-1-g13 p2-1-g14 24 168 156 67 1 24 227 204 154 13 26 449 312 257 11 26 538 360 602 27 27 861 372 776 37 27 950 420 787 11 28 4642 2268 25436 157 28 6147 3024 - -29 4230 2208 25610 163 29 5735 2964 - -p2-2-g21 p2-2-g22 24 74 82 37 9 24 151 144 88 13 26 289 237 253 19 26 420 299 388 21 27 701 297 240 1 27 832 359 347 1 28 2226 1065 1504 1 28 4205 2051 6139 25 29 1814 1005 1525 3 29 3793 1991 3966 7 p2-2-g23 p2-2-g24 24 100 102 103 9 24 45 47 18 1 26 340 257 243 5 26 140 111 36 1 27 752 317 568 11 27 312 143 97 1 28 2901 1397 4989 37 28 881 431 335 3 29 2489 1337 1932 3 29 709 399 214 1 p2-2-g25 p2-2-g26 24 52 64 28 1 24 30 46 40 7 26 252 219 231 3 26 214 202 46 1 27 664 279 259 1 27 626 262 461 9 28 1661 783 1244 1 28 1095 502 1161 7 29 1249 723 1071 3 29 683 442 354 1 p2-3-g31 p2-3-g32 24 115 146 90 15 24 158 183 843 129 26 884 818 22216 237 26 963 854 22506 205 27 2640 1010 79649 335 27 2719 1046 201628 1581 28 7513 3458 106420 299 28 9656 4526 - -29 5757 3266 24637 55 29 7900 4334 - -p2-3-g33 p2-3-g34 24 235 248 957 303 24 64 99 615 375 26 1102 926 15354 225 26 696 672 17467 227 27 2858 1118 - - 27 2174 848 16797 313 28 13491 6446 - - 28 4397 1970 - -29 11735 6254 - - 29 2919 1794 227465 1025
Model Rows Cols Iter Nodes Model Rows Cols Iter Nodes p2-4-g41 p2-4-g42 24 141 173 73 3 24 330 338 1365 295 26 941 871 659 1 26 1256 1041 5347 53 27 2721 1087 2019 9 27 3036 1257 12404 59 28 8794 4135 29202 1 28 18181 8841 - -29 7014 3919 9843 1 29 16401 8625 - -p2-4-g43 p2-4-g44 24 56 98 633 173 24 290 303 2419 401 26 812 797 166635 6395 26 1207 1010 19685 249 27 2592 1013 117606 2537 27 2987 1226 - -28 4585 2021 134844 1039 28 16212 7850 - -29 2805 1805 180614 2287 29 14432 7634 - -p2-4-g45 p2-4-g46 24 71 103 46 1 24 103 139 2167 411 26 610 580 213 5 26 892 842 574373 5559 27 1834 740 733 3 27 2672 1058 - -28 4135 1900 11877 51 28 6921 3194 - -29 2911 1740 2935 3 29 5141 2978 - -p2-5-g41 p2-5-g42 24 159 199 75 3 24 385 401 2174 303 26 1207 1127 965 1 26 1582 1335 10148 163 27 3619 1379 1847 1 27 3994 1587 - -28 11712 5439 - - 28 24743 11975 - -29 9300 5187 20175 7 29 22331 11723 - -p2-5-g43 p2-5-g44 24 63 113 140 47 24 340 361 7597 911 26 1061 1042 344349 3981 26 1530 1298 53294 403 27 3473 1294 - - 27 3942 1550 - -28 6190 2666 - - 28 22171 10678 - -29 3778 2414 - - 29 19759 10426 - -p2-5-g45 p2-5-g46 24 71 103 46 1 24 119 163 665 53 26 610 580 213 5 26 1157 1096 - -27 1834 740 733 3 27 3569 1348 - -28 4135 1900 11877 51 28 9422 4288 - -29 2911 1740 2935 3 29 7010 4036 -
Model Rows Cols Iter Nodes Model Rows Cols Iter Nodes p2-6-g61 p2-6-g62 24 121 172 103 1 24 291 324 151 21 26 1432 1360 1110 1 26 1726 1512 5718 21 27 4572 1648 2657 1 27 4866 1800 3578 11 28 11389 5072 54995 1 28 22563 10664 - -29 8249 4784 - - 29 19423 10376 - -p2-6-g63 p2-6-g64 24 624 625 19357 4749 24 148 197 199 61 26 2309 1818 17556 39 26 1481 1393 18406 97 27 5449 2106 - - 27 4621 1681 - -28 44458 21626 - - 28 13166 5969 - -29 41318 21338 - - 29 10026 5681 - -p2-6-g65 24 125 159 128 31 26 926 850 2326 13 27 2706 1066 6356 63 28 8011 3730 - -29 6231 3514 - -p2-7-g61 p2-7-g62 24 122 188 85 1 24 305 353 180 39 26 1999 1941 6013 9 26 2318 2106 6549 25 27 6525 2397 5934 1 27 6844 2562 9776 11 28 14468 6387 - - 28 28695 13506 - -29 9942 5931 - - 29 24169 13050 - -p2-7-g63 p2-7-g64 24 665 681 6462 1737 24 157 221 981 159 26 2945 2443 - - 26 2067 1986 231835 1059 27 7471 2899 - - 27 6593 2442 - -28 56682 27523 - - 28 17196 7762 - -29 52156 27067 - - 29 12670 7306 - -p2-7-g65 24 123 158 113 27 26 940 872 7559 75 27 2744 1112 - -28 7905 3704 - -29 6101 3464 -
Model Rows Cols Iter Nodes Model Rows Cols Iter Nodes p2-8-g81 p2-8-g82 24 99 182 4242 423 24 219 289 11924 2405 26 2637 2621 - - 26 2845 2754 - -27 8801 3281 - - 27 9009 3414 - -28 15710 6757 - - 28 26478 12170 - -29 9546 6097 - - 29 20314 11510 - -p2-8-g83 p2-8-g84 24 718 734 94895 17367 24 1325 1281 - -26 3695 3156 172149 457 26 4730 3700 - -27 9859 3816 - - 27 10894 4360 - -28 71240 34528 - - 28 125691 61780 - -29 65076 33868 - - 29 119527 61120 - -p2-8-g85 p2-8-g86 24 54 144 190 51 24 158 237 5104 1215 26 2556 2562 28022 727 26 2735 2677 - -27 8720 3222 - - 27 8899 3337 - -28 11669 4718 - - 28 21000 9409 - -29 5505 4058 - - 29 14836 8749 - -p2-8-g87 p2-9-g81 24 174 256 128 13 24 119 225 3989 571 26 2765 2666 998 1 26 3938 3920 - -27 8929 3326 2900 1 27 13284 4892 - -28 22438 10102 - - 28 23599 10076 - -29 16274 9442 - - 29 14253 9104 - -p2-9-g82 p2-9-g83 24 266 359 2485 335 24 860 899 6307 1289 26 4194 4082 - - 26 5210 4573 - -27 13540 5054 - - 27 14556 5545 - -28 39731 18176 - - 28 104899 50743 - -29 30385 17204 - - 29 95553 49771 - -p2-9-g84 p2-9-g85 24 1609 1588 - - 24 65 178 313 79 26 6500 5258 - - 26 3837 3846 - -27 15846 6230 - - 27 13183 4818 - -28 187081 91874 - - 28 17666 7086 - -29 177735 90902 - - 29 8320 6114 - -p2-9-g86 p2-9-g87 24 188 290 2513 451 24 200 305 131 13 26 4053 3985 - - 26 4064 3964 7438 27 27 13399 4957 - - 27 13410 4936 5560 1 28 31166 13867 - - 28 32473 14494 - -29 21820 12895 - - 29 23127 13522 -
Method 34 36 37 38 39 Problem Obj Time Obj Time Obj Time Obj Time Obj Time p2-1-g11 161.55 0.15 161.55 0.07 161.55 0.07 161.55 0.17 161.55 0.16 p2-1-g12 370.75 0.07 370.75 0.08 370.75 0.13 370.75 1.09 370.75 1.02 p2-1-g13 634.62 0.07 634.62 0.09 634.62 0.15 614.42 7.90 614.42 7.94 p2-1-g14 869.31 0.08 828.91 0.12 869.31 0.14 1162.99 61.42 1388.43 61.11 p2-2-g21 192.12 0.06 192.12 0.07 192.12 0.07 192.12 0.23 192.12 0.22 p2-2-g22 375.47 0.07 375.47 0.09 375.47 0.09 375.47 1.57 375.47 0.91 p2-2-g23 264.61 0.06 264.61 0.07 264.61 0.14 264.61 0.99 264.61 0.32 p2-2-g24 177.17 0.06 177.17 0.06 177.17 0.06 177.17 0.09 177.17 0.08 p2-2-g25 199.88 0.06 199.88 0.08 199.88 0.08 199.88 0.17 199.88 0.15 p2-2-g26 173.20 0.06 156.61 0.06 156.61 0.08 156.61 0.14 156.61 0.08 p2-3-g31 411.56 0.07 411.56 1.67 411.56 12.96 411.56 51.19 411.56 9.78 p2-3-g32 808.90 0.10 913.92 1.87 845.79 39.21 - - 808.90 66.23 p2-3-g33 1150.81 0.16 1150.81 1.72 1150.81 60.31 - - - -p2-3-g34 263.97 0.07 263.97 6.72 263.97 3.19 263.97 62.17 263.97 49.78 p2-4-g41 314.38 0.07 314.38 0.12 314.38 0.37 314.38 14.31 314.38 3.36 p2-4-g42 726.27 0.18 726.27 0.69 726.27 2.82 - - - -p2-4-g43 297.45 0.10 292.55 17.07 273.45 24.77 273.45 47.63 311.47 52.04 p2-4-g44 894.24 0.20 897.92 2.35 988.64 60.28 - - - -p2-4-g45 113.93 0.06 113.93 0.15 113.93 0.19 113.93 1.71 113.93 6.23 p2-4-g46 911.46 0.12 601.50 47.56 618.69 60.28 - - - -p2-5-g41 314.38 0.07 314.38 0.16 314.38 0.37 314.38 128.29 314.38 9.70 p2-5-g42 739.93 0.22 739.93 1.66 739.93 26.92 - - - -p2-5-g43 231.13 0.07 248.52 34.70 231.13 60.29 248.52 64.49 248.52 61.22 p2-5-g44 894.24 0.45 897.92 7.62 969.98 60.61 - - - -p2-5-g45 113.93 0.07 113.93 0.09 113.93 0.18 113.93 12.94 113.93 1.41 p2-5-g46 513.85 0.08 513.85 60.14 513.85 60.35 444.77 69.02 550.75 63.82 p2-6-g61 131.14 0.07 131.14 0.20 131.14 0.71 131.14 39.91 131.14 100.28 p2-6-g62 301.51 0.09 301.51 0.93 301.51 1.02 - - - -p2-6-g63 790.43 3.08 790.43 3.49 790.43 61.95 - - - -p2-6-g64 465.93 0.08 473.85 2.29 465.93 60.78 473.85 94.51 465.93 85.29 p2-6-g65 157.73 0.07 157.24 0.31 157.24 1.91 - - 419.79 73.19 p2-7-g61 256.84 0.07 256.84 0.87 256.84 1.88 256.84 84.19 432.35 0.15 p2-7-g62 435.86 1.26 432.35 3.74 1052.56 1.27 1091.18 60.37 1026.02 62.88 p2-7-g64 427.60 0.11 427.60 35.33 428.99 61.30 - - - -p2-7-g65 157.73 0.07 157.24 1.09 157.73 61.11 - - -
Method 34 36 37 39 Problem Obj Time Obj Time Obj Time Obj Time p2-8-g81 525.64 0.15 516.14 60.32 460.42 63.71 - -p2-8-g82 717.44 0.81 737.70 60.32 761.61 62.34 - -p2-8-g83 1734.25 13.79 1738.60 58.35 - - - -p2-8-g84 1593.38 60.21 1659.40 61.54 - - - -p2-8-g85 108.11 0.07 103.05 7.90 128.95 61.49 103.05 39.90 p2-8-g86 361.32 0.31 334.02 60.46 344.98 64.86 - -p2-8-g87 104.63 0.08 104.63 0.23 104.63 0.96 - -p2-9-g81 454.94 0.21 377.26 60.50 580.05 67.43 - -p2-9-g82 658.87 0.22 629.88 60.57 691.48 99.62 - -p2-9-g83 983.52 1.29 1097.54 61.95 - - - -p2-9-g84 805.80 60.26 - - - -p2-9-g85 108.11 0.08 148.93 60.28 103.05 64.03 - -p2-9-g86 435.95 0.19 404.61 61.71 - - - -p2-9-g87 104.63 0.08 104.63 2.07 104.63 2.61 -
-Table 31: Problem set 2, methods 34, 36, 37 and 39, without split. Method 38 failed for all.
Method 34 36 37 38 39
Problem Obj Time Obj Time Obj Time Obj Time Obj Time p2-1-g11 219.65 0.08 219.65 0.10 219.65 0.09 219.65 0.19 219.65 0.16 p2-1-g12 485.75 0.09 485.75 0.10 485.75 0.13 485.75 1.30 485.75 0.84 p2-1-g13 1048.75 0.12 1083.82 0.14 1088.72 0.17 1048.75 1.28 1063.62 0.83 p2-1-g14 1167.31 0.10 1167.31 0.12 1167.31 0.16 1103.55 1.95 1103.55 2.21 p2-4-g41 445.02 0.14 445.02 0.18 445.02 0.30 445.02 3.57 445.02 1.85 p2-4-g42 1284.71 0.19 1284.71 0.55 1284.71 5.22 1242.63 85.94 1273.19 70.20 p2-4-g45 134.13 0.08 134.13 0.11 134.13 0.20 134.13 0.92 134.13 0.71 p2-4-g46 866.55 0.10 750.21 11.88 806.04 63.98 658.36 122.49 666.44 48.61 p2-5-g41 445.02 0.14 445.02 0.24 436.22 0.42 436.22 6.06 445.02 3.00 p2-5-g42 1275.91 0.19 1284.71 4.03 1284.71 42.63 1305.36 256.99 1221.90 126.98 p2-5-g45 134.13 0.10 134.13 0.12 134.13 0.20 134.13 1.32 134.13 0.85 p2-5-g46 670.41 0.09 556.05 15.30 687.94 120.46 532.34 99.08 532.34 53.72 p2-6-g61 165.94 0.09 165.94 0.24 165.94 1.06 165.94 50.07 165.94 4.86 p2-6-g62 649.96 0.14 649.96 0.32 649.96 1.54 649.96 49.97 649.96 51.65 p2-6-g63 1378.95 0.15 1378.95 1.68 1378.95 19.97 - - - -p2-7-g61 291.64 0.10 291.64 0.76 291.64 1.41 291.64 42.24 291.64 14.90 p2-7-g62 817.77 0.12 818.07 2.35 817.77 5.70 - - - -p2-7-g63 1554.44 0.20 1554.44 5.13 1554.44 23.51 - - -
0 1 2 3 Problem Method Obj Time Obj Time Obj Time Obj Time p2-2-g24 300 228.41 0.04 205.77 0.06 205.77 0.44 205.77 0.04 p2-2-g24 302 205.77 0.05 205.77 0.06 205.77 0.05 p2-2-g24 303 177.17 0.06 177.17 0.07 177.17 0.05 p2-2-g24 304 177.17 0.06 177.17 0.06 177.17 0.04 p2-2-g24 305 228.41 0.04 228.41 0.03 228.41 0.04 p2-2-g24 306 205.77 0.05 205.77 0.05 205.77 0.04 p2-2-g24 307 228.41 0.04 228.41 0.03 228.41 0.04 p2-2-g24 308 177.17 0.05 177.17 0.06 177.17 0.05 p2-2-g24 310 228.41 0.03 177.17 0.05 177.17 0.10 177.17 0.05 p2-2-g24 312 177.17 0.05 177.17 0.09 177.17 0.04 p2-2-g24 313 177.17 0.05 177.17 0.09 177.17 0.04 p2-2-g24 314 177.17 0.05 177.17 0.09 177.17 0.04 p2-2-g24 315 228.41 0.04 228.41 0.04 228.41 0.03 p2-2-g24 316 177.17 0.05 177.17 0.09 177.17 0.04 p2-2-g24 317 228.41 0.04 228.41 0.04 228.41 0.04 p2-2-g24 318 177.17 0.05 177.17 0.10 177.17 0.04 p2-2-g24 320 228.41 0.04 177.17 0.06 177.17 0.05 177.17 0.05 p2-2-g24 322 177.17 0.06 177.17 0.06 177.17 0.05 p2-2-g24 323 177.17 0.05 177.17 0.06 177.17 0.05 p2-2-g24 324 177.17 0.06 177.17 0.06 177.17 0.05 p2-2-g24 325 177.17 0.05 177.17 0.05 177.17 0.05 p2-2-g24 326 177.17 0.06 177.17 0.06 177.17 0.05 p2-2-g24 327 177.17 0.05 177.17 0.05 177.17 0.05 p2-2-g24 328 177.17 0.06 177.17 0.06 177.17 0.04 p2-2-g24 330 228.41 0.04 177.17 0.05 177.17 0.09 177.17 0.03 p2-2-g24 332 177.17 0.64 177.17 0.09 177.17 0.04 p2-2-g24 333 177.17 0.05 177.17 0.09 177.17 0.04 p2-2-g24 334 177.17 0.05 177.17 0.09 177.17 0.04 p2-2-g24 335 177.17 0.04 177.17 0.04 177.17 0.04 p2-2-g24 336 177.17 0.05 177.17 0.09 177.17 0.04 p2-2-g24 337 177.17 0.04 177.17 0.04 177.17 0.04 p2-2-g24 338 177.17 0.05 177.17 0.09 177.17 0.04 Table 33: Problem p2-2-g24, n = 5, m = 5, q = 9, no split, improvement heuristics.
0 1 2 3 Problem Method Obj Time Obj Time Obj Time Obj Time p2-2-g25 300 236.47 0.04 236.47 0.05 236.47 0.05 236.47 0.04 p2-2-g25 302 199.88 0.08 199.88 0.07 199.88 0.04 p2-2-g25 303 236.47 0.05 236.47 0.05 236.47 0.04 p2-2-g25 304 236.47 0.07 236.47 0.06 236.47 0.04 p2-2-g25 305 199.88 0.04 199.88 0.04 199.88 0.04 p2-2-g25 306 199.88 0.06 199.88 0.06 199.88 0.04 p2-2-g25 307 199.88 0.04 199.88 0.04 199.88 0.04 p2-2-g25 308 236.47 0.06 236.47 0.06 236.47 0.05 p2-2-g25 310 236.47 0.04 236.47 0.05 236.47 0.11 236.47 0.04 p2-2-g25 312 200.04 0.06 200.04 0.11 200.04 0.05 p2-2-g25 313 236.47 0.05 236.47 0.12 236.47 0.05 p2-2-g25 314 236.47 0.06 236.47 0.11 236.47 0.04 p2-2-g25 315 200.04 0.04 200.04 0.05 200.04 0.05 p2-2-g25 316 200.04 0.06 200.04 0.11 200.04 0.05 p2-2-g25 317 200.04 0.05 200.04 0.04 200.04 0.05 p2-2-g25 318 236.47 0.06 236.47 0.10 236.47 0.04 p2-2-g25 320 236.47 0.04 236.47 0.06 236.47 0.06 236.47 0.04 p2-2-g25 322 199.88 0.08 199.88 0.67 199.88 0.05 p2-2-g25 323 236.47 0.05 236.47 0.06 236.47 0.04 p2-2-g25 324 236.47 0.07 236.47 0.08 236.47 0.04 p2-2-g25 325 199.88 0.05 199.88 0.05 199.88 0.05 p2-2-g25 326 199.88 0.07 199.88 0.09 199.88 0.05 p2-2-g25 327 199.88 0.05 199.88 0.05 199.88 0.05 p2-2-g25 328 236.47 0.07 236.47 0.08 236.47 0.04 p2-2-g25 330 236.47 0.04 236.47 0.05 236.47 0.10 236.47 0.04 p2-2-g25 332 199.88 0.06 199.88 0.09 199.88 0.04 p2-2-g25 333 236.47 0.05 236.47 0.09 236.47 0.04 p2-2-g25 334 236.47 0.06 236.47 0.09 236.47 0.04 p2-2-g25 335 199.88 0.04 199.88 0.04 199.88 0.04 p2-2-g25 336 199.88 0.06 199.88 0.10 199.88 0.04 p2-2-g25 337 199.88 0.04 199.88 0.04 199.88 0.04 p2-2-g25 338 236.47 0.06 236.47 0.10 236.47 0.04 Table 34: Problem p2-2-g25, n = 5, m = 5, q = 8, no split, improvement heuristics.
0 1 2 3 Problem Method Obj Time Obj Time Obj Time Obj Time p2-2-g26 300 173.20 0.04 159.07 0.06 159.07 0.05 159.07 0.05 p2-2-g26 302 156.61 0.06 156.61 0.06 173.20 0.05 p2-2-g26 303 173.20 0.07 173.20 0.06 173.20 0.04 p2-2-g26 304 156.61 0.05 156.61 0.06 173.20 0.04 p2-2-g26 305 173.20 0.04 173.20 0.07 173.20 0.04 p2-2-g26 306 156.61 0.06 156.61 0.06 173.20 0.05 p2-2-g26 307 173.20 0.04 173.20 0.04 173.20 0.04 p2-2-g26 308 156.61 0.06 156.61 0.05 173.20 0.04 p2-2-g26 310 173.20 0.03 159.07 0.05 163.39 0.07 159.07 0.05 p2-2-g26 312 156.61 0.05 156.61 0.07 173.20 0.04 p2-2-g26 313 173.20 0.05 163.39 0.07 173.20 0.04 p2-2-g26 314 156.61 0.05 156.61 0.07 173.20 0.04 p2-2-g26 315 173.20 0.04 173.20 0.04 173.20 0.03 p2-2-g26 316 156.61 0.05 156.61 0.07 173.20 0.04 p2-2-g26 317 173.20 0.04 173.20 0.04 173.20 0.04 p2-2-g26 318 156.61 0.05 156.61 0.07 173.20 0.04 p2-2-g26 320 173.20 0.03 159.07 0.05 159.07 0.54 159.07 0.05 p2-2-g26 322 156.61 0.05 156.61 0.05 173.20 0.04 p2-2-g26 323 173.20 0.07 173.20 0.06 173.20 0.04 p2-2-g26 324 156.61 0.05 156.61 0.05 173.20 0.04 p2-2-g26 325 173.20 0.04 173.20 0.04 173.20 0.04 p2-2-g26 326 156.61 0.05 156.61 0.06 173.20 0.04 p2-2-g26 327 173.20 0.04 173.20 0.04 173.20 0.04 p2-2-g26 328 156.61 0.05 156.61 0.06 173.20 0.04 p2-2-g26 330 173.20 0.03 159.07 0.05 163.39 0.07 159.07 0.05 p2-2-g26 332 156.61 0.05 156.61 0.07 173.20 0.04 p2-2-g26 333 173.20 0.05 163.39 0.06 173.20 0.04 p2-2-g26 334 156.61 0.04 156.61 0.07 173.20 0.04 p2-2-g26 335 173.20 0.04 173.20 0.04 173.20 0.05 p2-2-g26 336 156.61 0.04 156.61 0.07 173.20 0.04 p2-2-g26 337 173.20 0.04 173.20 0.04 173.20 0.04 p2-2-g26 338 156.61 0.05 156.61 0.07 173.20 0.04 p2-2-g26 340 173.20 0.0 156.61 0.0 156.61 0.0 156.61 0.0 p2-2-g26 342 173.20 0.0 173.20 0.0 156.61 0.0 p2-2-g26 343 173.20 0.0 173.20 0.0 173.20 0.0 p2-2-g26 344 173.20 0.0 173.20 0.0 173.20 0.0 p2-2-g26 345 173.20 0.0 173.20 0.0 173.20 0.0 p2-2-g26 346 173.20 0.0 173.20 0.0 156.61 0.0 p2-2-g26 347 173.20 0.0 173.20 0.0 173.20 0.0 p2-2-g26 348 173.20 0.0 173.20 0.0 173.20 0.0
0 1 2 3 Problem Method Obj Time Obj Time Obj Time Obj Time p2-3-g32 300 880.67 0.07 880.67 1.33 880.67 0.07 880.67 0.06 p2-3-g32 302 880.67 0.15 880.67 0.16 880.62 0.09 p2-3-g32 303 880.67 0.06 880.67 0.06 880.67 0.05 p2-3-g32 304 868.48 0.15 868.48 0.15 880.00 0.06 p2-3-g32 305 880.00 0.06 880.00 0.06 880.67 0.05 p2-3-g32 306 880.67 0.15 880.67 0.15 880.62 0.09 p2-3-g32 307 868.48 0.07 868.48 0.07 880.00 0.06 p2-3-g32 308 868.48 0.17 868.48 0.15 880.00 0.05 p2-3-g32 310 880.67 0.06 880.67 0.18 880.67 0.28 880.67 0.12 p2-3-g32 312 880.67 0.21 880.67 0.29 880.67 0.10 p2-3-g32 313 880.67 0.17 880.67 0.29 880.67 0.10 p2-3-g32 314 855.04 0.21 880.67 0.30 855.04 0.09 p2-3-g32 315 855.04 0.10 880.67 0.31 880.67 0.08 p2-3-g32 316 880.67 0.24 880.67 0.30 880.67 0.10 p2-3-g32 317 855.04 1.39 880.67 0.31 855.04 0.08 p2-3-g32 318 855.04 0.22 880.67 0.30 855.04 0.08 p2-3-g32 320 880.67 0.06 880.67 0.60 880.67 0.13 880.67 0.09 p2-3-g32 322 833.47 0.75 858.43 2.57 880.67 0.26 p2-3-g32 323 880.67 0.33 880.67 0.13 880.67 0.09 p2-3-g32 324 855.04 0.42 868.48 0.38 855.04 0.09 p2-3-g32 325 855.04 0.11 880.00 0.13 880.67 0.10 p2-3-g32 326 833.47 0.22 858.43 0.30 880.67 0.13 p2-3-g32 327 855.04 0.11 868.48 0.14 855.04 0.09 p2-3-g32 328 855.04 0.28 868.48 1.17 855.04 0.13 p2-3-g32 330 880.67 0.04 880.67 0.16 880.67 0.20 880.67 0.10 p2-3-g32 332 880.67 0.12 880.67 0.09 880.67 0.08 p2-3-g32 333 880.67 0.19 880.67 0.20 880.67 0.07 p2-3-g32 334 856.40 0.18 880.67 0.19 856.40 0.06 p2-3-g32 335 856.40 0.07 880.67 0.20 880.67 0.06 p2-3-g32 336 880.67 0.11 880.67 0.15 880.67 0.08 p2-3-g32 337 856.40 0.07 880.67 0.20 856.40 0.14 p2-3-g32 338 856.40 0.18 880.67 0.19 856.40 0.06 Table 36: Problem p2-3-g32, n = 8, m = 11, q = 22, no split, improvement heuristics.
0 1 2 3 Problem Method Obj Time Obj Time Obj Time Obj Time p2-3-g33 300 1150.81 0.08 1150.81 0.09 1150.81 0.21 1150.81 0.58 p2-3-g33 302 1150.81 0.56 1150.81 0.29 1150.81 0.08 p2-3-g33 303 1150.81 0.09 1150.81 0.38 1150.81 0.08 p2-3-g33 304 1150.81 0.17 1150.81 0.18 1150.81 0.06 p2-3-g33 305 1150.81 0.05 1150.81 0.05 1150.81 0.05 p2-3-g33 306 1150.81 0.17 1150.81 0.16 1150.81 0.08 p2-3-g33 307 1150.81 0.05 1150.81 0.06 1150.81 0.04 p2-3-g33 308 1150.81 0.17 1150.81 0.17 1150.81 0.07 p2-3-g33 310 1123.38 0.08 1123.38 0.22 1123.38 0.39 1123.38 0.21 p2-3-g33 312 1123.38 0.29 1051.30 0.44 1123.38 0.17 p2-3-g33 313 1123.38 0.20 1123.38 0.39 1123.38 0.16 p2-3-g33 314 1123.38 0.29 1123.38 0.43 1123.38 0.10 p2-3-g33 315 1123.38 0.08 1123.38 0.08 1123.38 0.08 p2-3-g33 316 1123.38 0.29 1051.30 0.47 1123.38 0.17 p2-3-g33 317 1123.38 0.07 1123.38 0.08 1123.38 0.07 p2-3-g33 318 1123.38 0.29 1123.38 0.41 1123.38 0.09 p2-3-g33 320 1121.21 0.09 1121.21 0.31 1121.21 0.21 1121.21 0.29 p2-3-g33 322 1121.21 0.31 1121.21 0.38 1121.21 0.24 p2-3-g33 323 1121.21 0.31 1121.21 0.21 1121.21 0.16 p2-3-g33 324 1121.21 0.41 1121.21 0.51 1121.21 0.11 p2-3-g33 325 1121.21 0.08 1121.21 0.09 1121.21 0.09 p2-3-g33 326 1121.21 0.32 1121.21 0.40 1121.21 0.25 p2-3-g33 327 1121.21 0.08 1121.21 0.09 1121.21 0.09 p2-3-g33 328 1121.21 0.40 1121.21 0.52 1121.21 0.11 p2-3-g33 330 1121.21 0.06 1121.21 0.12 1121.21 0.27 1121.21 0.12 p2-3-g33 332 1121.21 0.15 1049.15 0.28 1121.21 0.13 p2-3-g33 333 1121.21 0.15 1121.21 0.45 1121.21 0.12 p2-3-g33 334 1121.21 0.24 1121.21 0.28 1121.21 0.07 p2-3-g33 335 1121.21 0.06 1121.21 0.06 1121.21 0.06 p2-3-g33 336 1121.21 0.16 1049.15 0.31 1121.21 0.13 p2-3-g33 337 1121.21 0.05 1121.21 0.06 1121.21 0.05 p2-3-g33 338 1121.21 0.25 1121.21 0.27 1121.21 0.07 Table 37: Problem p2-3-g33, n = 8, m = 11, q = 34, no split, improvement heuristics.
0 1 2 3 Problem Method Obj Time Obj Time Obj Time Obj Time p2-4-g41 300 375.46 0.04 375.46 0.05 375.46 1.00 375.46 0.04 p2-4-g41 302 314.38 0.14 314.38 0.14 314.38 0.08 p2-4-g41 303 375.46 0.05 375.46 0.05 375.46 0.04 p2-4-g41 304 340.21 0.12 340.21 0.12 375.46 0.05 p2-4-g41 305 340.21 0.06 340.21 0.06 340.21 0.05 p2-4-g41 306 314.38 0.13 314.38 0.14 314.38 0.07 p2-4-g41 307 340.21 0.06 340.21 0.06 375.46 0.05 p2-4-g41 308 340.21 0.12 340.21 0.15 375.46 0.05 p2-4-g41 310 349.67 0.06 314.42 0.13 314.42 0.10 314.42 0.08 p2-4-g41 312 314.42 0.20 314.42 0.28 314.42 0.10 p2-4-g41 313 314.42 0.13 314.42 0.10 314.42 0.09 p2-4-g41 314 314.42 0.20 314.42 0.25 349.67 0.08 p2-4-g41 315 314.42 0.11 314.42 0.26 314.42 0.08 p2-4-g41 316 314.42 0.20 314.42 0.29 314.42 0.10 p2-4-g41 317 314.42 0.11 314.42 0.26 349.67 0.09 p2-4-g41 318 314.42 0.19 314.42 0.26 349.67 0.08 p2-4-g41 320 349.64 0.06 314.38 0.14 314.38 0.15 314.38 0.09 p2-4-g41 322 314.38 0.27 314.38 0.33 314.38 0.13 p2-4-g41 323 314.38 0.15 314.38 0.15 314.38 0.09 p2-4-g41 324 314.38 0.26 314.38 0.31 349.64 0.08 p2-4-g41 325 314.38 0.13 314.38 0.11 314.38 0.09 p2-4-g41 326 314.38 0.28 314.38 0.34 314.38 0.12 p2-4-g41 327 314.38 0.11 314.38 0.12 349.64 0.09 p2-4-g41 328 314.38 0.26 314.38 0.31 349.64 0.08 p2-4-g41 330 349.99 0.04 314.73 0.09 314.73 0.07 314.73 0.05 p2-4-g41 332 314.73 0.13 314.73 0.17 314.73 0.06 p2-4-g41 333 314.73 0.09 314.73 0.07 314.73 0.06 p2-4-g41 334 314.73 0.12 314.73 0.16 349.99 0.07 p2-4-g41 335 314.73 0.05 314.73 0.06 314.73 0.05 p2-4-g41 336 314.73 0.13 314.73 0.17 314.73 0.07 p2-4-g41 337 314.73 0.06 314.73 0.06 314.73 0.06 p2-4-g41 338 314.73 0.12 314.73 0.16 349.99 0.07 Table 38: Problem p2-4-g41, n = 9, m = 11, q = 16, no split, improvement heuristics.
0 1 2 3 Problem Method Obj Time Obj Time Obj Time Obj Time p2-4-g43 300 297.45 0.03 276.19 0.06 276.19 0.09 286.62 0.04 p2-4-g43 302 276.19 0.10 276.19 0.11 286.62 0.08 p2-4-g43 303 280.57 0.06 280.57 0.06 297.45 0.05 p2-4-g43 304 280.57 0.10 280.57 0.10 297.45 0.05 p2-4-g43 305 276.19 0.07 276.19 0.06 286.62 0.05 p2-4-g43 306 276.19 0.10 276.19 0.11 286.62 0.08 p2-4-g43 307 280.57 0.04 280.57 0.04 291.00 0.04 p2-4-g43 308 280.57 0.11 280.57 0.10 297.45 0.04 p2-4-g43 310 297.45 0.04 276.19 0.08 276.19 0.13 286.62 0.04 p2-4-g43 312 276.19 0.10 276.19 0.12 286.62 0.06 p2-4-g43 313 291.00 0.08 283.88 0.12 297.45 0.04 p2-4-g43 314 297.45 0.09 297.45 0.12 297.45 0.05 p2-4-g43 315 276.19 0.07 276.19 0.12 286.62 0.05 p2-4-g43 316 276.19 0.10 276.19 0.13 286.62 0.06 p2-4-g43 317 291.00 0.07 283.88 0.12 291.00 0.04 p2-4-g43 318 297.45 0.09 297.45 0.11 297.45 0.05 p2-4-g43 320 297.45 0.04 276.19 0.10 276.19 0.14 286.62 0.05 p2-4-g43 322 276.19 0.12 276.19 0.15 286.62 0.08 p2-4-g43 323 291.00 0.11 291.00 0.14 297.45 0.04 p2-4-g43 324 297.45 0.11 297.45 0.12 297.45 0.05 p2-4-g43 325 276.19 0.07 276.19 0.10 286.62 0.05 p2-4-g43 326 276.19 0.12 276.19 0.15 286.62 0.08 p2-4-g43 327 291.00 0.07 291.00 0.09 291.00 0.05 p2-4-g43 328 297.45 0.10 297.45 0.12 297.45 0.05 p2-4-g43 330 297.45 0.03 276.19 0.06 276.19 0.09 286.62 0.04 p2-4-g43 332 276.19 0.07 276.19 0.10 286.62 0.09 p2-4-g43 333 297.45 0.09 283.88 0.10 297.45 0.04 p2-4-g43 334 297.45 0.08 283.88 0.09 297.45 0.04 p2-4-g43 335 276.19 0.06 276.19 0.09 286.62 0.04 p2-4-g43 336 276.19 0.08 276.19 0.10 286.62 0.08 p2-4-g43 337 297.45 0.06 283.88 0.09 297.45 0.04 p2-4-g43 338 297.45 0.07 283.88 0.09 297.45 0.05 Table 39: Problem p2-4-g43, n = 9, m = 11, q = 6, no split, improvement heuristics.
