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The next version of Optimos, an Resource, Roster & Batching optimizer using Prosimos simulator

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Optimos V2

The next generation of Optimos. A Resource, Roster and Batching optimizer using Prosimos simulator.

Evaluation

Overview

This report includes data for the following agents, models, and modes. Click on a model to jump to its section. Refer to the Re-running the evaluation & getting the results section to see how to re-run the evaluation and get the results.

Agents

  • Proximal Policy Optimization (PPO): Heurisic-Guided Reinforce Learning using Proximal Policy Optimization (Acronym in paper: RL+).
  • Proximal Policy Optimization Random (PPO Random): NON-Heuristic-Guided Reinforce Learning using standard Proximal Policy Optimization approach (Acronym in paper: RL-).
  • Simulated Annealing (SA): Heuristic-Guided Simulated Annealing (Acronym in paper: SA+).
  • Simulated Annealing Random (SA Random): NON-Heuristic-Guided Simulated Annealing (Acronym in paper: SA-).
  • Tabu Search: Heuristic-guided Hill-Climbing approach, accepting non-optimal solutions in a given radius (Acronym in paper: HC+).
  • Tabu Search Random (Tabu Random): NON-Heuristic-Guided Hill-Climbing, accepting non-optimal solutions in a given radius (Acronym in paper: HC-).

Reference Pareto Fronts

  • Reference: Corresponds to the reference Pareto front, built considering all the Pareto-optimal solutions among all the batching policies produced by any of the six agents described before (i.e., RL+, SA+, HC+, RL-, SA-, and HC-).
  • Reference Optimos: Corresponds to the reference Pareto front, built considering only the Pareto-optimal solutions among all the batching policies produced by any heuristic-guided approaches (i.e., RL+, SA+, and HC+). (Acronym in the paper ++).
  • Reference Random: Corresponds to the reference Pareto front, built considering only the Pareto-optimal solutions among all the batching policies produced by any non-heuristic-guided approach (i.e., RL-, SA-, and HC-). (Acronym in the paper --).

Models

Modes

  • Easy -> (i.e., Parallel batching execution) Activities in the batch are executed concurrently. Processing time is amortized across instances so that batch execution time equals the time of the longest individual activity duration in the batch.
  • Hard -> (i.e., Sequential batching execution) Activities in the batch are executed sequentially, i.e., each activity starts after the previous one is completed. The processing time of the batch is the cumulative sum of all the independent activities included.
  • Mid -> (i.e., Hybrdid batching execution) Balances parallel and sequential execution by scaling processing time under sequential execution by a 0.5 factor.

Metrics Explanation

Below is an explanation of the metrics used in this report. Note that one simulation (or 'Solution') corresponds to one step on the x-axis.

  • Pareto Front Size: Number of solutions in the current Pareto Front.
  • Explored Solutions: Total number of solutions for which all neighbors have been explored.
  • Potential New Base Solutions: Potential new base solution within a small error radius for Tabu Search or within the temperature radius for Simulated Annealing.
  • Average Cycle Time: Average cycle time (from first enablement to the end of last activity) of all solutions in the current Pareto Front.
  • Min Cycle Time: Minimum cycle time among all solutions in the current Pareto Front.
  • Average Batch Size: Average number of tasks per batch (with a non batched task having a batch size of 1).
  • Iteration Number: In one iteration, multiple mutations are performed. Depending on the agent, the solutions will be treated differently. Note that the number of solutions per iteration is not the same for all agents.
  • Time per Step: Average wall time per simulation step computed from differences between consecutive steps.
  • Total Optimization Time: Total wall clock time from the first to the last iteration (in minutes)
  • Hyperarea (HA): Measures convergence and distribution. Hyperarea is the area in the objective space dominated by a Pareto front delimited by a point, which we set as the maximum cost and time among all the solutions explored. If PRef is available, the hyperarea ratio is a real number, between 0 and 1, given by HA(ParetoAprox)/HA(ParetoRef). A higher hyperarea ratio means a better PAprox, being 1 the maximum possible ratio indicating that PAprox dominates the same solution space as PRef.
  • Averaged Hausdorff Distance: Measures convergence as the mean root mean squared (RMS) distance between ParetoAprox and ParetoRef. A lower value means a better convergence.
  • Purity: Measures the proportion of ParetoAprox solutions included in ParetoRef. A higher purity indicates a better ParetoAprox, with a maximum value of 1.
  • Delta: Measures how well the solutions are spread and evenly distributed. It checks whether the solutions cover the full extent of the objective space (spread) and whether the spacing between them is uniform (distribution). A lower value of Delta means a better ParetoAprox.

Results

Bpi Challenge 2012

BP12 (Acronym in the paper) - It is a loan application process from a Dutch financial institution. This fragment contains only activities with defined start and end timestamps. Access Link: BPI Challenge 2012.

Analyzer Overview

Pareto Size
Agent / Reference Easy Mid Hard
Reference 58,00 46,00 38,00
Reference Random 37,00 39,00 33,00
Reference Optimos 53,00 40,00 35,00
SA 39,00 35,00 26,00
Tabu Search 35,00 17,00 25,00
PPO 46,00 41,00 22,00
Tabu Random 8,00 15,00 16,00
SA Random 26,00 20,00 18,00
PPO Random 41,00 38,00 28,00

Hyperarea Ratio
Agent / Reference Easy Mid Hard
Reference Random 0,98 1,00 1,00
Reference Optimos 1,00 0,99 1,00
SA 0,96 0,97 1,00
Tabu Search 0,92 0,94 1,00
PPO 1,00 0,99 1,00
Tabu Random 0,68 0,95 1,00
SA Random 0,86 0,95 1,00
PPO Random 0,98 1,00 1,00

Hausdorff
Agent / Reference Easy Mid Hard
Reference Random 9.987,18 3.703,22 3.415,36
Reference Optimos 272,36 5.523,63 10.161,03
SA 15.408,62 5.939,53 29.585,14
Tabu Search 9.883,80 6.427,54 29.616,95
PPO 306,40 5.514,86 10.727,28
Tabu Random 15.738,85 7.246,00 15.877,69
SA Random 17.805,24 6.174,27 22.952,28
PPO Random 9.989,72 3.703,29 11.101,33

Delta
Agent / Reference Easy Mid Hard
Reference Random 0,99 1,25 1,23
Reference Optimos 1,66 1,15 1,16
SA 1,03 1,04 1,04
Tabu Search 1,03 1,16 1,01
PPO 1,64 1,14 1,01
Tabu Random 1,19 1,05 1,44
SA Random 1,27 1,12 1,03
PPO Random 1,00 1,25 1,13

Purity
Agent / Reference Easy Mid Hard
Reference Random 0,28 0,46 0,37
Reference Optimos 0,72 0,54 0,63
SA 0,19 0,24 0,24
Tabu Search 0,17 0,09 0,34
PPO 0,33 0,22 0,05
Tabu Random 0,00 0,00 0,11
SA Random 0,00 0,00 0,08
PPO Random 0,26 0,46 0,18

Avg Cycle Time
Agent / Reference Easy Mid Hard
Base 1.218.264,58 1.218.354,45 1.218.264,60
Reference 1.231.617,45 1.393.767,17 2.425.820,43
Reference Random 1.212.931,15 1.436.835,71 3.367.277,38
Reference Optimos 1.233.554,65 1.435.539,34 5.363.983,24
SA 1.304.858,77 1.369.175,11 1.426.754,04
Tabu Search 1.228.740,83 1.356.749,39 1.568.009,15
PPO 1.221.187,53 1.431.114,38 6.589.850,99
Tabu Random 1.259.535,84 1.370.966,56 1.784.573,13
SA Random 1.353.113,82 1.371.905,30 1.606.825,51
PPO Random 1.212.012,24 1.433.278,06 4.959.761,62

Best Cycle Time
Agent / Reference Easy Mid Hard
Base 1.218.264,58 1.218.354,45 1.218.264,60
Reference 1.166.893,73 1.170.000,00 1.166.304,58
Reference Random 1.163.321,38 1.170.000,00 1.166.304,58
Reference Optimos 1.163.504,07 1.210.386,51 1.170.135,16
SA 1.209.128,12 1.213.770,44 1.210.526,41
Tabu Search 1.211.702,72 1.213.581,21 1.217.329,58
PPO 1.163.504,07 1.170.003,63 1.170.000,00
Tabu Random 1.170.000,00 1.170.000,00 1.211.329,39
SA Random 1.170.000,00 1.170.000,00 1.211.040,39
PPO Random 1.163.321,38 1.170.000,00 1.166.304,58

Easy

Metric Plots

Individual charts:

Summary Table (Final Values)
Agent Steps Explored Solutions Potential New Base Solutions Average Cycle Time Min Cycle Time Average Batch Size Iteration Number Time per Step Total Optimization Time
Proximal Policy Optimization 9991 1020 1.22262e+06 1.1635e+06 17.8497 10000 4.33396 549min
(for 9991 Steps)
Proximal Policy Optimization Random 9991 1347 1.21544e+06 1.16689e+06 2.54891 10000 3.13432 383min
(for 9991 Steps)
Simulated Annealing 9993 454 27 1.30261e+06 1.20913e+06 5.92322 602 3.59493 76min
(for 9993 Steps)
Simulated Annealing Random 915 459 0 1.3469e+06 1.21027e+06 4.44316 307 1.45809 24min
(for 915 Steps)
Tabu Search 6922 559 0 1.23741e+06 1.2117e+06 5.03646 390 3.05839 43min
(for 6922 Steps)
Tabu Search Random 60 35 0 1.27674e+06 1.21298e+06 2 22 1.56687 1min
(for 60 Steps)
Pareto Front Images

Individual Pareto images:

Hard

Metric Plots

Individual charts:

Summary Table (Final Values)
Agent Steps Explored Solutions Potential New Base Solutions Average Cycle Time Min Cycle Time Average Batch Size Iteration Number Time per Step Total Optimization Time
Proximal Policy Optimization 9991 1748 7.74888e+06 1.17014e+06 2 10000 2.76076 486min
(for 9991 Steps)
Proximal Policy Optimization Random 9991 1209 4.82441e+06 1.1663e+06 2 10000 5.43813 644min
(for 9991 Steps)
Simulated Annealing 8534 456 0 1.41545e+06 1.21131e+06 5.39286 565 0.252189 91min
(for 8534 Steps)
Simulated Annealing Random 720 354 0 1.58524e+06 1.21104e+06 0 242 1.85308 20min
(for 720 Steps)
Tabu Search 2933 297 0 1.52894e+06 1.21731e+06 16.5698 168 0.572584 27min
(for 2933 Steps)
Tabu Search Random 180 65 0 1.7864e+06 1.21133e+06 0 62 1.41545 5min
(for 180 Steps)
Pareto Front Images

Individual Pareto images:

Mid

Metric Plots

Individual charts:

Summary Table (Final Values)
Agent Steps Explored Solutions Potential New Base Solutions Average Cycle Time Min Cycle Time Average Batch Size Iteration Number Time per Step Total Optimization Time
Proximal Policy Optimization 9991 1754 1.42909e+06 1.17e+06 5.55513 10000 2.50255 429min
(for 9991 Steps)
Proximal Policy Optimization Random 9991 1677 1.46688e+06 1.17e+06 2.97665 10000 2.94587 471min
(for 9991 Steps)
Simulated Annealing 10006 696 9 1.37587e+06 1.21377e+06 2 642 0.275636 71min
(for 10006 Steps)
Simulated Annealing Random 759 429 0 1.39163e+06 1.21732e+06 2 255 1.0461 18min
(for 759 Steps)
Tabu Search 2496 146 0 1.36132e+06 1.21358e+06 2.63385 133 0.264846 16min
(for 2496 Steps)
Tabu Search Random 129 50 0 1.38085e+06 1.21129e+06 43.3714 45 1.22801 3min
(for 129 Steps)
Pareto Front Images

Individual Pareto images:

Bpi Challenge 2017

BP17 (Acronym in the paper) - It is an updated iteration of the BPI-2012 log, but extracted in 2017. Access Link: BPI 2017

Analyzer Overview

Pareto Size
Agent / Reference Easy Mid Hard
Reference 68,00 34,00 22,00
Reference Random 46,00 31,00 9,00
Reference Optimos 59,00 35,00 21,00
SA 34,00 26,00 25,00
Tabu Search 39,00 36,00 2,00
PPO 40,00 32,00 16,00
Tabu Random 19,00 11,00 4,00
SA Random 19,00 21,00 7,00
PPO Random 33,00 32,00 12,00

Hyperarea Ratio
Agent / Reference Easy Mid Hard
Reference Random 1,00 0,96 1,00
Reference Optimos 1,00 1,00 1,00
SA 0,81 0,93 1,00
Tabu Search 0,95 0,98 1,00
PPO 1,00 0,99 1,00
Tabu Random 0,85 0,86 1,00
SA Random 0,86 0,91 1,00
PPO Random 1,00 0,95 1,00

Hausdorff
Agent / Reference Easy Mid Hard
Reference Random 79,08 21.159,01 7.660,72
Reference Optimos 4.916,98 442,87 1.114,51
SA 13.998,34 3.563,03 764,08
Tabu Search 959,61 7.012,05 21.714,03
PPO 5.836,54 2.629,91 118.980,27
Tabu Random 10.561,28 4.241,19 14.593,91
SA Random 2.472,96 20.629,72 7.716,23
PPO Random 152,81 8.273,79 24.916,06

Delta
Agent / Reference Easy Mid Hard
Reference Random 1,07 1,33 1,43
Reference Optimos 1,36 1,27 0,95
SA 1,30 1,03 1,06
Tabu Search 0,89 1,12 1,00
PPO 1,34 1,29 0,96
Tabu Random 1,16 1,22 0,80
SA Random 1,38 1,09 1,36
PPO Random 1,03 1,07 1,01

Purity
Agent / Reference Easy Mid Hard
Reference Random 0,31 0,26 0,18
Reference Optimos 0,69 0,74 0,82
SA 0,29 0,21 0,68
Tabu Search 0,34 0,26 0,00
PPO 0,10 0,26 0,14
Tabu Random 0,01 0,00 0,00
SA Random 0,06 0,00 0,14
PPO Random 0,26 0,26 0,05

Avg Cycle Time
Agent / Reference Easy Mid Hard
Base 852.467,43 852.710,18 852.702,68
Reference 839.940,98 990.747,76 991.046,77
Reference Random 846.410,93 966.070,75 996.937,34
Reference Optimos 842.130,74 988.114,18 985.012,14
SA 941.847,55 951.636,32 964.062,54
Tabu Search 861.506,82 920.061,23 4.712.685,16
PPO 852.272,83 1.060.722,98 17.301.316,04
Tabu Random 894.732,99 1.100.928,34 914.196,55
SA Random 868.914,85 1.143.350,67 1.044.067,34
PPO Random 844.653,56 926.197,95 15.219.855,60

Best Cycle Time
Agent / Reference Easy Mid Hard
Base 852.467,43 852.710,18 852.702,68
Reference 696.456,31 840.352,05 837.243,10
Reference Random 773.072,94 838.151,30 837.243,10
Reference Optimos 622.341,70 840.352,05 838.174,03
SA 847.721,61 846.218,83 845.162,58
Tabu Search 696.456,31 846.408,80 852.516,38
PPO 622.341,70 825.269,43 838.174,03
Tabu Random 851.317,68 852.455,13 849.882,17
SA Random 850.046,38 848.571,22 851.497,36
PPO Random 773.072,94 833.972,70 837.243,10

Easy

Metric Plots

Individual charts:

Summary Table (Final Values)
Agent Steps Explored Solutions Potential New Base Solutions Average Cycle Time Min Cycle Time Average Batch Size Iteration Number Time per Step Total Optimization Time
Proximal Policy Optimization 9991 2296 851855 622342 2 10000 4.0034 641min
(for 9991 Steps)
Proximal Policy Optimization Random 9991 3480 846913 773073 9.13759 10000 4.41904 579min
(for 9991 Steps)
Simulated Annealing 9998 1495 564 941853 847722 2 655 0.717846 90min
(for 9998 Steps)
Simulated Annealing Random 1190 641 0 869780 850046 2.01457 398 2.4041 44min
(for 1190 Steps)
Tabu Search 10000 2778 829 878877 696456 5.55401 548 1.09289 103min
(for 10000 Steps)
Tabu Search Random 620 285 0 899299 851318 2.19473 208 2.49187 25min
(for 620 Steps)
Pareto Front Images

Individual Pareto images:

Hard

Metric Plots

Individual charts:

Summary Table (Final Values)
Agent Steps Explored Solutions Potential New Base Solutions Average Cycle Time Min Cycle Time Average Batch Size Iteration Number Time per Step Total Optimization Time
Proximal Policy Optimization 6299 734 1.9778e+07 838174 2 6309 2.62878 367min
(for 6299 Steps)
Proximal Policy Optimization Random 5489 649 1.71763e+07 837243 2 5499 3.2475 343min
(for 5489 Steps)
Simulated Annealing 9994 2069 211 974249 845163 2 698 1.04918 135min
(for 9994 Steps)
Simulated Annealing Random 896 494 0 1.04407e+06 851497 2 300 2.024 32min
(for 896 Steps)
Tabu Search 23 5 1 853221 852804 0 4 0.012678 0min
(for 23 Steps)
Tabu Search Random 26 13 0 884157 852467 0 10 1.5919 1min
(for 26 Steps)
Pareto Front Images

Individual Pareto images:

Mid

Metric Plots

Individual charts:

Summary Table (Final Values)
Agent Steps Explored Solutions Potential New Base Solutions Average Cycle Time Min Cycle Time Average Batch Size Iteration Number Time per Step Total Optimization Time
Proximal Policy Optimization 9991 1505 1.02846e+06 825269 2 10000 3.34574 518min
(for 9991 Steps)
Proximal Policy Optimization Random 9095 1668 933243 838151 2 9105 3.33356 493min
(for 9095 Steps)
Simulated Annealing 10000 835 115 955819 846219 0 684 0.568655 106min
(for 10000 Steps)
Simulated Annealing Random 947 511 0 1.11572e+06 850648 2 317 2.13876 34min
(for 947 Steps)
Tabu Search 10007 1426 563 924136 846409 2.88612 599 0.756378 105min
(for 10007 Steps)
Tabu Search Random 173 85 0 1.12352e+06 852813 2.0259 59 0.090271 6min
(for 173 Steps)
Pareto Front Images

Individual Pareto images:

Bpic2019 Das

BP19 (Acronym in the paper) - It comes from a Netherlands multinational coatings and paints company, describing the purchase order handling process for its 60 subsidiaries. Access Link: BPI Challenge 2019

Analyzer Overview

Pareto Size
Agent / Reference Easy Mid Hard
Reference 22,00 23,00 12,00
Reference Random 19,00 16,00 12,00
Reference Optimos 15,00 23,00 9,00
SA 6,00 7,00 12,00
Tabu Search 2,00 8,00 20,00
PPO 19,00 23,00 3,00
Tabu Random 1,00 1,00 5,00
SA Random 8,00 9,00 2,00
PPO Random 21,00 19,00 11,00

Hyperarea Ratio
Agent / Reference Easy Mid Hard
Reference Random 1,00 1,00 1,00
Reference Optimos 1,00 1,00 1,00
SA 0,98 0,96 1,00
Tabu Search 0,99 0,97 1,00
PPO 1,00 1,00 1,00
Tabu Random 0,99 0,96 1,00
SA Random 0,99 0,99 1,00
PPO Random 1,00 1,00 1,00

Hausdorff
Agent / Reference Easy Mid Hard
Reference Random 436,47 430.414,11 10.221,63
Reference Optimos 6.464,99 0,00 1.914.144,46
SA 30.437,76 19.742,85 1.916.109,07
Tabu Search 36.522,19 24.172,94 1.913.213,38
PPO 7.252,59 0,00 1.912.100,68
Tabu Random 36.850,45 22.667,19 1.913.565,79
SA Random 20.186,07 545.936,82 1.916.106,86
PPO Random 7.483,51 405.545,77 10.221,63

Delta
Agent / Reference Easy Mid Hard
Reference Random 0,78 1,11 1,62
Reference Optimos 1,18 1,03 1,00
SA 0,96 0,96 1,00
Tabu Search 0,96 0,98 1,00
PPO 1,07 1,03 1,00
Tabu Random 0,00 0,00 1,00
SA Random 1,08 1,33 1,00
PPO Random 0,90 1,12 1,62

Purity
Agent / Reference Easy Mid Hard
Reference Random 0,86 0,00 0,67
Reference Optimos 0,14 1,00 0,33
SA 0,00 0,00 0,17
Tabu Search 0,05 0,00 0,08
PPO 0,09 1,00 0,33
Tabu Random 0,05 0,00 0,17
SA Random 0,14 0,00 0,08
PPO Random 0,68 0,00 0,67

Avg Cycle Time
Agent / Reference Easy Mid Hard
Base 1.043.060,17 1.000.680,00 991.869,54
Reference 13.254.654,93 8.620.197,31 657.315.714,08
Reference Random 13.562.132,10 195.531.623,76 653.567.931,48
Reference Optimos 14.429.898,92 8.620.197,31 7.864.354,84
SA 1.507.097,88 1.956.373,35 1.413.361,82
Tabu Search 1.589.905,74 4.418.830,87 2.659.125,33
PPO 11.638.988,73 8.620.197,31 15.876.716,15
Tabu Random 1.746.895,25 2.076.818,41 1.044.893,23
SA Random 2.499.499,15 199.021.926,37 4.707.934,03
PPO Random 12.219.507,07 179.178.011,59 653.567.931,48

Best Cycle Time
Agent / Reference Easy Mid Hard
Base 1.043.060,17 1.000.680,00 991.869,54
Reference 1.067.163,66 3.005.361,94 925.020,00
Reference Random 1.067.163,66 2.048.507,77 925.020,00
Reference Optimos 1.371.193,29 3.005.361,94 1.000.620,00
SA 1.063.109,41 1.544.374,98 925.020,00
Tabu Search 1.371.193,29 3.042.646,84 925.020,00
PPO 1.082.014,13 3.005.361,94 925.020,00
Tabu Random 1.746.895,25 2.076.818,41 925.020,00
SA Random 1.067.163,66 2.048.507,77 925.020,00
PPO Random 1.690.399,18 2.151.928,20 925.020,00

Easy

Metric Plots

Individual charts:

Summary Table (Final Values)
Agent Steps Explored Solutions Potential New Base Solutions Average Cycle Time Min Cycle Time Average Batch Size Iteration Number Time per Step Total Optimization Time
Proximal Policy Optimization 2009 2 1.1639e+07 1.08201e+06 4.03617 2019 15.139 501min
(for 2009 Steps)
Proximal Policy Optimization Random 4067 2 1.22195e+07 1.6904e+06 6.67055 4077 20.129 1,043min
(for 4067 Steps)
Simulated Annealing 9999 202 938 1.5071e+06 1.06311e+06 2.78258 591 0.95725 419min
(for 9999 Steps)
Simulated Annealing Random 2633 1077 20 2.4995e+06 1.06716e+06 3.92252 868 1.46477 454min
(for 2633 Steps)
Tabu Search 3537 38 1255 1.58991e+06 1.37119e+06 3.50991 176 2.03933 137min
(for 3537 Steps)
Tabu Search Random 473 153 0 1.7469e+06 1.7469e+06 5.83961 155 2.20628 62min
(for 473 Steps)
Pareto Front Images

Individual Pareto images:

Hard

Metric Plots

Individual charts:

Summary Table (Final Values)
Agent Steps Explored Solutions Potential New Base Solutions Average Cycle Time Min Cycle Time Average Batch Size Iteration Number Time per Step Total Optimization Time
Proximal Policy Optimization 631 8 2.08606e+07 5.14389e+06 9.35763 640 111.327 773min
(for 631 Steps)
Proximal Policy Optimization Random 771 2 1.97393e+09 3.22863e+06 9.58205 780 127.342 1,760min
(for 771 Steps)
Simulated Annealing 9270 193 1695 2.19567e+06 1.00062e+06 3.10955 502 0.382867 358min
(for 9270 Steps)
Simulated Annealing Random 705 297 0 6.59939e+06 3.35898e+06 5 254 6.81138 314min
(for 705 Steps)
Tabu Search 7986 161 1055 3.98648e+06 1.42871e+06 3.54196 425 1.25507 333min
(for 7986 Steps)
Tabu Search Random 128 34 0 2.48004e+06 1.00068e+06 3.72706 40 9.28795 25min
(for 128 Steps)
Pareto Front Images

Individual Pareto images:

Mid

Metric Plots

Individual charts:

Summary Table (Final Values)
Agent Steps Explored Solutions Potential New Base Solutions Average Cycle Time Min Cycle Time Average Batch Size Iteration Number Time per Step Total Optimization Time
Proximal Policy Optimization 241 1 2.89777e+08 3.21102e+06 8.79699 250 44.0296 196min
(for 241 Steps)
Proximal Policy Optimization Random 2541 1 1.79178e+08 2.15193e+06 5.65822 2550 20.6542 1,436min
(for 2541 Steps)
Simulated Annealing 10001 200 2726 1.95637e+06 1.54438e+06 2.70882 593 0.388852 401min
(for 10001 Steps)
Simulated Annealing Random 1049 423 0 1.77198e+08 2.04851e+06 4.1509 347 5.50982 225min
(for 1049 Steps)
Tabu Search 6357 96 280 4.26219e+06 3.04265e+06 3.03069 346 1.85831 262min
(for 6357 Steps)
Tabu Search Random 29 5 0 2.07682e+06 2.07682e+06 2.96169 7 7.34266 2min
(for 29 Steps)
Pareto Front Images

Individual Pareto images:

Callcentre

CALL (Acronym in the paper) - It comes from a call center process. This event log includes a high volume of cases with short duration (on average, two activities per case).

Analyzer Overview

Pareto Size
Agent / Reference Easy Mid Hard
Reference 15,00 14,00 13,00
Reference Random 9,00 17,00 17,00
Reference Optimos 15,00 5,00 9,00
SA 7,00 4,00 5,00
Tabu Search 1,00 4,00 1,00
PPO 17,00 5,00 9,00
Tabu Random 9,00 2,00 3,00
SA Random 11,00 9,00 15,00
PPO Random 9,00 12,00 8,00

Hyperarea Ratio
Agent / Reference Easy Mid Hard
Reference Random 1,00 1,00 1,00
Reference Optimos 1,00 1,00 1,00
SA 0,98 0,91 1,00
Tabu Search 0,98 0,91 1,00
PPO 1,00 1,00 1,00
Tabu Random 0,99 0,84 1,00
SA Random 1,00 1,00 1,00
PPO Random 1,00 1,00 1,00

Hausdorff
Agent / Reference Easy Mid Hard
Reference Random 20.522,85 1.199,31 17.646,90
Reference Optimos 0,00 26.800,08 3.270,60
SA 33.019,80 271.567,49 517.182,71
Tabu Search 29.609,43 216.393,82 581.762,66
PPO 0,00 26.800,08 3.270,60
Tabu Random 24.933,62 409.015,90 891.974,32
SA Random 54.507,65 2.173,16 18.693,25
PPO Random 20.522,85 17.516,95 13.509,85

Delta
Agent / Reference Easy Mid Hard
Reference Random 0,99 1,21 1,23
Reference Optimos 1,74 1,00 1,60
SA 0,93 0,95 0,00
Tabu Search 0,00 0,94 0,00
PPO 1,74 1,00 1,60
Tabu Random 1,02 0,97 0,92
SA Random 1,29 1,01 1,19
PPO Random 0,99 0,97 1,01

Purity
Agent / Reference Easy Mid Hard
Reference Random 0,00 0,64 0,62
Reference Optimos 1,00 0,36 0,38
SA 0,00 0,00 0,00
Tabu Search 0,00 0,00 0,00
PPO 1,00 0,36 0,38
Tabu Random 0,00 0,00 0,00
SA Random 0,00 0,21 0,62
PPO Random 0,00 0,43 0,00

Avg Cycle Time
Agent / Reference Easy Mid Hard
Base 11.106.584,79 10.889.027,63 11.738.570,26
Reference 71.718,79 114.388,32 83.654,70
Reference Random 14.570,07 108.691,65 143.569,65
Reference Optimos 71.718,79 6.096,85 49.050,92
SA 1.738.604,64 7.956.488,84 9.698.842,92
Tabu Search 1.527.949,36 9.167.885,21 10.225.921,16
PPO 71.718,79 6.096,85 49.050,92
Tabu Random 1.146.321,93 9.011.205,66 19.606.665,88
SA Random 15.340.975,24 191.474,45 172.392,03
PPO Random 14.570,07 79.599,66 15.676,56

Best Cycle Time
Agent / Reference Easy Mid Hard
Base 11.106.584,79 10.889.027,63 11.738.570,26
Reference 1.881,05 5.758,89 4.876,96
Reference Random 1.902,42 4.281,56 4.876,96
Reference Optimos 1.881,05 5.758,89 4.417,33
SA 1.387.596,57 7.093.163,15 9.698.842,92
Tabu Search 1.527.949,36 8.719.642,93 10.225.921,16
PPO 1.881,05 5.758,89 4.417,33
Tabu Random 1.066.232,87 8.773.247,05 10.438.156,55
SA Random 191.679,36 4.281,56 4.876,96
PPO Random 1.902,42 34.311,62 4.562,45

Easy

Metric Plots

Individual charts:

Summary Table (Final Values)
Agent Steps Explored Solutions Potential New Base Solutions Average Cycle Time Min Cycle Time Average Batch Size Iteration Number Time per Step Total Optimization Time
Proximal Policy Optimization 6600 405 73793.5 1881.05 25.3167 6610 3.35217 361min
(for 6600 Steps)
Proximal Policy Optimization Random 5241 326 12413.4 1951.83 4.70833 5250 9.54398 717min
(for 5241 Steps)
Simulated Annealing 10002 360 1088 1.7386e+06 1.3876e+06 2.54301 664 0.907438 82min
(for 10002 Steps)
Simulated Annealing Random 2600 1314 542 1.5341e+07 191679 3.18854 868 2.347 104min
(for 2600 Steps)
Tabu Search 305 4 0 1.52795e+06 1.52795e+06 2.27386 21 1.54933 2min
(for 305 Steps)
Tabu Search Random 2600 1536 356 1.19836e+06 1.06623e+06 2.60242 868 1.45499 88min
(for 2600 Steps)
Pareto Front Images

Individual Pareto images:

Hard

Metric Plots

Individual charts:

Summary Table (Final Values)
Agent Steps Explored Solutions Potential New Base Solutions Average Cycle Time Min Cycle Time Average Batch Size Iteration Number Time per Step Total Optimization Time
Proximal Policy Optimization 3511 349 45649.9 4417.33 26.3333 3520 17.117 716min
(for 3511 Steps)
Proximal Policy Optimization Random 4347 590 15676.6 4562.45 26.1556 4357 14.0817 601min
(for 4347 Steps)
Simulated Annealing 7152 311 0 1.02421e+07 9.80554e+06 5.39037 468 0.367432 45min
(for 7152 Steps)
Simulated Annealing Random 2600 1339 655 172392 4876.96 7.15138 868 3.11103 107min
(for 2600 Steps)
Tabu Search 103 4 0 1.02259e+07 1.02259e+07 3.53407 9 2.63266 0min
(for 103 Steps)
Tabu Search Random 47 16 0 1.98113e+07 1.10522e+07 3.45809 18 2.05723 1min
(for 47 Steps)
Pareto Front Images

Individual Pareto images:

Mid

Metric Plots

Individual charts:

Summary Table (Final Values)
Agent Steps Explored Solutions Potential New Base Solutions Average Cycle Time Min Cycle Time Average Batch Size Iteration Number Time per Step Total Optimization Time
Proximal Policy Optimization 2106 84 6096.85 5758.89 2.72419 2116 3.47716 140min
(for 2106 Steps)
Proximal Policy Optimization Random 8994 494 80850.5 34311.6 8.81466 9004 4.83608 699min
(for 8994 Steps)
Simulated Annealing 10011 389 52 7.95649e+06 7.09316e+06 2.88614 668 0.000984311 78min
(for 10011 Steps)
Simulated Annealing Random 2600 1290 671 191474 4281.56 10.7397 868 2.08443 98min
(for 2600 Steps)
Tabu Search 3393 129 323 9.4731e+06 8.71964e+06 3.07424 221 0.338917 31min
(for 3393 Steps)
Tabu Search Random 35 11 0 9.01121e+06 8.77325e+06 2.24764 14 1.19283 1min
(for 35 Steps)
Pareto Front Images

Individual Pareto images:

Consulta Data Mining

ACC (Acronym in the paper) - This business process, also known as academic credentials, is an anonymized log of an academic recognition process at a university. In this process, a worker performs one task at a time, but occasionally, a worker may take on a second or a third activity instance concurrently. This event log contains many resources with low participation in the process, meaning each resource performs only a handful of activity instances across the entire period covered by the event log.

Analyzer Overview

Pareto Size
Agent / Reference Easy Mid Hard
Reference 77,00 32,00 24,00
Reference Random 50,00 25,00 21,00
Reference Optimos 77,00 30,00 28,00
SA 26,00 19,00 6,00
Tabu Search 42,00 21,00 13,00
PPO 50,00 28,00 30,00
Tabu Random 29,00 10,00 9,00
SA Random 34,00 21,00 10,00
PPO Random 34,00 15,00 16,00

Hyperarea Ratio
Agent / Reference Easy Mid Hard
Reference Random 0,98 0,99 1,00
Reference Optimos 1,00 0,96 0,99
SA 0,73 0,70 0,97
Tabu Search 0,87 0,96 0,98
PPO 0,99 0,82 0,99
Tabu Random 0,88 0,63 0,97
SA Random 0,81 0,98 1,00
PPO Random 0,97 0,61 0,98

Hausdorff
Agent / Reference Easy Mid Hard
Reference Random 2.833,58 1.319,03 18.702,87
Reference Optimos 3,08 90.263,12 35.620,70
SA 7.078,89 90.612,63 78.466,39
Tabu Search 11.310,39 90.300,65 62.127,93
PPO 981,75 92.517,95 36.111,28
Tabu Random 4.486,89 91.019,64 56.746,92
SA Random 38.498,23 1.372,92 19.515,43
PPO Random 3.219,77 93.659,12 69.173,02

Delta
Agent / Reference Easy Mid Hard
Reference Random 1,12 1,72 1,60
Reference Optimos 1,20 1,01 1,09
SA 1,05 1,02 1,01
Tabu Search 0,95 1,01 1,03
PPO 1,11 1,01 1,06
Tabu Random 0,98 1,02 1,00
SA Random 1,38 1,63 1,49
PPO Random 1,01 1,00 0,99

Purity
Agent / Reference Easy Mid Hard
Reference Random 0,01 0,16 0,25
Reference Optimos 0,99 0,84 0,75
SA 0,06 0,19 0,00
Tabu Search 0,58 0,66 0,42
PPO 0,36 0,00 0,33
Tabu Random 0,01 0,03 0,00
SA Random 0,01 0,12 0,21
PPO Random 0,00 0,00 0,04

Avg Cycle Time
Agent / Reference Easy Mid Hard
Base 10.924.190,73 11.498.316,15 11.845.078,32
Reference 11.505.477,29 11.360.135,58 12.438.262,75
Reference Random 11.595.106,20 11.443.018,69 11.625.892,84
Reference Optimos 11.510.016,25 11.401.558,01 12.432.425,07
SA 11.523.864,35 11.760.911,87 11.371.253,37
Tabu Search 11.397.259,22 11.343.615,08 14.404.102,38
PPO 11.573.728,00 11.892.906,21 12.519.200,95
Tabu Random 11.899.980,67 11.533.807,71 11.899.414,42
SA Random 11.487.427,01 11.406.146,05 11.686.354,37
PPO Random 11.582.461,74 11.581.298,14 11.884.449,70

Best Cycle Time
Agent / Reference Easy Mid Hard
Base 10.924.190,73 11.498.316,15 11.845.078,32
Reference 10.653.552,98 10.906.582,86 10.908.571,55
Reference Random 10.908.046,39 10.867.316,03 10.912.591,09
Reference Optimos 10.653.552,98 10.906.582,86 10.908.571,55
SA 10.899.817,14 11.162.809,30 11.150.692,54
Tabu Search 10.653.552,98 10.906.582,86 10.908.571,55
PPO 10.559.397,46 11.248.319,30 11.182.600,34
Tabu Random 10.924.190,73 10.917.768,17 11.250.920,54
SA Random 10.908.046,39 10.917.768,17 11.246.504,00
PPO Random 10.729.651,35 10.867.316,03 11.250.920,54

Easy

Metric Plots

Individual charts:

Summary Table (Final Values)
Agent Steps Explored Solutions Potential New Base Solutions Average Cycle Time Min Cycle Time Average Batch Size Iteration Number Time per Step Total Optimization Time
Proximal Policy Optimization 6611 1806 1.15599e+07 1.05594e+07 2.38727 6620 5.96561 717min
(for 6611 Steps)
Proximal Policy Optimization Random 6951 1536 1.16295e+07 1.07297e+07 2.25017 6960 6.38168 718min
(for 6951 Steps)
Simulated Annealing 10012 897 2623 1.15301e+07 1.08998e+07 2.65326 505 1.82837 112min
(for 10012 Steps)
Simulated Annealing Random 1976 953 0 1.15087e+07 1.0908e+07 2.86636 656 2.43394 92min
(for 1976 Steps)
Tabu Search 10009 3770 1811 1.14301e+07 1.06536e+07 3.1152 497 1.9764 135min
(for 10009 Steps)
Tabu Search Random 611 292 0 1.19551e+07 1.10942e+07 2.72866 200 2.85947 30min
(for 611 Steps)
Pareto Front Images

Individual Pareto images:

Hard

Metric Plots

Individual charts:

Summary Table (Final Values)
Agent Steps Explored Solutions Potential New Base Solutions Average Cycle Time Min Cycle Time Average Batch Size Iteration Number Time per Step Total Optimization Time
Proximal Policy Optimization 8191 1536 1.25242e+07 1.12337e+07 4.74331 8200 5.6872 718min
(for 8191 Steps)
Proximal Policy Optimization Random 9831 595 1.18351e+07 1.08675e+07 3.41973 9840 3.92619 717min
(for 9831 Steps)
Simulated Annealing 10011 1039 61 1.13937e+07 1.11507e+07 3.20584 536 0.0011173 142min
(for 10011 Steps)
Simulated Annealing Random 1084 480 0 1.18439e+07 1.13304e+07 4.63462 357 2.51622 47min
(for 1084 Steps)
Tabu Search 3893 156 407 1.53945e+07 1.09086e+07 4.27273 210 0.696202 47min
(for 3893 Steps)
Tabu Search Random 83 26 0 1.19013e+07 1.12509e+07 2.58917 25 0.0934325 3min
(for 83 Steps)
Pareto Front Images

Individual Pareto images:

Mid

Metric Plots

Individual charts:

Summary Table (Final Values)
Agent Steps Explored Solutions Potential New Base Solutions Average Cycle Time Min Cycle Time Average Batch Size Iteration Number Time per Step Total Optimization Time
Proximal Policy Optimization 8401 2371 1.18794e+07 1.12483e+07 4.20479 8410 4.76213 717min
(for 8401 Steps)
Proximal Policy Optimization Random 8621 2491 1.15323e+07 1.08673e+07 2.2739 8630 5.6891 717min
(for 8621 Steps)
Simulated Annealing 9993 1028 1435 1.17937e+07 1.13394e+07 3.71206 538 1.57184 121min
(for 9993 Steps)
Simulated Annealing Random 1433 755 0 1.14658e+07 1.10758e+07 3.30315 475 0.267463 63min
(for 1433 Steps)
Tabu Search 9994 1443 1374 1.14417e+07 1.09137e+07 2.24465 508 3.14961 115min
(for 9994 Steps)
Tabu Search Random 95 29 0 1.16251e+07 1.12549e+07 3.58079 29 1.82635 3min
(for 95 Steps)
Pareto Front Images

Individual Pareto images:

Gov

GOV (Acronym in the paper) corresponds to an application-to-approval process in a government agency. In this process, each worker handles multiple applications concurrently.

Analyzer Overview

Pareto Size
Agent / Reference Easy Mid Hard
Reference 17,00 26,00 7,00
Reference Random 9,00 17,00 5,00
Reference Optimos 25,00 24,00 10,00
SA 13,00 14,00 8,00
Tabu Search 16,00 23,00 9,00
PPO 18,00 9,00 3,00
Tabu Random 4,00 9,00 6,00
SA Random 6,00 13,00 5,00
PPO Random 8,00 10,00 3,00

Hyperarea Ratio
Agent / Reference Easy Mid Hard
Reference Random 0,95 0,98 0,99
Reference Optimos 1,00 1,00 1,00
SA 0,92 0,98 1,00
Tabu Search 0,94 1,00 1,00
PPO 1,00 0,99 0,96
Tabu Random 0,82 0,95 0,97
SA Random 0,82 0,93 0,99
PPO Random 0,95 0,98 0,97

Hausdorff
Agent / Reference Easy Mid Hard
Reference Random 51.182,11 390.275,62 4.786,74
Reference Optimos 8.498,87 601,78 3.742,73
SA 139.807,66 399.659,68 12.229,69
Tabu Search 42.046,65 1.052,23 3.611,52
PPO 16.998,45 194.094,43 18.849,23
Tabu Random 189.850,69 455.733,28 10.109,15
SA Random 175.418,86 478.082,00 4.786,74
PPO Random 52.002,22 402.914,79 16.354,39

Delta
Agent / Reference Easy Mid Hard
Reference Random 0,98 1,19 1,11
Reference Optimos 1,17 1,03 0,92
SA 1,28 1,17 1,12
Tabu Search 0,94 1,02 0,84
PPO 0,87 1,06 0,94
Tabu Random 1,24 1,11 0,32
SA Random 1,29 1,27 1,11
PPO Random 0,95 1,05 0,88

Purity
Agent / Reference Easy Mid Hard
Reference Random 0,35 0,15 0,71
Reference Optimos 0,65 0,85 0,29
SA 0,35 0,00 0,14
Tabu Search 0,00 0,85 0,14
PPO 0,29 0,00 0,00
Tabu Random 0,00 0,00 0,00
SA Random 0,06 0,08 0,71
PPO Random 0,29 0,08 0,00

Avg Cycle Time
Agent / Reference Easy Mid Hard
Base 13.369.643,07 16.047.474,92 15.756.570,78
Reference 20.382.094,57 13.905.885,40 17.864.736,16
Reference Random 18.702.461,88 32.724.482,55 16.897.205,28
Reference Optimos 20.768.290,18 13.521.404,64 19.964.244,16
SA 19.893.274,06 28.990.146,10 19.213.421,38
Tabu Search 20.151.717,82 13.179.858,35 18.573.617,82
PPO 22.807.284,80 53.598.662,45 16.241.664,63
Tabu Random 17.216.198,55 29.225.441,19 18.454.174,16
SA Random 17.674.868,00 22.470.807,00 16.897.205,28
PPO Random 19.708.624,27 53.107.122,04 19.719.892,00

Best Cycle Time
Agent / Reference Easy Mid Hard
Base 13.369.643,07 16.047.474,92 15.756.570,78
Reference 15.788.366,74 10.521.791,54 14.582.036,26
Reference Random 14.811.805,42 14.796.008,26 14.582.036,26
Reference Optimos 15.788.366,74 10.521.791,54 14.914.682,03
SA 15.788.366,74 13.734.908,48 13.402.862,80
Tabu Search 16.655.749,35 10.521.791,54 14.914.682,03
PPO 13.369.643,07 16.357.230,91 15.756.570,78
Tabu Random 14.480.629,67 16.723.485,01 17.763.490,08
SA Random 14.811.805,42 15.523.152,37 14.582.036,26
PPO Random 16.639.415,98 14.796.008,26 15.756.570,78

Easy

Metric Plots

Individual charts:

Summary Table (Final Values)
Agent Steps Explored Solutions Potential New Base Solutions Average Cycle Time Min Cycle Time Average Batch Size Iteration Number Time per Step Total Optimization Time
Proximal Policy Optimization 2951 1513 2.29747e+07 1.65511e+07 3.71509 2960 27.4838 1,431min
(for 2951 Steps)
Proximal Policy Optimization Random 40 1292 1.97086e+07 1.66394e+07 3.69476 2141 6664.29 1,016min
(for 40 Steps)
Simulated Annealing 9996 380 5397 1.98933e+07 1.57884e+07 2.13291 436 1.81164 513min
(for 9996 Steps)
Simulated Annealing Random 680 283 0 1.77299e+07 1.48118e+07 2.02718 224 16.4456 178min
(for 680 Steps)
Tabu Search 2105 279 0 1.96246e+07 1.66557e+07 2.11111 107 1.12742 89min
(for 2105 Steps)
Tabu Search Random 35 9 0 1.63184e+07 1.44806e+07 2.11628 9 13.3734 4min
(for 35 Steps)
Pareto Front Images

Individual Pareto images:

Hard

Metric Plots

Individual charts:

Summary Table (Final Values)
Agent Steps Explored Solutions Potential New Base Solutions Average Cycle Time Min Cycle Time Average Batch Size Iteration Number Time per Step Total Optimization Time
Proximal Policy Optimization 995 1002 1.70208e+07 1.58872e+07 2.4 1005 8.21465 73min
(for 995 Steps)
Proximal Policy Optimization Random 1114 955 2.02035e+07 1.72073e+07 2.05263 1124 8.24061 141min
(for 1114 Steps)
Simulated Annealing 81 2 57 2.2491e+07 1.57653e+07 2.10574 4 0.001033 5min
(for 81 Steps)
Simulated Annealing Random 648 260 0 1.68972e+07 1.4582e+07 2.10256 208 12.569 198min
(for 648 Steps)
Tabu Search 978 21 0 1.8935e+07 1.49147e+07 2.12903 47 0.361706 167min
(for 978 Steps)
Tabu Search Random 44 10 0 1.86589e+07 1.57566e+07 2.09605 12 12.8511 12min
(for 44 Steps)
Pareto Front Images

Individual Pareto images:

Mid

Metric Plots

Individual charts:

Summary Table (Final Values)
Agent Steps Explored Solutions Potential New Base Solutions Average Cycle Time Min Cycle Time Average Batch Size Iteration Number Time per Step Total Optimization Time
Proximal Policy Optimization 1731 311 5.06741e+07 1.63572e+07 4.92711 1740 57.1054 1,424min
(for 1731 Steps)
Proximal Policy Optimization Random 31 2 2.06983e+07 1.87449e+07 2.46479 40 28.9958 14min
(for 31 Steps)
Simulated Annealing 9996 261 5965 2.84575e+07 1.37349e+07 4.65205 436 1.25878 736min
(for 9996 Steps)
Simulated Annealing Random 760 329 0 2.25602e+07 1.55232e+07 2.03125 245 13.5362 220min
(for 760 Steps)
Tabu Search 5119 251 0 1.33973e+07 1.05218e+07 2.53326 263 5.93512 297min
(for 5119 Steps)
Tabu Search Random 125 35 0 3.18784e+07 1.67235e+07 2.0061 39 10.9127 35min
(for 125 Steps)
Pareto Front Images

Individual Pareto images:

Insurance

INS (Acronym in the paper) - It originates from an insurance claims process, holding a high number of traces.

Analyzer Overview

Pareto Size
Agent / Reference Easy Mid Hard
Reference 102,00 35,00 9,00
Reference Random 49,00 18,00 11,00
Reference Optimos 83,00 35,00 9,00
SA 35,00 15,00 9,00
Tabu Search 66,00 24,00 9,00
PPO 34,00 19,00 6,00
Tabu Random 20,00 10,00 2,00
SA Random 42,00 15,00 4,00
PPO Random 23,00 15,00 13,00

Hyperarea Ratio
Agent / Reference Easy Mid Hard
Reference Random 1,00 0,96 1,00
Reference Optimos 0,86 1,00 1,00
SA 0,63 0,67 1,00
Tabu Search 0,86 0,65 1,00
PPO 0,84 0,99 1,00
Tabu Random 0,76 0,72 1,00
SA Random 1,00 0,96 1,00
PPO Random 0,73 0,83 1,00

Hausdorff
Agent / Reference Easy Mid Hard
Reference Random 820,72 2.021,48 405,81
Reference Optimos 20.828,96 300,91 0,00
SA 25.189,49 8.911,26 239,13
Tabu Search 20.873,41 9.904,22 514,92
PPO 22.266,42 1.265,45 6.938,30
Tabu Random 23.137,72 5.116,44 694,27
SA Random 1.089,10 2.175,18 731,99
PPO Random 22.317,59 2.574,28 360,41

Delta
Agent / Reference Easy Mid Hard
Reference Random 1,20 1,12 0,90
Reference Optimos 0,97 0,97 1,08
SA 0,98 1,00 1,21
Tabu Search 0,97 1,01 0,86
PPO 0,99 0,79 1,24
Tabu Random 0,96 0,96 0,69
SA Random 1,13 1,23 0,73
PPO Random 0,98 0,71 0,81

Purity
Agent / Reference Easy Mid Hard
Reference Random 0,19 0,11 0,00
Reference Optimos 0,81 0,89 1,00
SA 0,17 0,26 0,22
Tabu Search 0,64 0,34 0,67
PPO 0,01 0,34 0,22
Tabu Random 0,01 0,03 0,11
SA Random 0,17 0,11 0,11
PPO Random 0,01 0,03 0,11

Avg Cycle Time
Agent / Reference Easy Mid Hard
Base 21.523.074,51 21.367.016,55 21.992.001,65
Reference 22.163.701,21 22.480.273,77 21.980.061,32
Reference Random 22.520.861,70 22.715.030,13 22.230.347,40
Reference Optimos 21.940.447,08 22.319.156,40 21.980.061,32
SA 21.997.410,60 21.882.992,74 21.868.122,18
Tabu Search 21.931.262,97 22.084.117,64 22.034.900,76
PPO 21.866.011,73 22.512.018,90 22.017.415,53
Tabu Random 21.910.472,47 22.448.677,25 21.575.390,94
SA Random 22.575.855,21 22.727.193,86 21.591.259,18
PPO Random 21.976.390,66 22.504.743,76 22.192.879,69

Best Cycle Time
Agent / Reference Easy Mid Hard
Base 21.523.074,51 21.367.016,55 21.992.001,65
Reference 21.072.069,32 21.367.016,55 21.506.333,06
Reference Random 21.265.421,23 21.209.398,29 21.840.288,41
Reference Optimos 21.072.069,32 21.449.581,76 21.506.333,06
SA 20.944.858,00 21.367.016,55 21.221.099,75
Tabu Search 21.072.069,32 21.288.200,25 21.776.404,35
PPO 20.709.108,80 21.250.656,59 21.517.242,02
Tabu Random 21.285.666,80 21.367.016,55 21.370.047,01
SA Random 21.265.421,23 21.282.481,73 21.370.047,01
PPO Random 21.114.791,87 21.209.398,29 21.780.734,88

Easy

Metric Plots

Individual charts:

Summary Table (Final Values)
Agent Steps Explored Solutions Potential New Base Solutions Average Cycle Time Min Cycle Time Average Batch Size Iteration Number Time per Step Total Optimization Time
Proximal Policy Optimization 7031 2074 2.18687e+07 2.07091e+07 2.2981 7040 5.88667 718min
(for 7031 Steps)
Proximal Policy Optimization Random 6371 576 2.18484e+07 2.11148e+07 2.0819 6380 7.42354 718min
(for 6371 Steps)
Simulated Annealing 9996 331 531 2.20013e+07 2.09449e+07 2 675 1.37837 147min
(for 9996 Steps)
Simulated Annealing Random 1592 609 0 2.26663e+07 2.12654e+07 5.37885 532 2.87519 99min
(for 1592 Steps)
Tabu Search 9992 261 539 2.19604e+07 2.10721e+07 2 582 25.6315 159min
(for 9992 Steps)
Tabu Search Random 266 96 0 2.20979e+07 2.15495e+07 2 90 2.74988 16min
(for 266 Steps)
Pareto Front Images

Individual Pareto images:

Hard

Metric Plots

Individual charts:

Summary Table (Final Values)
Agent Steps Explored Solutions Potential New Base Solutions Average Cycle Time Min Cycle Time Average Batch Size Iteration Number Time per Step Total Optimization Time
Proximal Policy Optimization 3259 388 2.23003e+07 2.15172e+07 2 3269 6.66236 287min
(for 3259 Steps)
Proximal Policy Optimization Random 7361 650 2.22657e+07 2.18403e+07 2 7370 6.16649 718min
(for 7361 Steps)
Simulated Annealing 10008 385 33 2.1984e+07 2.12211e+07 2 693 0.0935161 162min
(for 10008 Steps)
Simulated Annealing Random 704 355 0 2.21125e+07 2.1791e+07 2.99432 236 3.75098 44min
(for 704 Steps)
Tabu Search 3862 117 1117 2.21161e+07 2.17764e+07 2 257 0.96359 60min
(for 3862 Steps)
Tabu Search Random 8 2 0 2.2355e+07 2.20561e+07 0 4 3.28029 0min
(for 8 Steps)
Pareto Front Images

Individual Pareto images:

Mid

Metric Plots

Individual charts:

Summary Table (Final Values)
Agent Steps Explored Solutions Potential New Base Solutions Average Cycle Time Min Cycle Time Average Batch Size Iteration Number Time per Step Total Optimization Time
Proximal Policy Optimization 5891 213 2.25286e+07 2.12507e+07 2.27108 5900 5.97208 718min
(for 5891 Steps)
Proximal Policy Optimization Random 2741 81 2.24371e+07 2.12094e+07 2.11444 2750 18.2748 716min
(for 2741 Steps)
Simulated Annealing 10006 372 135 2.19224e+07 2.14326e+07 2 691 0.402094 145min
(for 10006 Steps)
Simulated Annealing Random 821 389 0 2.30258e+07 2.19076e+07 2.95062 274 3.65792 51min
(for 821 Steps)
Tabu Search 7908 250 973 2.21005e+07 2.12882e+07 2 521 2.20827 125min
(for 7908 Steps)
Tabu Search Random 173 56 0 2.2328e+07 2.15111e+07 2 59 0.200568 10min
(for 173 Steps)
Pareto Front Images

Individual Pareto images:

Production

PRD (Acronym in the paper) corresponds to a manufacturing process extracted by an Enterprise Resource Planning (ERP) system, where tasks are individual steps or ‘‘stations’’ in the manufacturing workflow. Access Link

Analyzer Overview

Pareto Size
Agent / Reference Easy Mid Hard
Reference 80,00 44,00 13,00
Reference Random 76,00 41,00 12,00
Reference Optimos 69,00 44,00 16,00
SA 37,00 30,00 12,00
Tabu Search 47,00 44,00 18,00
PPO 50,00 41,00 8,00
Tabu Random 41,00 15,00 8,00
SA Random 35,00 17,00 8,00
PPO Random 45,00 39,00 13,00

Hyperarea Ratio
Agent / Reference Easy Mid Hard
Reference Random 0,96 0,86 1,00
Reference Optimos 0,99 1,00 1,00
SA 0,68 0,80 0,98
Tabu Search 0,94 0,88 1,00
PPO 0,94 0,94 0,98
Tabu Random 0,78 0,60 0,98
SA Random 0,73 0,68 1,00
PPO Random 0,90 0,84 0,98

Hausdorff
Agent / Reference Easy Mid Hard
Reference Random 11.943,84 57.288,56 13.093,12
Reference Optimos 1.231,15 0,00 16.105,32
SA 44.380,42 145.330,56 32.912,96
Tabu Search 32.572,43 96.853,24 16.542,56
PPO 3.905,48 11.508,62 54.021,29
Tabu Random 44.322,42 140.492,35 35.702,53
SA Random 9.194,47 141.978,28 13.963,67
PPO Random 19.913,55 58.921,94 25.432,49

Delta
Agent / Reference Easy Mid Hard
Reference Random 0,97 0,96 1,33
Reference Optimos 0,95 1,09 0,99
SA 0,97 0,97 1,17
Tabu Search 0,88 1,00 1,06
PPO 0,97 0,98 0,99
Tabu Random 0,97 1,00 1,01
SA Random 1,25 0,97 1,15
PPO Random 0,83 0,97 1,37

Purity
Agent / Reference Easy Mid Hard
Reference Random 0,53 0,00 0,31
Reference Optimos 0,47 1,00 0,69
SA 0,04 0,09 0,00
Tabu Search 0,26 0,61 0,54
PPO 0,17 0,30 0,15
Tabu Random 0,45 0,00 0,00
SA Random 0,07 0,00 0,23
PPO Random 0,00 0,00 0,08

Avg Cycle Time
Agent / Reference Easy Mid Hard
Base 42.044.521,00 41.035.979,10 41.461.760,95
Reference 42.190.396,40 42.625.614,35 42.689.935,34
Reference Random 42.366.701,18 42.561.152,22 42.480.832,52
Reference Optimos 42.179.962,73 42.625.614,35 42.651.001,36
SA 42.295.871,86 42.079.724,37 42.323.845,15
Tabu Search 42.150.131,94 42.650.766,40 42.692.566,31
PPO 42.229.110,27 42.672.010,76 42.214.365,71
Tabu Random 42.198.516,53 41.983.662,10 41.447.310,40
SA Random 42.334.991,62 42.370.681,44 42.297.213,99
PPO Random 42.507.066,35 42.483.845,26 42.512.857,09

Best Cycle Time
Agent / Reference Easy Mid Hard
Base 42.044.521,00 41.035.979,10 41.461.760,95
Reference 40.511.363,26 40.891.617,05 41.496.367,12
Reference Random 40.511.363,26 40.924.274,21 41.510.903,62
Reference Optimos 40.615.200,00 40.891.617,05 41.496.367,12
SA 41.215.377,05 40.649.684,84 40.341.465,75
Tabu Search 40.889.476,81 40.891.617,05 41.222.681,50
PPO 40.297.020,43 40.937.649,95 41.448.152,63
Tabu Random 40.511.363,26 40.649.684,84 40.341.465,75
SA Random 41.149.958,32 40.957.056,09 40.341.465,75
PPO Random 41.098.342,91 40.403.956,28 41.510.903,62

Easy

Metric Plots

Individual charts:

Summary Table (Final Values)
Agent Steps Explored Solutions Potential New Base Solutions Average Cycle Time Min Cycle Time Average Batch Size Iteration Number Time per Step Total Optimization Time
Proximal Policy Optimization 5181 433 4.22143e+07 4.0297e+07 2.51078 5190 8.38344 718min
(for 5181 Steps)
Proximal Policy Optimization Random 5407 715 4.25095e+07 4.10983e+07 2.15238 5417 6.30004 538min
(for 5407 Steps)
Simulated Annealing 10001 909 4850 4.24021e+07 4.12154e+07 2 510 0.18976 85min
(for 10001 Steps)
Simulated Annealing Random 2626 1076 22 4.23852e+07 4.115e+07 3.20748 868 1.39887 94min
(for 2626 Steps)
Tabu Search 9991 1613 1150 4.21807e+07 4.08895e+07 2.91931 470 0.0067332 92min
(for 9991 Steps)
Tabu Search Random 2378 967 0 4.22467e+07 4.05114e+07 2.42581 790 1.83766 82min
(for 2378 Steps)
Pareto Front Images

Individual Pareto images:

Hard

Metric Plots

Individual charts:

Summary Table (Final Values)
Agent Steps Explored Solutions Potential New Base Solutions Average Cycle Time Min Cycle Time Average Batch Size Iteration Number Time per Step Total Optimization Time
Proximal Policy Optimization 5999 198 4.26699e+07 4.14482e+07 2.69663 6009 4.8629 501min
(for 5999 Steps)
Proximal Policy Optimization Random 9991 454 4.27135e+07 4.15109e+07 2.83544 10000 4.04198 683min
(for 9991 Steps)
Simulated Annealing 10006 1142 478 4.275e+07 4.14388e+07 13.5676 478 0.131001 77min
(for 10006 Steps)
Simulated Annealing Random 839 363 0 4.25681e+07 4.18752e+07 16.7407 274 1.79834 30min
(for 839 Steps)
Tabu Search 6988 421 1607 4.27518e+07 4.12227e+07 2.6 349 0.196693 51min
(for 6988 Steps)
Tabu Search Random 128 38 0 4.20802e+07 4.10975e+07 2.61017 40 1.43653 3min
(for 128 Steps)
Pareto Front Images

Individual Pareto images:

Mid

Metric Plots

Individual charts:

Summary Table (Final Values)
Agent Steps Explored Solutions Potential New Base Solutions Average Cycle Time Min Cycle Time Average Batch Size Iteration Number Time per Step Total Optimization Time
Proximal Policy Optimization 8051 2676 4.27068e+07 4.09376e+07 3.06264 8060 5.65617 718min
(for 8051 Steps)
Proximal Policy Optimization Random 8751 1528 4.25273e+07 4.0404e+07 2.1759 8760 4.94335 718min
(for 8751 Steps)
Simulated Annealing 10008 1185 4965 4.21387e+07 4.06497e+07 3.35955 533 0.151647 84min
(for 10008 Steps)
Simulated Annealing Random 1067 494 0 4.25709e+07 4.1036e+07 2.73571 353 2.06465 35min
(for 1067 Steps)
Tabu Search 9996 2104 1121 4.27049e+07 4.08916e+07 2.44721 528 1.03266 83min
(for 9996 Steps)
Tabu Search Random 272 107 0 4.21376e+07 4.09571e+07 2.53165 88 0.154355 8min
(for 272 Steps)
Pareto Front Images

Individual Pareto images:

Sepsis Das

SEP (Acronym in the paper) records patient pathways with suspected sepsis, a life-threatening infection, over one year in a hospital.

Analyzer Overview

Pareto Size
Agent / Reference Easy Mid Hard
Reference 27,00 8,00 7,00
Reference Random 19,00 5,00 7,00
Reference Optimos 25,00 12,00 5,00
SA 2,00 8,00 8,00
Tabu Search 11,00 14,00 2,00
PPO 25,00 10,00 3,00
Tabu Random 9,00 1,00 1,00
SA Random 15,00 5,00 12,00
PPO Random 7,00 10,00 5,00

Hyperarea Ratio
Agent / Reference Easy Mid Hard
Reference Random 1,00 1,00 1,00
Reference Optimos 1,00 0,94 0,95
SA 0,64 0,56 0,95
Tabu Search 1,00 0,85 0,95
PPO 1,00 0,93 0,95
Tabu Random 0,91 0,51 0,95
SA Random 1,00 1,00 1,00
PPO Random 0,75 0,59 0,95

Hausdorff
Agent / Reference Easy Mid Hard
Reference Random 18.889,32 11.197,12 0,00
Reference Optimos 13.178,20 342.611,80 827.929,58
SA 46.659,30 559.260,76 763.095,91
Tabu Search 45.575,56 206.833,75 179.710,58
PPO 18.746,65 369.574,35 311.571,90
Tabu Random 60.559,17 640.252,01 218.352,75
SA Random 18.465,39 11.197,12 0,00
PPO Random 58.972,12 1.385.123,39 287.407,49

Delta
Agent / Reference Easy Mid Hard
Reference Random 1,03 1,18 0,44
Reference Optimos 0,89 0,88 0,71
SA 0,88 0,91 0,84
Tabu Search 1,39 0,71 0,86
PPO 0,84 0,95 0,81
Tabu Random 0,98 0,00 0,00
SA Random 0,84 1,18 0,44
PPO Random 0,95 1,11 0,84

Purity
Agent / Reference Easy Mid Hard
Reference Random 0,07 0,62 1,00
Reference Optimos 0,93 0,38 0,00
SA 0,00 0,00 0,00
Tabu Search 0,33 0,38 0,00
PPO 0,59 0,00 0,00
Tabu Random 0,04 0,00 0,00
SA Random 0,04 0,62 1,00
PPO Random 0,00 0,00 0,00

Avg Cycle Time
Agent / Reference Easy Mid Hard
Base 81.884.663,83 78.354.184,84 77.382.542,97
Reference 48.953.445,18 90.904.175,17 118.667.196,38
Reference Random 49.748.043,43 100.127.438,39 118.667.196,38
Reference Optimos 48.887.886,84 86.763.900,52 79.868.329,19
SA 48.981.957,29 75.362.790,22 79.854.360,14
Tabu Search 49.340.890,25 78.094.062,27 77.669.925,99
PPO 48.852.202,85 92.318.161,88 80.056.716,20
Tabu Random 49.408.974,71 75.073.704,05 77.983.503,98
SA Random 49.981.451,71 100.127.438,39 118.667.196,38
PPO Random 48.593.383,09 74.766.027,53 79.378.748,37

Best Cycle Time
Agent / Reference Easy Mid Hard
Base 81.884.663,83 78.354.184,84 77.382.542,97
Reference 47.054.511,43 71.528.257,84 95.169.098,95
Reference Random 47.054.511,43 93.615.262,32 95.169.098,95
Reference Optimos 47.409.540,37 71.528.257,84 77.504.818,50
SA 47.433.718,09 73.779.573,57 78.350.481,99
Tabu Search 47.409.540,37 71.528.257,84 77.504.818,50
PPO 45.437.286,89 85.317.002,71 79.791.185,01
Tabu Random 47.054.511,43 75.073.704,05 77.983.503,98
SA Random 47.241.669,76 93.615.262,32 95.169.098,95
PPO Random 46.879.543,35 71.455.570,34 77.905.095,08

Easy

Metric Plots

Individual charts:

Summary Table (Final Values)
Agent Steps Explored Solutions Potential New Base Solutions Average Cycle Time Min Cycle Time Average Batch Size Iteration Number Time per Step Total Optimization Time
Proximal Policy Optimization 4821 7 4.88522e+07 4.54373e+07 2.65374 4830 8.7928 716min
(for 4821 Steps)
Proximal Policy Optimization Random 2839 18 4.88577e+07 4.68795e+07 2.28247 2849 10.2445 445min
(for 2839 Steps)
Simulated Annealing 81 1 69 4.98798e+07 4.98798e+07 2.1224 4 0.0010123 1min
(for 81 Steps)
Simulated Annealing Random 2622 1180 1008 5.0022e+07 4.72417e+07 3.66416 868 0.631759 280min
(for 2622 Steps)
Tabu Search 101 1 30 4.93868e+07 4.81111e+07 2.46034 5 0.00157211 1min
(for 101 Steps)
Tabu Search Random 2501 1126 1136 4.91912e+07 4.70545e+07 2.37901 830 6.26755 298min
(for 2501 Steps)
Pareto Front Images

Individual Pareto images:

Hard

Metric Plots

Individual charts:

Summary Table (Final Values)
Agent Steps Explored Solutions Potential New Base Solutions Average Cycle Time Min Cycle Time Average Batch Size Iteration Number Time per Step Total Optimization Time
Proximal Policy Optimization 2945 9 8.00567e+07 7.97912e+07 2.32697 2955 7.66747 403min
(for 2945 Steps)
Proximal Policy Optimization Random 3855 15 7.93788e+07 7.79051e+07 2.81407 3865 9.76478 510min
(for 3855 Steps)
Simulated Annealing 131 2 114 7.80104e+07 7.74798e+07 2.10698 7 0.0012939 2min
(for 131 Steps)
Simulated Annealing Random 2231 926 36 1.16187e+08 9.51691e+07 3.42619 740 6.37437 297min
(for 2231 Steps)
Tabu Search 121 1 20 8.00764e+07 7.80771e+07 2.1309 6 0.00122361 2min
(for 121 Steps)
Tabu Search Random 17 1 0 7.79835e+07 7.79835e+07 2.11549 3 3.10532 0min
(for 17 Steps)
Pareto Front Images

Individual Pareto images:

Mid

Metric Plots

Individual charts:

Summary Table (Final Values)
Agent Steps Explored Solutions Potential New Base Solutions Average Cycle Time Min Cycle Time Average Batch Size Iteration Number Time per Step Total Optimization Time
Proximal Policy Optimization 5207 20 9.44429e+07 8.5317e+07 2.51837 5217 8.0266 705min
(for 5207 Steps)
Proximal Policy Optimization Random 5231 47 7.47033e+07 7.14556e+07 2.55251 5240 8.67956 717min
(for 5231 Steps)
Simulated Annealing 141 2 152 7.4814e+07 7.4814e+07 2.7255 8 2.00736 2min
(for 141 Steps)
Simulated Annealing Random 2402 1045 0 1.00127e+08 9.36153e+07 3.30269 798 0.234691 293min
(for 2402 Steps)
Tabu Search 121 1 18 7.27851e+07 7.11963e+07 2.30249 6 0.0011708 2min
(for 121 Steps)
Tabu Search Random 29 4 0 7.50737e+07 7.50737e+07 3.06194 7 5.81616 1min
(for 29 Steps)
Pareto Front Images

Individual Pareto images:

Trafic Das

TRF (Acronym in the paper) - A road fines (Traffic) log that comes from an Italian local police information system handling traffic fines.

Analyzer Overview

Pareto Size
Agent / Reference Easy Mid Hard
Reference 10,00 16,00 22,00
Reference Random 8,00 15,00 22,00
Reference Optimos 5,00 15,00 32,00
SA 7,00 3,00 9,00
Tabu Search 4,00 6,00 5,00
PPO 5,00 17,00 29,00
Tabu Random 5,00 15,00 6,00
SA Random 4,00 3,00 6,00
PPO Random 8,00 15,00 22,00

Hyperarea Ratio
Agent / Reference Easy Mid Hard
Reference Random 1,00 1,00 1,00
Reference Optimos 1,00 1,00 1,00
SA 0,93 0,96 1,00
Tabu Search 0,94 0,97 1,00
PPO 1,00 1,00 1,00
Tabu Random 0,97 0,99 1,00
SA Random 0,96 1,00 1,00
PPO Random 1,00 1,00 1,00

Hausdorff
Agent / Reference Easy Mid Hard
Reference Random 30.622,38 21.885,52 0,00
Reference Optimos 13.820,94 227.175,14 148.348,66
SA 109.147,00 248.862,10 309.816,74
Tabu Search 110.960,66 237.025,86 469.460,00
PPO 13.820,94 227.175,14 198.400,91
Tabu Random 108.571,56 114.943,76 1.203.658,64
SA Random 110.626,92 96.732,90 331.225,12
PPO Random 30.622,38 47.134,59 166.156,72

Delta
Agent / Reference Easy Mid Hard
Reference Random 1,51 1,01 0,97
Reference Optimos 1,40 1,33 0,88
SA 0,81 0,98 1,27
Tabu Search 0,90 0,93 0,95
PPO 1,40 1,33 0,85
Tabu Random 0,79 0,98 1,22
SA Random 0,83 0,50 0,91
PPO Random 1,51 1,01 0,80

Purity
Agent / Reference Easy Mid Hard
Reference Random 0,70 0,31 1,00
Reference Optimos 0,30 0,69 0,00
SA 0,00 0,00 0,00
Tabu Search 0,00 0,00 0,00
PPO 0,30 0,69 0,00
Tabu Random 0,00 0,00 0,23
SA Random 0,00 0,12 0,05
PPO Random 0,70 0,19 0,73

Avg Cycle Time
Agent / Reference Easy Mid Hard
Base 4.406.883,21 4.237.002,88 4.235.563,50
Reference 1.245.508,53 3.236.511,47 11.249.272,88
Reference Random 832.853,83 3.020.570,10 11.249.272,88
Reference Optimos 2.558.990,90 12.385.577,44 11.269.135,07
SA 2.334.547,68 4.668.437,81 60.213.221,47
Tabu Search 2.324.422,20 10.161.927,77 4.546.275,16
PPO 2.558.990,90 12.385.577,44 12.641.990,69
Tabu Random 1.781.635,13 15.554.223,59 54.923.323,88
SA Random 2.594.287,50 6.540.162,08 19.816.682,85
PPO Random 832.853,83 3.400.742,03 11.422.093,12

Best Cycle Time
Agent / Reference Easy Mid Hard
Base 4.406.883,21 4.237.002,88 4.235.563,50
Reference 89.304,46 520.078,31 2.594.306,70
Reference Random 89.304,46 520.078,31 2.594.306,70
Reference Optimos 607.541,34 1.471.187,97 3.890.929,73
SA 1.469.943,01 4.150.208,86 3.890.929,73
Tabu Search 1.903.540,02 5.703.105,99 4.147.636,37
PPO 607.541,34 1.471.187,97 4.235.563,50
Tabu Random 866.616,18 1.471.969,73 2.940.590,48
SA Random 1.730.491,24 520.078,31 2.594.306,70
PPO Random 89.304,46 1.298.623,46 4.235.563,50

Easy

Metric Plots

Individual charts:

Summary Table (Final Values)
Agent Steps Explored Solutions Potential New Base Solutions Average Cycle Time Min Cycle Time Average Batch Size Iteration Number Time per Step Total Optimization Time
Proximal Policy Optimization 4808 136 2.55899e+06 607541 21.3091 4818 5.81425 415min
(for 4808 Steps)
Proximal Policy Optimization Random 6224 414 832854 89304.5 6.77143 6234 5.06246 427min
(for 6224 Steps)
Simulated Annealing 9992 427 2248 2.33455e+06 1.46994e+06 2.56383 577 4.71075 119min
(for 9992 Steps)
Simulated Annealing Random 2614 1327 243 2.59429e+06 1.73049e+06 3.97904 868 4.64431 186min
(for 2614 Steps)
Tabu Search 7057 216 3412 2.31422e+06 1.90354e+06 3.61417 485 2.00739 101min
(for 7057 Steps)
Tabu Search Random 2615 1405 383 1.78164e+06 866616 4.03289 868 2.71143 153min
(for 2615 Steps)
Pareto Front Images

Individual Pareto images:

Hard

Metric Plots

Individual charts:

Summary Table (Final Values)
Agent Steps Explored Solutions Potential New Base Solutions Average Cycle Time Min Cycle Time Average Batch Size Iteration Number Time per Step Total Optimization Time
Proximal Policy Optimization 1581 44 1.23984e+07 3.63188e+06 7.29797 1590 46.16 712min
(for 1581 Steps)
Proximal Policy Optimization Random 3811 280 1.14576e+07 8.03874e+06 9.57933 3820 12.2776 716min
(for 3811 Steps)
Simulated Annealing 9997 573 773 6.02035e+07 3.89093e+06 2.17771 598 0.238621 142min
(for 9997 Steps)
Simulated Annealing Random 2581 1185 165 3.05005e+07 2.59431e+06 2.08344 857 5.73251 298min
(for 2581 Steps)
Tabu Search 2977 181 1214 4.54628e+06 4.14764e+06 2.01762 186 0.0343043 47min
(for 2977 Steps)
Tabu Search Random 1286 600 0 5.49233e+07 2.94059e+06 2.5 426 3.56618 184min
(for 1286 Steps)
Pareto Front Images

Individual Pareto images:

Mid

Metric Plots

Individual charts:

Summary Table (Final Values)
Agent Steps Explored Solutions Potential New Base Solutions Average Cycle Time Min Cycle Time Average Batch Size Iteration Number Time per Step Total Optimization Time
Proximal Policy Optimization 8001 170 1.15895e+07 1.47119e+06 3.97139 8010 5.28506 717min
(for 8001 Steps)
Proximal Policy Optimization Random 7171 146 3.52303e+06 1.29862e+06 49.9739 7180 5.20373 717min
(for 7171 Steps)
Simulated Annealing 9998 522 1045 4.66844e+06 4.15021e+06 2.02184 573 0.437328 197min
(for 9998 Steps)
Simulated Annealing Random 2614 1160 119 6.54016e+06 520078 2.102 868 6.59526 258min
(for 2614 Steps)
Tabu Search 5098 229 2118 1.15793e+07 5.70311e+06 2.95782 276 0.121986 61min
(for 5098 Steps)
Tabu Search Random 2615 1306 723 1.55542e+07 1.47197e+06 3.90977 868 4.81121 188min
(for 2615 Steps)
Pareto Front Images

Individual Pareto images:

Re-running the evaluation & getting the results

Running the evaluation

  • After following the steps in Installation, you can just run the scripts in the o2_evaluation/scripts-folder.
  • The names of the scripts are self-explanatory, e.g. insurance_proximal_policy_optimization_hard.sh will run the proximal policy optimization agent on the insurance scenario with the hard mode.
  • The scripts are designed to be run in a conda enviorment named opti2, please modify the scripts if you want to use a different environment.
  • You may of course also run the optimizer with the current python version, for that you may modify the script files. E.g. change
export LD_LIBRARY_PATH="$HOME/lib"
module load any/python/3.8.3-conda
conda activate opti2

conda run -n opti2 --no-capture-output python ./o2_evaluation/data_collector.py \
    --name "insurance_hard" \
    --active-scenarios "insurance" \
    --agents "Proximal Policy Optimization" \
    ....

to

python ./o2_evaluation/data_collector.py \
    --name "insurance_hard" \
    --active-scenarios "insurance" \
    --agents "Proximal Policy Optimization" \
    ....
  • You can use the data_collector cli tool to create any other scenario you want to evaluate. You may use the -h flag to see the available options. E.g.
python ./o2_evaluation/data_collector.py -h
  • The Results will be saved in the stores/run_<timestamp> folder. There you find a pickled Store object, that contains all the application state for the whole optimization run.
  • Refer to the following sections to see on how to parse that to a human readable format.

Analyze the results

  • After running the evaluation, you can analyze the results by running the o2_evaluation/data_analyzer.py script.
  • This Script will look at all the data in the o2_evaluation/redumped_stores folder and create a summary of the results.
    • Before running the script, you may want to copy over the stores_* and solutions_* files from your stores folder to the redumped_stores folder.
    • Also you should copy the evaluations and states folders to the root of the repository.
  • After running the analyzer, the results will be printed to the console and saved to the o2_evaluation/analyzer_report.ssv file.
  • Finally you can create a markdown report with the results by running the o2_evaluation/markdown_creator.py script.

Installation & Basic Usage

Installation

  1. Create a fresh Python 3.10 virtual environment, e.g. with conda create --name optimos-python python=3.10
  2. Install poetry on your system by following the offical guide. Make sure, poetry is NOT installed in the virtual environment.
  3. Activate the environment, e.g. with conda activate optimos-python
  4. Run poetry install in the root directory of this repository

Standalone Usage

For now there is no CLI interface for the optimizer, so you have to modify the main.py script to your needs

  1. Open main.py in your editor
  2. Change the timetable_path, constraints_path and bpmn_path to your needs.
    • If you need a basic set of constraints for your model, you can use the create_constraints.py script
  3. Run python main.py to start the optimizer, you will see the output and process in the console
  4. If you want to change settings like the number of iterations you can do so in the main.py script as well
  5. LEGACY OPTIMOS SUPPORT: If you want optimos_v2 to behave like the old optimos, you can set the optimos_legacy_mode setting to True. This will disable all batching optimizations.

Usage within PIX (docker)

  1. Install Docker and Docker-Compose, refer to the official website for installation instructions
  2. Clone the pix-portal repository (git clone https://github.com/AutomatedProcessImprovement/pix-portal.git)
  3. Checkout the integrate-optimos-v2 branch (git checkout integrate-optimos-v2)
  4. Create the following secrets:
    • frontend/pix-web-ui/.session.secret
    • backend/services/api-server/.superuser_email.secret
    • backend/services/api-server/.system_email.secret
    • backend/services/api-server/.superuser_password.secret
    • backend/services/api-server/.key.secret
    • backend/services/api-server/.system_password.secret
    • For local development/testing you can just fill them with example values, e.g. "secret" or "[email protected]".
    • Furthermore create the following files: backend/workers/mail/.secret_gmail_username & backend/workers/mail/.secret_gmail_app_password; Those are the credentials for the gmail account that sends out mails. The Password is a gmail app password, not the actual password. If you don't want to send out mails, you still need to create the files, but can enter any value.
  5. Create the following .env files:
    • backend/workers/mail/.env
    • backend/workers/kronos/.env
    • backend/workers/simulation-prosimos/.env
    • backend/workers/bps-discovery-simod/.env
    • backend/workers/optimos/.env
    • backend/services/api-server/.env
    • backend/services/kronos/.env
    • You will find a .env.example file in each of the folders, you can copy those file and rename them to .env
  6. Run docker compose up --build in the root directory of the pix-portal repository. You may add the -d flag to run it in detached mode, so you can close the terminal afterwards.
  7. This will take some time
  8. Open your browser and go to localhost:9999. You can use the credentials from the .superuser_email.secret and .superuser_password.secret files to login.

Usage within PIX (local + debugging)

  1. Do all of the Usage within PIX (docker) steps above
  2. Stop the docker-based optimos: docker compose stop optimos
  3. Modify the backend/workers/optimos/.env file to use the local host instead of the docker container, you can rename .env.example-local to .env for that
  4. Create a new Python 3.10 virtual environment (e.g. with conda create --name optimos-python python=3.10)
  5. Activate the environment, e.g. with conda activate optimos-python
  6. Navigate to the backend/workers/optimos folder in the pix repo
  7. Install the dependencies with poetry install
  8. Start the optimos worker with python python optimos_worker/main.py
  9. Alteratively: Start the optimos worker with the vs code debugger by running the Launch Optimos Worker configuration (most likely you'll need to adjust the python binary used there, you can do that in the .vscode/launch.json file)

Development

Updating the Optimos Version used by PIX

If you have pushed commits to the master, this change needs to be picked up by PIX, to do that do the following:

  1. Navigate to the folder backend/workers/optimos in the pix project
  2. Update the poetry.lock file: poetry lock
  3. Rebuild & restart the optimos container: docker compose up -d --build optimos

Running Tests

To run the tests, run pytest. The tests should also automatically show up in the test explorer of your IDE. (For VSCode, you need to install the Python extension)

Collecting Coverage

To collect coverage, run pytest --cov --cov-report=lcov:lcov.info --cov-report=term. You can display it e.g. with the vscode extension Coverage Gutters.

Docs

While the code should be documented in most places, you can find additional information on e.g. the architecture in the docs folder

Improvements over Legacy Optimos

  • Support to optimize Batching
  • Fully Typed
  • Unit Tested (with ~90% coverage)
  • Follows a Action-Store-Reducer pattern, similar to Flux
  • Multi-Threaded at important parts, takes cpu core count of host machine into account
  • Almost all public interfaces are documented
  • Class-Based (Not a huge monolithic script)
  • No throwaway file creation; Everything in memory
  • Immutable Data Structures, so no change to the timetable is ever unexpected

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The next version of Optimos, an Resource, Roster & Batching optimizer using Prosimos simulator

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