Google OR-Tools was used to solve the problem.
Note: For a simpler solution using Histograms and a cut-ff threshold, check out this branch.
Results:
Processing dataset a_an_example...
Solution #0: time = 0.00 s. Objective Value: 2
Objective value: 2 in 0.0142506 ms
Score: 2
Processing dataset b_basic...
Solution #0: time = 0.00 s. Objective Value: 5
Objective value: 5 in 0.0177235 ms
Score: 5
Processing dataset c_coarse...
Solution #0: time = 0.00 s. Objective Value: 5
Objective value: 5 in 0.015345300000000001 ms
Score: 5
Processing dataset d_difficult...
Solution #0: time = 3.08 s. Objective Value: 1502
Solution #1: time = 3.25 s. Objective Value: 1508
Solution #2: time = 3.34 s. Objective Value: 1515
Solution #3: time = 3.43 s. Objective Value: 1537
Solution #4: time = 3.46 s. Objective Value: 1543
Solution #5: time = 3.66 s. Objective Value: 1573
Solution #6: time = 3.92 s. Objective Value: 1585
Solution #7: time = 4.23 s. Objective Value: 1587
Solution #8: time = 4.52 s. Objective Value: 1595
Solution #9: time = 5.74 s. Objective Value: 1605
Solution #10: time = 6.13 s. Objective Value: 1610
Solution #11: time = 6.24 s. Objective Value: 1613
Solution #12: time = 6.33 s. Objective Value: 1614
Solution #13: time = 6.38 s. Objective Value: 1626
Solution #14: time = 6.52 s. Objective Value: 1627
Solution #15: time = 8.10 s. Objective Value: 1671
Solution #16: time = 8.50 s. Objective Value: 1673
Solution #17: time = 9.03 s. Objective Value: 1679
Solution #18: time = 9.25 s. Objective Value: 1683
Solution #19: time = 10.38 s. Objective Value: 1691
Solution #20: time = 11.05 s. Objective Value: 1692
Solution #21: time = 11.24 s. Objective Value: 1697
Solution #22: time = 11.50 s. Objective Value: 1698
Solution #23: time = 11.63 s. Objective Value: 1702
Solution #24: time = 11.98 s. Objective Value: 1703
Solution #25: time = 13.92 s. Objective Value: 1719
Solution #26: time = 14.61 s. Objective Value: 1721
Solution #27: time = 15.00 s. Objective Value: 1723
Solution #28: time = 16.85 s. Objective Value: 1724
Solution #29: time = 16.98 s. Objective Value: 1802
Solution #30: time = 21.84 s. Objective Value: 1803
Solution #31: time = 32.88 s. Objective Value: 1804
Solution #32: time = 44.03 s. Objective Value: 1805
Objective value: 1805 in 100.16756332300001 ms
Score: 1805
Processing dataset e_elaborate...
Solution #0: time = 1.80 s. Objective Value: 1669
Solution #1: time = 1.90 s. Objective Value: 1670
Solution #2: time = 1.93 s. Objective Value: 1707
Solution #3: time = 2.44 s. Objective Value: 1716
Solution #4: time = 2.86 s. Objective Value: 1733
Solution #5: time = 3.12 s. Objective Value: 1776
Solution #6: time = 3.25 s. Objective Value: 1801
Solution #7: time = 3.45 s. Objective Value: 1806
Solution #8: time = 3.59 s. Objective Value: 1823
Solution #9: time = 4.95 s. Objective Value: 1855
Solution #10: time = 5.82 s. Objective Value: 1863
Solution #11: time = 6.03 s. Objective Value: 1871
Solution #12: time = 6.17 s. Objective Value: 1876
Solution #13: time = 6.34 s. Objective Value: 1891
Solution #14: time = 6.90 s. Objective Value: 1908
Solution #15: time = 7.09 s. Objective Value: 1913
Solution #16: time = 8.36 s. Objective Value: 1926
Solution #17: time = 8.48 s. Objective Value: 1935
Solution #18: time = 9.03 s. Objective Value: 1939
Solution #19: time = 9.68 s. Objective Value: 1944
Solution #20: time = 9.88 s. Objective Value: 1951
Solution #21: time = 10.10 s. Objective Value: 1958
Solution #22: time = 10.27 s. Objective Value: 1963
Solution #23: time = 11.46 s. Objective Value: 1971
Solution #24: time = 13.08 s. Objective Value: 1975
Solution #25: time = 13.83 s. Objective Value: 1982
Solution #26: time = 14.15 s. Objective Value: 1983
Solution #27: time = 14.33 s. Objective Value: 1984
Solution #28: time = 14.48 s. Objective Value: 1988
Solution #29: time = 15.18 s. Objective Value: 1993
Solution #30: time = 15.34 s. Objective Value: 1994
Solution #31: time = 16.88 s. Objective Value: 1996
Solution #32: time = 17.08 s. Objective Value: 1997
Solution #33: time = 17.28 s. Objective Value: 2000
Solution #34: time = 17.71 s. Objective Value: 2002
Solution #35: time = 22.14 s. Objective Value: 2005
Solution #36: time = 23.39 s. Objective Value: 2007
Solution #37: time = 24.45 s. Objective Value: 2008
Solution #38: time = 24.50 s. Objective Value: 2009
Solution #39: time = 25.12 s. Objective Value: 2010
Solution #40: time = 25.26 s. Objective Value: 2011
Solution #41: time = 26.05 s. Objective Value: 2012
Solution #42: time = 26.66 s. Objective Value: 2014
Solution #43: time = 26.85 s. Objective Value: 2016
Solution #44: time = 27.01 s. Objective Value: 2017
Solution #45: time = 29.16 s. Objective Value: 2018
Solution #46: time = 30.02 s. Objective Value: 2019
Solution #47: time = 32.04 s. Objective Value: 2020
Solution #48: time = 34.81 s. Objective Value: 2021
Solution #49: time = 36.54 s. Objective Value: 2023
Solution #50: time = 37.83 s. Objective Value: 2024
Solution #51: time = 39.48 s. Objective Value: 2025
Solution #52: time = 41.51 s. Objective Value: 2027
Solution #53: time = 45.07 s. Objective Value: 2028
Solution #54: time = 46.74 s. Objective Value: 2029
Solution #55: time = 47.28 s. Objective Value: 2030
Solution #56: time = 47.48 s. Objective Value: 2031
Solution #57: time = 52.63 s. Objective Value: 2032
Solution #58: time = 59.26 s. Objective Value: 2033
Solution #59: time = 63.61 s. Objective Value: 2034
Solution #60: time = 65.73 s. Objective Value: 2035
Solution #61: time = 67.30 s. Objective Value: 2036
Solution #62: time = 101.06 s. Objective Value: 2037
Solution #63: time = 107.98 s. Objective Value: 2038
Solution #64: time = 115.31 s. Objective Value: 2039
Solution #65: time = 119.29 s. Objective Value: 2040
Solution #66: time = 121.34 s. Objective Value: 2041
Solution #67: time = 128.12 s. Objective Value: 2042
Solution #68: time = 130.21 s. Objective Value: 2044
Solution #69: time = 164.64 s. Objective Value: 2045
Solution #70: time = 175.38 s. Objective Value: 2046
Solution #71: time = 190.95 s. Objective Value: 2047
Solution #72: time = 207.98 s. Objective Value: 2048
Solution #73: time = 236.81 s. Objective Value: 2049
Solution #74: time = 287.57 s. Objective Value: 2050
Solution #75: time = 288.56 s. Objective Value: 2051
Solution #76: time = 295.44 s. Objective Value: 2052
Solution #77: time = 315.96 s. Objective Value: 2053
Solution #78: time = 332.38 s. Objective Value: 2054
Solution #79: time = 335.28 s. Objective Value: 2056
Objective value: 2056 in 600.918113649 ms
Score: 2056
Done.