CP-Sat: Python 3.6.9, ortools 8.0.8283 wrong optimization result #2253

ZhiWeiCui · 2020-12-02T08:39:13Z

ZhiWeiCui
Dec 2, 2020

Model:

The 40 cities are divided into num_groups clusters, and the total distance from each city to the cluster center is the shortest.The maximum number of each cluster is num_max, and the minimum number is num_min.The result clearly violated the constraints in case1 and case2. The result of case3 is correct.

Case:

case 1:

    num_groups = 5
    num_min = 5
    num_max = 10

result1:

{3: [0, 1, 2, 5, 6, 33, 34, 35],
4: [],
14: [10, 11, 12, 13, 15, 16, 17, 18, 19],
26: [20, 21, 22, 23, 24, 25, 27, 28, 29],
36: [7, 8, 9, 30, 31, 32, 37, 38, 39]}

case 2:

    num_groups = 6
    num_min = 5
    num_max = 10

result2:

{0: [1, 2, 3, 5, 6, 9, 35],
4: [],
14: [10, 11, 12, 13, 15, 16, 17, 18],
21: [19, 20, 22, 23, 24, 25, 26, 27, 28],
33: [34],
36: [7, 8, 29, 30, 31, 32, 37, 38, 39]}

case 3:

   num_groups = 4
   num_min = 6
   num_max = 15

result3:
{3: [0, 1, 2, 4, 5, 6, 33, 34, 35],
14: [10, 11, 12, 13, 15, 16, 17, 18],
21: [19, 20, 22, 23, 24, 25, 26, 27, 28],
36: [7, 8, 9, 29, 30, 31, 32, 37, 38, 39]}

Code:

    from __future__ import print_function
    from __future__ import division
    
    from ortools.sat.python import cp_model
    import networkx as nx
    import matplotlib.pyplot as plt
    
    distance_matrix = [
        [0, 10938, 4542, 2835, 29441, 2171, 1611, 9208, 9528, 11111, 16120, 22606, 22127, 20627, 21246, 23387, 16697, 33609,
         26184, 24772, 22644, 20655, 30492, 23296, 32979, 18141, 19248, 17129, 17192, 15645, 12658, 11210, 12094, 13175,
         18162, 4968, 12308, 10084, 13026, 15056],
        [10938, 0, 6422, 9742, 18988, 12974, 11216, 19715, 19004, 18271, 25070, 31971, 31632, 30571, 31578, 33841, 27315,
         43964, 36944, 35689, 33569, 31481, 41360, 33760, 43631, 28730, 29976, 27803, 28076, 26408, 23504, 22025, 22000,
         13197, 14936, 15146, 23246, 20956, 23963, 25994],
        [4542, 6422, 0, 3644, 25173, 6552, 5092, 13584, 13372, 13766, 19805, 26537, 26117, 24804, 25590, 27784, 21148,
         37981, 30693, 29315, 27148, 25071, 34943, 27472, 37281, 22389, 23592, 21433, 21655, 20011, 17087, 15612, 15872,
         11653, 15666, 8842, 16843, 14618, 17563, 19589],
        [2835, 9742, 3644, 0, 28681, 3851, 4341, 11660, 12294, 13912, 18893, 25283, 24777, 23173, 23636, 25696, 18950,
         35927, 28233, 26543, 24127, 21864, 31765, 24018, 33904, 19005, 20295, 18105, 18551, 16763, 13958, 12459, 12296,
         10370, 15331, 5430, 14044, 12135, 14771, 16743],
        [29441, 18988, 25173, 28681, 0, 31590, 29265, 37173, 35501, 32929, 40239, 47006, 46892, 46542, 48112, 50506, 44539,
         60103, 54208, 53557, 51878, 50074, 59849, 52645, 62415, 47544, 48689, 46560, 46567, 45086, 42083, 40648, 40971,
         29929, 28493, 34015, 41473, 38935, 42160, 44198],
        [2171, 12974, 6552, 3851, 31590, 0, 3046, 7856, 8864, 11330, 15411, 21597, 21065, 19382, 19791, 21845, 15099, 32076,
         24425, 22848, 20600, 18537, 28396, 21125, 30825, 15975, 17101, 14971, 15104, 13503, 10544, 9080, 9983, 13435,
         18755, 2947, 10344, 8306, 11069, 13078],
        [1611, 11216, 5092, 4341, 29265, 3046, 0, 8526, 8368, 9573, 14904, 21529, 21085, 19719, 20504, 22713, 16118, 32898,
         25728, 24541, 22631, 20839, 30584, 23755, 33278, 18557, 19545, 17490, 17309, 15936, 12881, 11498, 12944, 14711,
         19589, 5993, 12227, 9793, 12925, 14967],
        [9208, 19715, 13584, 11660, 37173, 7856, 8526, 0, 3248, 7855, 8245, 13843, 13272, 11526, 12038, 14201, 7599, 24411,
         17259, 16387, 15050, 13999, 23134, 17899, 26460, 12894, 13251, 11680, 10455, 9997, 7194, 6574, 10678, 20959, 26458,
         8180, 5255, 2615, 5730, 7552],
        [9528, 19004, 13372, 12294, 35501, 8864, 8368, 3248, 0, 4626, 6598, 13168, 12746, 11567, 12731, 15083, 9120, 25037,
         18718, 18433, 17590, 16888, 25630, 20976, 29208, 16055, 16300, 14838, 13422, 13165, 10430, 9813, 13777, 22300,
         27564, 10126, 8388, 5850, 8778, 10422],
        [11111, 18271, 13766, 13912, 32929, 11330, 9573, 7855, 4626, 0, 7318, 14185, 14005, 13655, 15438, 17849, 12839,
         27179, 21947, 22230, 21814, 21366, 29754, 25555, 33535, 20674, 20872, 19457, 17961, 17787, 15048, 14372, 18115,
         24280, 29101, 13400, 13008, 10467, 13375, 14935],
        [16120, 25070, 19805, 18893, 40239, 15411, 14904, 8245, 6598, 7318, 0, 6939, 6702, 6498, 8610, 10961, 7744, 19889,
         15350, 16403, 16975, 17517, 24357, 22176, 28627, 18093, 17672, 16955, 14735, 15510, 13694, 13768, 18317, 28831,
         34148, 16326, 11276, 9918, 11235, 11891],
        [22606, 31971, 26537, 25283, 47006, 21597, 21529, 13843, 13168, 14185, 6939, 0, 793, 3401, 5562, 6839, 8923, 13433,
         11264, 13775, 15853, 17629, 21684, 22315, 26411, 19539, 18517, 18636, 16024, 17632, 16948, 17587, 22131, 34799,
         40296, 21953, 14739, 14568, 14366, 14002],
        [22127, 31632, 26117, 24777, 46892, 21065, 21085, 13272, 12746, 14005, 6702, 793, 0, 2608, 4809, 6215, 8151, 13376,
         10702, 13094, 15099, 16845, 21039, 21535, 25744, 18746, 17725, 17845, 15232, 16848, 16197, 16859, 21391, 34211,
         39731, 21345, 14006, 13907, 13621, 13225],
        [20627, 30571, 24804, 23173, 46542, 19382, 19719, 11526, 11567, 13655, 6498, 3401, 2608, 0, 2556, 4611, 5630, 13586,
         9157, 11005, 12681, 14285, 19044, 18996, 23644, 16138, 15126, 15240, 12625, 14264, 13736, 14482, 18958, 32292,
         37879, 19391, 11621, 11803, 11188, 10671],
        [21246, 31578, 25590, 23636, 48112, 19791, 20504, 12038, 12731, 15438, 8610, 5562, 4809, 2556, 0, 2411, 4917, 12395,
         6757, 8451, 10292, 12158, 16488, 16799, 21097, 14374, 13194, 13590, 10943, 12824, 12815, 13779, 18042, 32259,
         37918, 19416, 10975, 11750, 10424, 9475],
        [23387, 33841, 27784, 25696, 50506, 21845, 22713, 14201, 15083, 17849, 10961, 6839, 6215, 4611, 2411, 0, 6760,
         10232, 4567, 7010, 9607, 12003, 14846, 16408, 19592, 14727, 13336, 14109, 11507, 13611, 14104, 15222, 19237, 34013,
         39703, 21271, 12528, 13657, 11907, 10633],
        [16697, 27315, 21148, 18950, 44539, 15099, 16118, 7599, 9120, 12839, 7744, 8923, 8151, 5630, 4917, 6760, 0, 16982,
         9699, 9400, 9302, 9823, 16998, 14534, 21042, 10911, 10190, 9900, 7397, 8758, 8119, 8948, 13353, 27354, 33023,
         14542, 6106, 6901, 5609, 5084],
        [33609, 43964, 37981, 35927, 60103, 32076, 32898, 24411, 25037, 27179, 19889, 13433, 13376, 13586, 12395, 10232,
         16982, 0, 8843, 12398, 16193, 19383, 16423, 22583, 20997, 22888, 21194, 22640, 20334, 22636, 23801, 25065, 28675,
         44048, 49756, 31426, 22528, 23862, 21861, 20315],
        [26184, 36944, 30693, 28233, 54208, 24425, 25728, 17259, 18718, 21947, 15350, 11264, 10702, 9157, 6757, 4567, 9699,
         8843, 0, 3842, 7518, 10616, 10666, 14237, 15515, 14053, 12378, 13798, 11537, 13852, 15276, 16632, 19957, 35660,
         41373, 23361, 14333, 16125, 13624, 11866],
        [24772, 35689, 29315, 26543, 53557, 22848, 24541, 16387, 18433, 22230, 16403, 13775, 13094, 11005, 8451, 7010, 9400,
         12398, 3842, 0, 3795, 7014, 8053, 10398, 12657, 10633, 8889, 10569, 8646, 10938, 12906, 14366, 17106, 33171, 38858,
         21390, 12507, 14748, 11781, 9802],
        [22644, 33569, 27148, 24127, 51878, 20600, 22631, 15050, 17590, 21814, 16975, 15853, 15099, 12681, 10292, 9607,
         9302, 16193, 7518, 3795, 0, 3250, 8084, 6873, 11763, 6949, 5177, 7050, 5619, 7730, 10187, 11689, 13792, 30012,
         35654, 18799, 10406, 12981, 9718, 7682],
        [20655, 31481, 25071, 21864, 50074, 18537, 20839, 13999, 16888, 21366, 17517, 17629, 16845, 14285, 12158, 12003,
         9823, 19383, 10616, 7014, 3250, 0, 9901, 4746, 12531, 3737, 1961, 4036, 3588, 5109, 7996, 9459, 10846, 27094,
         32690, 16451, 8887, 11624, 8304, 6471],
        [30492, 41360, 34943, 31765, 59849, 28396, 30584, 23134, 25630, 29754, 24357, 21684, 21039, 19044, 16488, 14846,
         16998, 16423, 10666, 8053, 8084, 9901, 0, 9363, 4870, 13117, 11575, 13793, 13300, 15009, 17856, 19337, 20454,
         36551, 42017, 26352, 18403, 21033, 17737, 15720],
        [23296, 33760, 27472, 24018, 52645, 21125, 23755, 17899, 20976, 25555, 22176, 22315, 21535, 18996, 16799, 16408,
         14534, 22583, 14237, 10398, 6873, 4746, 9363, 0, 10020, 5211, 4685, 6348, 7636, 8010, 11074, 12315, 11926, 27537,
         32880, 18634, 12644, 15358, 12200, 10674],
        [32979, 43631, 37281, 33904, 62415, 30825, 33278, 26460, 29208, 33535, 28627, 26411, 25744, 23644, 21097, 19592,
         21042, 20997, 15515, 12657, 11763, 12531, 4870, 10020, 0, 14901, 13738, 15855, 16118, 17348, 20397, 21793, 21936,
         37429, 42654, 28485, 21414, 24144, 20816, 18908],
        [18141, 28730, 22389, 19005, 47544, 15975, 18557, 12894, 16055, 20674, 18093, 19539, 18746, 16138, 14374, 14727,
         10911, 22888, 14053, 10633, 6949, 3737, 13117, 5211, 14901, 0, 1777, 1217, 3528, 2896, 5892, 7104, 7338, 23517,
         29068, 13583, 7667, 10304, 7330, 6204],
        [19248, 29976, 23592, 20295, 48689, 17101, 19545, 13251, 16300, 20872, 17672, 18517, 17725, 15126, 13194, 13336,
         10190, 21194, 12378, 8889, 5177, 1961, 11575, 4685, 13738, 1777, 0, 2217, 2976, 3610, 6675, 8055, 8965, 25197,
         30774, 14865, 8007, 10742, 7532, 6000],
        [17129, 27803, 21433, 18105, 46560, 14971, 17490, 11680, 14838, 19457, 16955, 18636, 17845, 15240, 13590, 14109,
         9900, 22640, 13798, 10569, 7050, 4036, 13793, 6348, 15855, 1217, 2217, 0, 2647, 1686, 4726, 6000, 6810, 23060,
         28665, 12674, 6450, 9094, 6117, 5066],
        [17192, 28076, 21655, 18551, 46567, 15104, 17309, 10455, 13422, 17961, 14735, 16024, 15232, 12625, 10943, 11507,
         7397, 20334, 11537, 8646, 5619, 3588, 13300, 7636, 16118, 3528, 2976, 2647, 0, 2320, 4593, 6093, 8479, 24542,
         30219, 13194, 5301, 8042, 4735, 3039],
        [15645, 26408, 20011, 16763, 45086, 13503, 15936, 9997, 13165, 17787, 15510, 17632, 16848, 14264, 12824, 13611,
         8758, 22636, 13852, 10938, 7730, 5109, 15009, 8010, 17348, 2896, 3610, 1686, 2320, 0, 3086, 4444, 6169, 22301,
         27963, 11344, 4780, 7408, 4488, 3721],
        [12658, 23504, 17087, 13958, 42083, 10544, 12881, 7194, 10430, 15048, 13694, 16948, 16197, 13736, 12815, 14104,
         8119, 23801, 15276, 12906, 10187, 7996, 17856, 11074, 20397, 5892, 6675, 4726, 4593, 3086, 0, 1501, 5239, 20390,
         26101, 8611, 2418, 4580, 2599, 3496],
        [11210, 22025, 15612, 12459, 40648, 9080, 11498, 6574, 9813, 14372, 13768, 17587, 16859, 14482, 13779, 15222, 8948,
         25065, 16632, 14366, 11689, 9459, 19337, 12315, 21793, 7104, 8055, 6000, 6093, 4444, 1501, 0, 4608, 19032, 24747,
         7110, 2860, 4072, 3355, 4772],
        [12094, 22000, 15872, 12296, 40971, 9983, 12944, 10678, 13777, 18115, 18317, 22131, 21391, 18958, 18042, 19237,
         13353, 28675, 19957, 17106, 13792, 10846, 20454, 11926, 21936, 7338, 8965, 6810, 8479, 6169, 5239, 4608, 0, 16249,
         21866, 7146, 7403, 8446, 7773, 8614],
        [13175, 13197, 11653, 10370, 29929, 13435, 14711, 20959, 22300, 24280, 28831, 34799, 34211, 32292, 32259, 34013,
         27354, 44048, 35660, 33171, 30012, 27094, 36551, 27537, 37429, 23517, 25197, 23060, 24542, 22301, 20390, 19032,
         16249, 0, 5714, 12901, 21524, 20543, 22186, 23805],
        [18162, 14936, 15666, 15331, 28493, 18755, 19589, 26458, 27564, 29101, 34148, 40296, 39731, 37879, 37918, 39703,
         33023, 49756, 41373, 38858, 35654, 32690, 42017, 32880, 42654, 29068, 30774, 28665, 30219, 27963, 26101, 24747,
         21866, 5714, 0, 18516, 27229, 26181, 27895, 29519],
        [4968, 15146, 8842, 5430, 34015, 2947, 5993, 8180, 10126, 13400, 16326, 21953, 21345, 19391, 19416, 21271, 14542,
         31426, 23361, 21390, 18799, 16451, 26352, 18634, 28485, 13583, 14865, 12674, 13194, 11344, 8611, 7110, 7146, 12901,
         18516, 0, 9029, 7668, 9742, 11614],
        [12308, 23246, 16843, 14044, 41473, 10344, 12227, 5255, 8388, 13008, 11276, 14739, 14006, 11621, 10975, 12528, 6106,
         22528, 14333, 12507, 10406, 8887, 18403, 12644, 21414, 7667, 8007, 6450, 5301, 4780, 2418, 2860, 7403, 21524,
         27229, 9029, 0, 2747, 726, 2749],
        [10084, 20956, 14618, 12135, 38935, 8306, 9793, 2615, 5850, 10467, 9918, 14568, 13907, 11803, 11750, 13657, 6901,
         23862, 16125, 14748, 12981, 11624, 21033, 15358, 24144, 10304, 10742, 9094, 8042, 7408, 4580, 4072, 8446, 20543,
         26181, 7668, 2747, 0, 3330, 5313],
        [13026, 23963, 17563, 14771, 42160, 11069, 12925, 5730, 8778, 13375, 11235, 14366, 13621, 11188, 10424, 11907, 5609,
         21861, 13624, 11781, 9718, 8304, 17737, 12200, 20816, 7330, 7532, 6117, 4735, 4488, 2599, 3355, 7773, 22186, 27895,
         9742, 726, 3330, 0, 2042],
        [15056, 25994, 19589, 16743, 44198, 13078, 14967, 7552, 10422, 14935, 11891, 14002, 13225, 10671, 9475, 10633, 5084,
         20315, 11866, 9802, 7682, 6471, 15720, 10674, 18908, 6204, 6000, 5066, 3039, 3721, 3496, 4772, 8614, 23805, 29519,
         11614, 2749, 5313, 2042, 0],
    ]  # yapf: disable
    
    
    def main():
        """Entry point of the program."""
        num_nodes = len(distance_matrix)
        print('Num nodes =', num_nodes)
    
        # case1:
        # num_groups = 5
        # num_min = 5
        # num_max = 10
    
        # case2:
        # num_groups = 6
        # num_min = 5
        # num_max = 10
    
        # case3:
        num_groups = 4
        num_min = 6
        num_max = 15
    
        # Model.
        model = cp_model.CpModel()
    
        # Variables.
        neighbors = {}
        obj_vars = []
        obj_coeffs = []
        for n1 in range(num_nodes):
            for n2 in range(num_nodes):
                if n1 != n2:
                    same = model.NewBoolVar('neighbors_%i_%i' % (n1, n2))
                    neighbors[n1, n2] = same
                    obj_vars.append(same)
                    obj_coeffs.append(distance_matrix[n1][n2])
    
        nodes = []
        for n in range(num_nodes):
            node = model.NewBoolVar('nodes_%i' % n)
            nodes.append(node)
    
        # The number of center points is equal to the number of clusters
        model.Add(sum(nodes[i] for i in range(num_nodes)) == num_groups)
    
        for n in range(num_nodes):
            # Out-degree and In-degree constraints of the center point
    
            model.Add(sum(neighbors[n, i] for i in range(num_nodes) if i != n) == 0).OnlyEnforceIf(nodes[n])
    
            model.Add(num_min - 1 <= sum(neighbors[i, n] for i in range(num_nodes) if i != n) <= num_max - 1).OnlyEnforceIf(nodes[n])
    
            # Out-degree and In-degree constraints of non-central points
            model.Add(sum(neighbors[n, i] for i in range(num_nodes) if i != n) == 1).OnlyEnforceIf(nodes[n].Not())
            model.Add(sum(neighbors[i, n] for i in range(num_nodes) if i != n) == 0).OnlyEnforceIf(nodes[n].Not())
    
        # Minimize weighted sum of arcs.
        model.Minimize(sum(obj_vars[i] * obj_coeffs[i] for i in range(len(obj_vars))))
    
        # Solve and print out the solution.
        solver = cp_model.CpSolver()
        solver.parameters.log_search_progress = True
        solver.parameters.num_search_workers = 10
    
        status = solver.Solve(model)
        print(solver.ResponseStats())
    
        DG = nx.DiGraph()
    
        result = {}
        for n in range(num_nodes):
            # print('node {0} : {1}'.format(n, solver.BooleanValue(nodes[n])))
            DG.add_node(n, labels=solver.BooleanValue(nodes[n]))
            if solver.BooleanValue(nodes[n]):
                # print('node {0} : {1}'.format(n, solver.BooleanValue(nodes[n])))
                result[n] = []
    
        for n1 in range(num_nodes):
            for n2 in range(num_nodes):
                if n1 != n2:
                    # print('edege {0} --> {1} : {2}'.format(n1, n2, solver.BooleanValue(neighbors[n1, n2])))
                    if solver.BooleanValue(neighbors[n1, n2]):
                        result[n2].append(n1)
                        DG.add_edge(n1, n2)
    
        print(result)
    
        nx.draw(DG)
        plt.show()
    
    if __name__ == '__main__':
        main()

Answered by ghost

Dec 2, 2020

Split this line into 2 constraints:

model.Add(
    num_min - 1
    <= sum(neighbors[i, n] for i in range(num_nodes) if i != n)
    <= num_max - 1
).OnlyEnforceIf(nodes[n])

View full answer

lperron · 2020-12-02T08:53:31Z

lperron
Dec 2, 2020
Maintainer

Unless you prove this is a solver issue, it is most likely a model issue.
Thus I will move this to discussions.

0 replies

lperron · 2020-12-02T09:12:22Z

lperron
Dec 2, 2020
Maintainer

why are you creating 2 boolvars for n1 is neighbor of n2 and n2 is neighbor of n1 ?

0 replies

ZhiWeiCui · 2020-12-02T09:28:32Z

ZhiWeiCui
Dec 2, 2020
Author

The following constraints are based on the out-degree and in-degree of each node. Therefore, the edges need to be regarded as directional. For each node: Out-degree In-degree the center point 0 [num_min -1, num_max-1] non-central points 1 0 Laurent Perron <[email protected]> 于2020年12月2日周三下午5:12写道：

…

why are you creating 2 boolvars for n1 is neighbor of n2 and n2 is neighbor of n1 ? — You are receiving this because you authored the thread. Reply to this email directly, view it on GitHub <#2253 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AFOKUUSCXVWBJCIWAPDHFKTSSYAILANCNFSM4UKGI5PA> .

0 replies

ghost · 2020-12-02T09:57:01Z

ghost
Dec 2, 2020

Split this line into 2 constraints:

model.Add(
    num_min - 1
    <= sum(neighbors[i, n] for i in range(num_nodes) if i != n)
    <= num_max - 1
).OnlyEnforceIf(nodes[n])

0 replies

lperron · 2020-12-02T10:05:26Z

lperron
Dec 2, 2020
Maintainer

yes, this does not work IMO Laurent Perron | Operations Research | [email protected] | (33) 1 42 68 53 00 Le mer. 2 déc. 2020 à 10:57, Xiang Chen <[email protected]> a écrit :

…

Split this line into 2 constraints: model.Add( num_min - 1 <= sum(neighbors[i, n] for i in range(num_nodes) if i != n) <= num_max - 1 ).OnlyEnforceIf(nodes[n]) — You are receiving this because you commented. Reply to this email directly, view it on GitHub <#2253 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/ACUPL3OXZ767GTB4O4A6H3TSSYFPZANCNFSM4UKGI5PA> .

0 replies

ZhiWeiCui · 2020-12-02T11:46:47Z

ZhiWeiCui
Dec 2, 2020
Author

It does work according to your suggestion, thank you very much.

0 replies

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CP-Sat: Python 3.6.9, ortools 8.0.8283 wrong optimization result #2253

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CP-Sat: Python 3.6.9, ortools 8.0.8283 wrong optimization result #2253

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ZhiWeiCui Dec 2, 2020

Model:

Case:

Code:

Replies: 6 comments

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lperron Dec 2, 2020 Maintainer

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ZhiWeiCui
Dec 2, 2020

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ZhiWeiCui
Dec 2, 2020
Author

ghost
Dec 2, 2020

lperron
Dec 2, 2020
Maintainer

ZhiWeiCui
Dec 2, 2020
Author