Research Article

A Hybrid Harmony Search Algorithm with Distribution Estimation for Solving the 0-1 Knapsack Problem

Table 2

Description of 10 low-dimensional 0–1 instances of the knapsack problem.

InstanceDimensionOptimal capacityParameters

KP110295 = (95, 4, 60, 32, 23, 72, 80, 62, 65, 46), Vmax = 269,  = (55, 10, 47, 5, 4, 50, 8, 61, 85, 87)
KP2201024 = (92, 4, 43, 83, 84, 68, 92, 82, 6, 44, 32, 18, 56, 83, 25, 96, 70, 48, 14, 58), Vmax = 878,  = (44, 46, 90, 72, 91, 40, 75, 35, 8, 54, 78, 40, 77, 15, 61, 17, 75, 29, 75, 63)
KP3435 = (6, 5, 9, 7), Vmax = 20,  = (9, 11, 13, 15)
KP4423 = (2, 4, 6, 7), Vmax = 11,  = (6, 10, 12, 13)
KP515481.0694 = (56.358531, 80.874050, 47.987304, 89.596240, 74.660482, 85.894345, 51.353496, 1.498459, 36.445204, 16.589862, 44.569231, 0.466933, 37.788018, 57.118442, 60.716575), Vmax = 375,  = (0.125126, 19.330424, 58.500931, 35.029145, 82.284005, 17.410810, 71.050142, 30.399487, 9.140294, 14.731285, 98.852504, 11.908322, 0.891140, 53.166295, 60.176397)
KP61052 = (30, 25, 20, 18, 17, 11, 5, 2, 1, 1), Vmax = 60,  = (20, 18, 17, 15, 15, 10, 5, 3, 1, 1)
KP77107 = (31, 10, 20, 19, 4, 3, 6), Vmax = 50,  = (70, 20, 39, 37, 7, 5, 10)
KP8239767 = (983, 982, 981, 980, 979, 978, 488, 976, 972, 486, 486, 972, 972, 485, 485, 969, 966, 483, 964, 963, 961, 958, 959), Vmax = 10000,  = (981, 980, 979, 978, 977, 976, 487, 974, 970, 485, 485, 970, 970, 484, 484, 976, 974, 482, 962, 961, 959, 958, 857)
KP95130 = (15, 20, 17, 8, 31), Vmax = 80,  = (33, 24, 36, 37, 12)
KP10201025 = (84, 83, 43, 4, 44, 6, 82, 92, 25, 83, 56, 18, 58, 14, 48, 70, 96, 32, 68, 92), Vmax = 879,  = (91, 72, 90, 46, 55, 8, 35, 75, 61, 15, 77, 40, 63, 75, 29, 75, 17, 78, 40, 44)