A Hybrid Genetic Algorithm with Solution Archive for the Discrete (r p)-centroid Problem Full Result Tables
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1 A Hybrid Genetic Algorithm with Solution Archive for the Discrete (r p)-centroid Problem Full Result Tables Benjamin Biesinger Bin Hu Günther Raidl {biesinger hu Institute of Computer Graphics and Algorithms Vienna University of Technology Favoritenstraße 9-11/1861, 1040 Vienna, Austria May 2, Scope This document contains the full result tables of the tests performed with our hybrid genetic algorithm as described in the paper A Hybrid Genetic Algorithm with Solution Archive for the Discrete (r p)-centroid Problem submitted to Journal of Heuristics. 2 Result Tables The next four sections contain the full result tables including the values not listed in the original paper. All tests were carried out on a single core of an Intel Xeon Quadcore with 2.53 GHz. 2.1 Solution Evaluation Table 1 shows the results of the tests for the different types of solution evaluation methods as described in the paper. Table 1: Results of different solution evaluation methods using the standard configuration and a runtime of 600 seconds. greedy LP exact Instance obj sd t best [s] obj sd t best [s] obj sd t best [s] Code111w rp ,00 0,00 14, ,00 0,00 130, ,00 0,00 70,60 Code111w rp ,11 6,01 20, ,00 0,00 64, ,00 0,00 55,60 Code111w rp ,50 6,09 253, ,47 11,22 343, ,90 11,26 217,70 Code1 150w rp ,20 130,36 250, ,37 112,88 88, ,43 51,47 94,00 Code1 150w rp ,63 54,17 138, ,97 35,79 341, ,83 43,99 398,50 Code1 150w rp ,67 52,46 314, ,27 19,01 380, ,53 22,50 370,60 Code1 200w rp ,60 69,78 406, ,17 107,30 200, ,50 92,39 369,70 Code1 200w rp ,13 185,24 351, ,40 92,78 394, ,30 82,92 475,60 Code1 200w rp ,13 135,94 411, ,07 77,54 572, ,53 85,19 586,90 Code211w rp ,47 2,92 26, ,00 0,00 43, ,00 0,00 46,10 Code211w rp ,00 0,00 97, ,00 0,00 111, ,00 0,00 95,70 Code211w rp ,57 2,37 284, ,43 29,69 291, ,63 31,19 365,20 Code2 150w rp ,53 52,91 332, ,47 53,43 292, ,30 71,29 291,00 Code2 150w rp ,23 92,37 154, ,20 4,70 281, ,00 5,57 358,40 Code2 150w rp ,90 83,24 255, ,13 40,91 349, ,50 46,49 347,80 Code2 200w rp ,00 71,74 221, ,63 75,55 249, , ,00 448,00 Code2 200w rp ,23 153,66 312, ,27 70,94 516, ,43 109,72 438,40 Code2 200w rp ,90 138,87 475, ,83 118,18 508, ,30 110,98 548,80 Code311w rp ,47 42,88 17, ,00 0,00 25, ,00 0,00 24,50 Code311w rp ,10 18,23 221, ,00 0,00 73, ,00 0,00 63,20 Code311w rp ,47 8,76 100, ,80 0,61 297, ,67 0,76 250,80 Code3 150w rp ,20 75,69 362, ,93 16,36 310, ,87 13,30 369,20 Code3 150w rp ,30 44,12 161, ,00 18,83 285, ,27 18,01 200,50 Code3 150w rp ,40 63,06 303, ,43 34,03 309, ,37 34,20 411,20 Code3 200w rp ,03 52,98 202, ,23 70,30 291, ,13 74,85 362,90 Code3 200w rp ,17 210,97 378, ,57 71,44 386, ,37 70,27 459,10 Code3 200w rp ,30 210,90 468, ,97 155,51 516, ,73 107,33 574,10 Code411w rp ,00 0,00 10, ,00 0,00 22, ,00 0,00 22,40 Code411w rp ,43 4,26 108, ,00 0,00 117, ,00 0,00 125,40 Code411w rp ,70 5,87 34, ,73 16,24 298, ,63 13,61 189,80 Code4 150w rp ,53 62,64 156, ,33 98,75 290, ,73 112,80 151,40 1
2 Code4 150w rp ,93 79,35 120, ,00 0,00 285, ,07 14,62 329,30 Code4 150w rp ,20 7,92 213, ,93 7,44 276, ,37 8,83 260,00 Code4 200w rp ,47 77,24 231, ,40 43,37 191, ,50 30,67 289,40 Code4 200w rp ,20 189,16 387, ,43 87,24 403, ,47 99,50 410,80 Code4 200w rp ,10 194,06 373, ,67 113,20 502, ,20 88,94 521,90 Code511w rp ,93 6,96 7, ,00 0,00 39, ,00 0,00 38,50 Code511w rp ,00 0,00 162, ,90 7,40 332, ,07 8,37 276,80 Code511w rp ,00 0,00 70, ,33 9,94 101, ,27 9,65 223,70 Code5 150w rp ,63 16,27 169, ,73 10,59 329, ,27 6,38 276,90 Code5 150w rp ,60 24,26 374, ,93 34,91 392, ,00 33,52 323,90 Code5 150w rp ,87 55,66 291, ,77 8,91 343, ,73 24,91 408,30 Code5 200w rp ,13 96,25 398, ,13 66,25 338, ,13 95,30 308,30 Code5 200w rp ,07 87,52 395, ,60 71,37 413, ,10 78,45 374,40 Code5 200w rp ,33 143,66 398, ,13 90,25 499, ,00 101,19 502,20 Code611w rp ,13 3,60 112, ,73 1,46 110, ,00 0,00 95,30 Code611w rp ,97 25,55 74, ,00 0,00 74, ,00 0,00 83,00 Code611w rp ,33 8,91 173, ,53 18,58 248, ,13 11,68 266,50 Code6 150w rp ,83 63,95 129, ,83 64,84 242, ,17 65,40 321,50 Code6 150w rp ,13 70,94 198, ,53 32,51 319, ,63 50,74 202,60 Code6 150w rp ,03 48,11 197, ,23 39,25 368, ,60 37,80 353,60 Code6 200w rp ,23 143,32 233, ,17 130,57 207, ,83 107,38 247,90 Code6 200w rp ,10 242,75 361, ,27 150,55 442, ,77 137,66 439,00 Code6 200w rp ,70 190,84 406, ,63 116,02 570, ,63 131,96 580,60 Code711w rp ,27 10,51 25, ,00 0,00 79, ,00 0,00 85,00 Code711w rp ,43 3,10 162, ,00 0,00 83, ,00 0,00 94,70 Code711w rp ,00 0,00 38, ,00 0,00 73, ,00 0,00 55,70 Code7 150w rp ,90 71,68 177, ,90 44,98 293, ,60 41,73 220,00 Code7 150w rp ,17 70,04 292, ,00 0,00 231, ,00 0,00 218,40 Code7 150w rp ,33 23,61 215, ,87 42,85 290, ,97 41,70 273,00 Code7 200w rp ,33 166,84 260, ,37 149,21 274, ,20 144,57 375,00 Code7 200w rp ,57 127,38 385, ,73 61,94 518, ,67 73,61 424,10 Code7 200w rp ,33 83,12 330, ,63 58,28 476, ,23 53,11 482,90 Code811w rp ,33 41,45 280, ,20 14,09 301, ,60 1,52 356,80 Code811w rp ,70 19,03 45, ,77 11,42 180, ,87 24,49 223,80 Code811w rp ,00 0,00 212, ,00 0,00 77, ,00 0,00 75,10 Code8 150w rp ,70 57,34 236, ,33 14,61 217, ,43 14,06 246,90 Code8 150w rp ,13 100,02 171, ,73 8,45 340, ,13 7,04 340,30 Code8 150w rp ,87 24,04 215, ,13 19,77 285, ,87 29,02 294,40 Code8 200w rp ,83 125,44 382, ,83 122,64 375, ,00 89,40 413,80 Code8 200w rp ,87 111,97 429, ,57 81,04 530, ,33 59,87 501,80 Code8 200w rp ,37 192,45 480, ,93 97,88 512, ,87 105,27 565,80 Code911w rp ,00 0,00 8, ,00 0,00 21, ,00 0,00 21,00 Code911w rp ,93 6,90 48, ,07 6,15 339, ,10 13,94 332,30 Code911w rp ,87 4,97 20, ,00 2,03 239, ,63 1,97 195,10 Code9 150w rp ,07 137,08 323, ,70 39,05 220, ,60 24,36 231,40 Code9 150w rp ,40 48,96 362, ,93 15,49 274, ,97 31,32 327,80 Code9 150w rp ,60 97,04 321, ,23 63,63 365, ,53 52,19 432,00 Code9 200w rp ,00 253,61 192, ,73 119,21 204, ,73 162,21 209,30 Code9 200w rp ,57 84,92 226, ,87 75,56 445, ,67 53,24 547,00 Code9 200w rp ,07 172,46 445, ,13 62,21 539, ,50 78,89 515,80 Code1011w rp ,00 0,00 49, ,53 11,83 110, ,73 13,05 93,10 Code1011w rp ,00 0,00 98, ,00 0,00 254, ,60 2,19 189,00 Code1011w rp ,03 37,90 101, ,00 0,00 222, ,00 0,00 204,10 Code10 150w rp ,80 76,84 226, ,30 43,97 114, ,90 48,60 171,00 Code10 150w rp ,63 127,95 148, ,00 34,14 228, ,47 17,54 313,30 Code10 150w rp ,93 89,07 237, ,17 40,36 336, ,73 54,05 277,90 Code10 200w rp ,37 108,47 313, ,13 118,39 437, ,03 116,95 438,50 Code10 200w rp ,13 164,61 307, ,83 63,44 465, ,70 79,54 533,60 Code10 200w rp ,17 184,23 433, ,33 100,70 512, ,63 133,12 522,80 geometric mean 6907, , ,29 #best results #unique best res Genetic Algorithm In Table 2 the computational results of different configurations of the genetic algorithm are given. Table 2: Results for the different configurations of the GA. The pure genetic algorithm (GA), the genetic algorithm with the local search (GA + LS), the genetic algorithm with the solution archive (GA + sola) and the genetic algorithm with the solution archive and the local search (GA + LS + sola) with a runtime of 600 seconds. GA GA + LS GA + sola GA + LS + sola Instance obj sd t best [s] obj sd t best [s] obj sd t best [s] obj sd t best [s] Code111w rp ,80 12,32 338, ,97 25,00 113, ,20 10,75 402, ,00 0,00 14,70 Code111w rp ,37 21,18 461, ,43 16,65 38, ,67 6,63 412, ,00 0,00 16,10 Code111w rp ,23 17,50 538, ,97 23,52 162, ,17 21,42 521, ,47 11,22 209,50 Code1 150w rp ,63 123,24 538, ,57 54,75 113, ,03 120,76 530, ,37 112,88 29,20 Code1 150w rp ,13 63,36 549, ,47 75,64 149, ,50 49,83 546, ,97 35,79 133,00 Code1 150w rp ,63 109,91 550, ,03 58,69 187, ,63 105,85 560, ,27 19,01 241,40 Code1 200w rp ,10 201,26 531, ,60 105,48 246, ,30 189,46 509, ,17 107,30 243,10 Code1 200w rp ,43 265,11 572, ,77 112,63 349, ,53 227,11 553, ,40 92,78 297,10 Code1 200w rp ,63 157,41 562, ,20 119,85 479, ,93 219,23 560, ,07 77,54 460,50 Code211w rp ,47 25,60 521, ,00 0,00 51, ,13 28,09 473, ,00 0,00 8,10 2
3 Code211w rp ,47 35,12 546, ,33 19,73 42, ,43 31,31 493, ,00 0,00 23,10 Code211w rp ,03 52,47 556, ,80 55,16 135, ,93 47,01 546, ,43 29,69 82,40 Code2 150w rp ,67 46,48 519, ,90 89,61 233, ,40 43,43 512, ,47 53,43 242,70 Code2 150w rp ,00 94,91 537, ,23 103,32 148, ,67 66,09 516, ,20 4,70 96,90 Code2 150w rp ,37 65,12 540, ,43 70,96 208, ,33 60,97 551, ,13 40,91 211,50 Code2 200w rp ,17 151,04 524, ,07 127,89 228, ,20 131,21 529, ,63 75,55 130,10 Code2 200w rp ,43 159,89 523, ,17 119,41 342, ,77 144,79 520, ,27 70,94 392,00 Code2 200w rp ,47 119,66 557, ,30 119,17 521, ,30 112,43 547, ,83 118,18 421,30 Code311w rp ,50 34,65 331, ,00 0,00 21, ,00 0,00 336, ,00 0,00 8,10 Code311w rp ,93 19,79 473, ,40 22,85 70, ,13 21,89 534, ,00 0,00 13,30 Code311w rp ,77 15,62 534, ,17 14,61 116, ,67 11,70 495, ,80 0,61 65,20 Code3 150w rp ,17 75,29 522, ,50 69,75 136, ,47 71,96 493, ,93 16,36 35,40 Code3 150w rp ,73 124,31 551, ,00 47,95 131, ,33 95,72 523, ,00 18,83 142,50 Code3 150w rp ,33 70,60 543, ,30 45,29 214, ,17 50,70 559, ,43 34,03 274,00 Code3 200w rp ,40 181,41 553, ,40 86,17 239, ,23 185,09 535, ,23 70,30 227,00 Code3 200w rp ,10 269,27 563, ,43 98,36 333, ,40 203,87 562, ,57 71,44 281,90 Code3 200w rp ,83 188,37 564, ,37 174,73 509, ,03 134,42 550, ,97 155,51 426,90 Code411w rp ,67 9,57 466, ,00 0,00 22, ,00 9,03 506, ,00 0,00 7,90 Code411w rp ,90 19,96 476, ,63 16,87 113, ,83 15,50 431, ,00 0,00 48,80 Code411w rp ,93 27,01 514, ,80 55,58 129, ,10 26,28 468, ,73 16,24 39,60 Code4 150w rp ,53 136,21 530, ,67 90,48 110, ,83 117,85 534, ,33 98,75 38,30 Code4 150w rp ,27 174,97 551, ,67 74,30 237, ,40 139,91 536, ,00 0,00 71,30 Code4 150w rp ,80 148,05 549, ,00 25,49 201, ,40 139,86 565, ,93 7,44 251,30 Code4 200w rp ,63 93,41 496, ,43 45,21 232, ,77 105,28 493, ,40 43,37 115,60 Code4 200w rp ,87 139,43 541, ,10 101,98 339, ,60 141,00 519, ,43 87,24 241,30 Code4 200w rp ,17 137,69 570, ,53 98,52 482, ,83 178,30 550, ,67 113,20 388,50 Code511w rp ,00 0,00 318, ,00 0,00 49, ,00 0,00 254, ,00 0,00 8,90 Code511w rp ,73 37,47 534, ,10 31,13 141, ,93 30,46 466, ,90 7,40 63,40 Code511w rp ,03 26,17 524, ,67 37,00 208, ,90 33,37 565, ,33 9,94 76,00 Code5 150w rp ,10 78,29 509, ,27 20,27 190, ,97 75,57 514, ,73 10,59 32,90 Code5 150w rp ,03 80,05 507, ,03 60,02 161, ,83 63,76 524, ,93 34,91 214,60 Code5 150w rp ,50 86,03 560, ,87 47,62 345, ,43 99,17 555, ,77 8,91 227,30 Code5 200w rp ,63 138,43 512, ,57 74,39 220, ,13 106,16 527, ,13 66,25 268,20 Code5 200w rp ,37 151,08 554, ,17 120,27 319, ,67 216,45 547, ,60 71,37 320,90 Code5 200w rp ,77 94,42 511, ,47 103,93 480, ,77 72,74 509, ,13 90,25 345,90 Code611w rp ,17 26,63 435, ,50 11,28 107, ,27 36,36 452, ,73 1,46 17,70 Code611w rp ,67 37,81 528, ,90 41,88 56, ,70 40,16 508, ,00 0,00 15,70 Code611w rp ,00 29,47 554, ,00 36,56 187, ,60 12,76 536, ,53 18,58 96,00 Code6 150w rp ,50 86,69 512, ,53 76,38 100, ,37 67,94 523, ,83 64,84 36,90 Code6 150w rp ,40 97,73 556, ,77 82,94 165, ,50 91,48 564, ,53 32,51 71,60 Code6 150w rp ,73 98,39 550, ,33 94,63 194, ,80 55,80 541, ,23 39,25 133,90 Code6 200w rp ,10 181,04 464, ,20 139,67 283, ,30 195,73 520, ,17 130,57 197,50 Code6 200w rp ,43 178,65 545, ,50 164,71 396, ,73 235,39 564, ,27 150,55 326,70 Code6 200w rp ,03 170,11 561, ,33 129,86 521, ,47 158,70 567, ,63 116,02 452,50 Code711w rp ,73 95,76 531, ,10 4,93 26, ,20 72,86 525, ,00 0,00 8,70 Code711w rp ,40 18,20 486, ,17 17,61 67, ,93 18,34 500, ,00 0,00 31,60 Code711w rp ,40 12,67 512, ,30 11,29 51, ,47 28,80 537, ,00 0,00 29,80 Code7 150w rp ,37 81,25 531, ,73 75,22 160, ,43 75,72 544, ,90 44,98 190,10 Code7 150w rp ,50 71,31 543, ,97 39,32 142, ,40 46,97 542, ,00 0,00 82,90 Code7 150w rp ,20 56,37 573, ,87 60,19 211, ,73 46,05 530, ,87 42,85 203,10 Code7 200w rp ,73 205,33 548, ,83 192,16 250, ,80 130,13 532, ,37 149,21 222,80 Code7 200w rp ,93 138,58 550, ,50 96,36 356, ,03 112,83 543, ,73 61,94 283,90 Code7 200w rp ,53 183,23 564, ,93 58,16 482, ,63 94,41 545, ,63 58,28 361,90 Code811w rp ,77 31,34 447, ,27 34,34 148, ,23 33,97 483, ,20 14,09 21,60 Code811w rp ,03 55,21 562, ,97 47,53 210, ,60 56,09 544, ,77 11,42 41,60 Code811w rp ,47 23,40 553, ,03 9,35 162, ,70 9,89 524, ,00 0,00 24,40 Code8 150w rp ,50 178,99 562, ,23 123,59 113, ,93 132,71 529, ,33 14,61 28,70 Code8 150w rp ,27 128,62 542, ,73 48,91 161, ,30 148,03 551, ,73 8,45 103,10 Code8 150w rp ,20 31,35 530, ,50 86,49 199, ,07 37,92 531, ,13 19,77 188,20 Code8 200w rp ,73 167,54 496, ,87 103,59 282, ,03 194,36 476, ,83 122,64 170,60 Code8 200w rp ,33 159,99 534, ,00 107,96 349, ,93 133,65 546, ,57 81,04 357,90 Code8 200w rp ,23 120,61 563, ,30 88,44 511, ,77 72,10 559, ,93 97,88 484,30 Code911w rp ,80 6,57 294, ,00 0,00 23, ,00 0,00 235, ,00 0,00 7,50 Code911w rp ,77 55,79 527, ,67 35,51 140, ,17 60,71 551, ,07 6,15 220,60 Code911w rp ,73 36,02 562, ,63 12,93 58, ,17 16,11 552, ,00 2,03 92,50 Code9 150w rp ,50 67,94 499, ,67 69,48 271, ,13 59,01 521, ,70 39,05 55,50 Code9 150w rp ,50 65,00 528, ,50 91,06 164, ,00 54,31 505, ,93 15,49 148,40 Code9 150w rp ,43 59,53 563, ,67 87,25 207, ,47 48,97 552, ,23 63,63 299,90 Code9 200w rp ,73 178,59 552, ,20 134,15 254, ,03 164,39 506, ,73 119,21 182,90 Code9 200w rp ,90 135,00 558, ,63 105,81 357, ,27 138,26 550, ,87 75,56 335,40 Code9 200w rp ,97 112,10 519, ,47 83,44 486, ,93 161,26 554, ,13 62,21 416,80 Code1011w rp ,47 31,00 515, ,97 22,94 95, ,87 26,25 487, ,53 11,83 18,20 Code1011w rp ,80 17,34 517, ,60 22,95 126, ,57 10,31 428, ,00 0,00 29,20 Code1011w rp ,87 35,60 546, ,00 31,38 80, ,20 35,12 544, ,00 0,00 60,80 Code10 150w rp ,23 111,42 514, ,80 84,69 108, ,10 96,49 522, ,30 43,97 30,20 Code10 150w rp ,40 112,59 523, ,43 31,17 131, ,60 104,47 554, ,00 34,14 104,30 Code10 150w rp ,33 88,64 512, ,63 80,67 219, ,37 66,04 548, ,17 40,36 175,30 Code10 200w rp ,50 185,66 514, ,07 125,38 297, ,13 174,75 535, ,13 118,39 151,70 Code10 200w rp ,93 89,75 488, ,60 94,69 328, ,43 64,82 470, ,83 63,44 434,30 Code10 200w rp ,50 118,03 549, ,57 97,67 485, ,20 154,75 541, ,33 100,70 460,40 geometric mean 6643, , , ,12 #best results #unique best res
4 2.3 Neighborhoods of the Local Search Table 3 shows the results of using the different strategies for utilizing the solution archive within the local / tabu search as described in the paper. Table 3: Results of using different neighborhood structures for intermediate local search with a total runtime of 600 seconds. complete NB reduced NB conversion NB TS with reduced NB Instance obj sd t best [s] obj sd t best [s] obj sd t best [s] obj sd t best [s] Code1011w rp ,73 13,05 249, ,53 11,83 110, ,07 11,43 123, ,67 7,30 93,80 Code111w rp ,00 0,00 133, ,00 0,00 130, ,00 0,00 72, ,00 0,00 47,00 Code111w rp ,00 0,00 44, ,00 0,00 64, ,00 0,00 79, ,00 0,00 55,10 Code111w rp ,20 22,42 299, ,47 11,22 343, ,93 14,69 343, ,23 8,39 268,70 Code1 150w rp ,07 89,96 113, ,37 112,88 88, ,30 47,65 137, ,00 0,00 118,00 Code1 150w rp ,70 39,71 240, ,97 35,79 341, ,77 45,79 339, ,30 31,63 337,00 Code1 150w rp ,87 22,59 289, ,27 19,01 380, ,87 24,84 400, ,50 27,75 455,20 Code1 200w rp ,80 85,42 286, ,17 107,30 200, ,00 67,29 400, ,50 56,10 350,30 Code1 200w rp ,17 133,66 483, ,40 92,78 394, ,87 100,51 461, ,13 99,43 500,60 Code1 200w rp ,37 70,27 530, ,07 77,54 572, ,67 74,29 521, ,10 69,67 600,00 Code211w rp ,00 0,00 85, ,00 0,00 43, ,00 0,00 29, ,00 0,00 33,10 Code211w rp ,60 8,39 62, ,00 0,00 111, ,00 0,00 100, ,00 0,00 162,80 Code211w rp ,77 37,42 291, ,43 29,69 291, ,13 30,62 439, ,37 9,90 200,00 Code2 150w rp ,77 55,54 303, ,47 53,43 292, ,53 58,72 216, ,17 48,81 401,10 Code2 150w rp ,40 13,75 306, ,20 4,70 281, ,30 5,53 367, ,60 6,29 342,30 Code2 150w rp ,80 51,87 360, ,13 40,91 349, ,40 39,29 390, ,13 59,61 317,60 Code2 200w rp ,43 102,90 266, ,63 75,55 249, ,23 94,53 395, ,07 89,10 376,50 Code2 200w rp ,37 92,86 419, ,27 70,94 516, ,10 93,23 439, ,30 83,08 591,40 Code2 200w rp ,93 106,14 549, ,83 118,18 508, ,43 101,89 549, ,70 67,33 600,00 Code311w rp ,00 0,00 25, ,00 0,00 25, ,00 0,00 23, ,00 0,00 31,10 Code311w rp ,00 0,00 85, ,00 0,00 73, ,00 0,00 50, ,00 0,00 49,20 Code311w rp ,63 3,95 183, ,80 0,61 297, ,67 0,76 264, ,73 0,69 213,90 Code3 150w rp ,67 15,76 113, ,93 16,36 310, ,10 12,10 314, ,00 0,00 130,90 Code3 150w rp ,03 34,68 193, ,00 18,83 285, ,90 18,86 286, ,77 20,38 192,40 Code3 150w rp ,33 47,90 298, ,43 34,03 309, ,93 26,49 331, ,67 46,21 429,70 Code3 200w rp ,97 102,41 247, ,23 70,30 291, ,87 85,79 320, ,97 76,46 375,40 Code3 200w rp ,60 91,05 383, ,57 71,44 386, ,60 68,80 438, ,83 66,40 496,10 Code3 200w rp ,43 118,80 518, ,97 155,51 516, ,50 115,48 517, ,97 105,33 600,00 Code411w rp ,00 0,00 25, ,00 0,00 22, ,00 0,00 25, ,00 0,00 32,50 Code411w rp ,97 10,25 140, ,00 0,00 117, ,27 6,67 191, ,80 1,10 125,10 Code411w rp ,60 38,10 211, ,73 16,24 298, ,73 12,42 239, ,00 0,00 163,80 Code4 150w rp ,10 93,32 225, ,33 98,75 290, ,53 108,65 230, ,60 67,11 152,70 Code4 150w rp ,97 30,96 363, ,00 0,00 285, ,00 29,61 304, ,00 0,00 225,20 Code4 150w rp ,43 10,11 229, ,93 7,44 276, ,17 10,51 232, ,00 7,47 300,30 Code4 200w rp ,13 32,68 228, ,40 43,37 191, ,47 35,77 360, ,80 28,02 312,40 Code4 200w rp ,50 119,82 352, ,43 87,24 403, ,27 131,37 417, ,73 112,00 476,90 Code4 200w rp ,47 115,51 520, ,67 113,20 502, ,10 99,60 531, ,20 82,14 600,00 Code511w rp ,00 0,00 39, ,00 0,00 39, ,00 0,00 53, ,00 0,00 52,60 Code511w rp ,53 20,20 206, ,90 7,40 332, ,77 14,33 212, ,30 5,54 259,30 Code511w rp ,53 15,85 233, ,33 9,94 101, ,40 14,62 165, ,57 7,85 122,00 Code5 150w rp ,43 11,62 215, ,73 10,59 329, ,13 9,49 265, ,20 5,70 144,80 Code5 150w rp ,87 42,55 275, ,93 34,91 392, ,03 41,84 352, ,03 45,75 320,90 Code5 150w rp ,07 30,18 416, ,77 8,91 343, ,43 34,81 375, ,13 23,14 454,70 Code5 200w rp ,27 86,31 278, ,13 66,25 338, ,13 99,28 242, ,97 63,13 327,20 Code5 200w rp ,30 79,24 385, ,60 71,37 413, ,13 68,50 482, ,50 81,90 480,60 Code5 200w rp ,07 75,87 490, ,13 90,25 499, ,60 108,68 514, ,87 84,16 591,40 Code611w rp ,00 0,00 104, ,73 1,46 110, ,00 0,00 155, ,00 0,00 81,50 Code611w rp ,33 9,13 86, ,00 0,00 74, ,00 0,00 75, ,00 0,00 61,80 Code611w rp ,80 25,44 237, ,53 18,58 248, ,23 11,56 321, ,17 18,24 146,10 Code6 150w rp ,53 50,58 356, ,83 64,84 242, ,67 36,71 269, ,00 0,00 146,00 Code6 150w rp ,17 55,31 270, ,53 32,51 319, ,30 51,89 309, ,37 25,38 288,80 Code6 150w rp ,67 25,43 320, ,23 39,25 368, ,20 42,01 394, ,00 0,00 328,20 Code6 200w rp ,27 127,43 278, ,17 130,57 207, ,67 130,58 252, ,00 65,27 348,40 Code6 200w rp ,10 146,05 410, ,27 150,55 442, ,57 156,43 430, ,83 106,40 552,90 Code6 200w rp ,07 107,08 539, ,63 116,02 570, ,33 118,35 528, ,30 77,10 600,00 Code711w rp ,00 0,00 96, ,00 0,00 79, ,10 4,93 100, ,00 0,00 39,50 Code711w rp ,00 0,00 74, ,00 0,00 83, ,00 0,00 105, ,00 0,00 111,40 Code711w rp ,00 0,00 79, ,00 0,00 73, ,00 0,00 52, ,00 0,00 98,40 Code7 150w rp ,60 54,54 304, ,90 44,98 293, ,33 60,52 237, ,20 49,09 262,70 Code7 150w rp ,93 6,60 141, ,00 0,00 231, ,57 2,37 313, ,00 0,00 214,90 Code7 150w rp ,87 57,45 279, ,87 42,85 290, ,03 41,55 299, ,90 38,74 444,80 Code7 200w rp ,07 146,47 242, ,37 149,21 274, ,00 90,67 241, ,97 97,00 331,50 Code7 200w rp ,87 49,08 416, ,73 61,94 518, ,90 56,23 511, ,90 75,55 503,80 Code7 200w rp ,40 62,92 524, ,63 58,28 476, ,83 79,96 492, ,83 64,06 600,00 Code811w rp ,37 35,63 432, ,20 14,09 301, ,43 9,62 340, ,00 0,00 134,10 Code811w rp ,07 25,37 247, ,77 11,42 180, ,20 14,13 187, ,63 20,80 214,30 Code811w rp ,00 0,00 116, ,00 0,00 77, ,00 0,00 86, ,00 0,00 79,30 Code8 150w rp ,33 14,61 176, ,33 14,61 217, ,00 0,00 294, ,47 46,74 142,90 Code8 150w rp ,80 30,24 364, ,73 8,45 340, ,67 24,28 303, ,80 3,66 261,90 Code8 150w rp ,23 55,06 301, ,13 19,77 285, ,63 59,88 302, ,13 17,64 360,60 Code8 200w rp ,17 132,27 302, ,83 122,64 375, ,93 94,40 268, ,13 95,65 406,70 Code8 200w rp ,00 79,88 460, ,57 81,04 530, ,13 83,64 500, ,90 76,47 527,50 Code8 200w rp ,17 128,52 536, ,93 97,88 512, ,07 93,85 527, ,60 86,11 600,00 Code911w rp ,00 0,00 21, ,00 0,00 21, ,00 0,00 24, ,00 0,00 33,10 Code911w rp ,67 22,18 313, ,07 6,15 339, ,77 6,22 357, ,53 2,47 307,50 Code911w rp ,70 2,98 200, ,00 2,03 239, ,60 1,99 167, ,70 1,76 175,90 4
5 Code9 150w rp ,00 26,98 240, ,70 39,05 220, ,80 17,53 185, ,97 19,90 278,10 Code9 150w rp ,70 42,20 281, ,93 15,49 274, ,10 46,96 248, ,87 18,06 324,40 Code9 150w rp ,17 64,04 307, ,23 63,63 365, ,07 60,49 324, ,70 55,41 508,00 Code9 200w rp ,53 105,05 260, ,73 119,21 204, ,93 143,98 259, ,87 146,19 352,30 Code9 200w rp ,40 56,97 348, ,87 75,56 445, ,70 96,45 500, ,77 53,21 489,00 Code9 200w rp ,40 104,99 496, ,13 62,21 539, ,87 81,97 512, ,07 44,51 600,00 Code1011w rp ,10 7,92 297, ,00 0,00 254, ,60 2,19 209, ,00 0,00 134,70 Code1011w rp ,00 28,86 169, ,00 0,00 222, ,00 0,00 246, ,00 0,00 178,60 Code10 150w rp ,30 55,79 154, ,30 43,97 114, ,47 43,41 155, ,43 35,97 122,20 Code10 150w rp ,17 17,42 220, ,00 34,14 228, ,53 46,09 290, ,00 18,09 290,70 Code10 150w rp ,17 60,73 394, ,17 40,36 336, ,10 40,19 390, ,20 19,17 435,10 Code10 200w rp ,00 95,62 337, ,13 118,39 437, ,50 94,90 454, ,07 83,08 477,00 Code10 200w rp ,87 74,97 431, ,83 63,44 465, ,40 83,05 397, ,80 60,00 468,90 Code10 200w rp ,93 101,29 512, ,33 100,70 512, ,77 126,69 516, ,97 106,61 600,00 geometric mean 6983, , , , #best results #unique best results Multi-Level Evaluation Scheme The computational results for testing the multi-level evaluation scheme (ML-ES) are listed in Table 4. Table 4: Results for the multi-level evaluation scheme and the local/tabu search improvement compared to the standard LP solution evaluation with a runtime of 600 seconds. GA + sola + GA + sola + GA + sola + GA + sola + LP + LS ML-ES + LS ML-ES + improved LS ML-ES + improved TS Instance obj sd t best [s] obj sd t best [s] obj sd t best [s] obj sd t best [s] Code111w rp ,00 0,00 130, ,00 0,00 13, ,00 0,00 12, ,00 0,00 14,70 Code111w rp ,00 0,00 64, ,00 0,00 22, ,00 0,00 12, ,00 0,00 16,10 Code111w rp ,47 11,22 343, ,77 4,15 181, ,47 1,38 231, ,87 0,73 209,50 Code1 150w rp ,37 112,88 88, ,00 0,00 23, ,00 0,00 33, ,00 0,00 29,20 Code1 150w rp ,97 35,79 341, ,23 45,92 110, ,97 36,67 291, ,93 0,25 133,00 Code1 150w rp ,27 19,01 380, ,70 23,39 264, ,13 18,97 282, ,27 7,97 241,40 Code1 200w rp ,17 107,30 200, ,23 54,65 201, ,83 37,26 298, ,00 10,37 243,10 Code1 200w rp ,40 92,78 394, ,23 67,17 134, ,10 42,96 289, ,00 37,02 297,10 Code1 200w rp ,07 77,54 572, ,10 93,20 225, ,57 74,67 460, ,97 56,35 460,50 Code211w rp ,00 0,00 43, ,00 0,00 8, ,00 0,00 8, ,00 0,00 8,10 Code211w rp ,00 0,00 111, ,00 0,00 37, ,00 0,00 17, ,00 0,00 23,10 Code211w rp ,43 29,69 291, ,80 10,53 252, ,00 0,00 165, ,57 2,37 82,40 Code2 150w rp ,47 53,43 292, ,70 61,74 98, ,97 23,91 166, ,00 0,00 242,70 Code2 150w rp ,20 4,70 281, ,93 9,15 60, ,00 3,81 102, ,00 0,00 96,90 Code2 150w rp ,13 40,91 349, ,60 40,59 181, ,27 28,71 177, ,03 15,79 211,50 Code2 200w rp ,63 75,55 249, ,23 78,81 58, ,13 53,11 236, ,13 26,28 130,10 Code2 200w rp ,27 70,94 516, ,07 78,21 119, ,53 53,40 345, ,67 17,34 392,00 Code2 200w rp ,83 118,18 508, ,40 88,02 241, ,80 80,47 402, ,37 52,72 421,30 Code311w rp ,00 0,00 25, ,00 0,00 5, ,00 0,00 7, ,00 0,00 8,10 Code311w rp ,00 0,00 73, ,00 0,00 13, ,00 0,00 19, ,00 0,00 13,30 Code311w rp ,80 0,61 297, ,33 6,19 100, ,00 0,00 103, ,00 0,00 65,20 Code3 150w rp ,93 16,36 310, ,50 13,38 62, ,83 8,33 64, ,00 0,00 35,40 Code3 150w rp ,00 18,83 285, ,97 23,60 45, ,77 13,80 207, ,10 2,75 142,50 Code3 150w rp ,43 34,03 309, ,77 60,47 111, ,47 15,28 289, ,87 4,32 274,00 Code3 200w rp ,23 70,30 291, ,53 62,72 164, ,97 48,66 283, ,30 28,15 227,00 Code3 200w rp ,57 71,44 386, ,33 71,22 192, ,33 39,29 388, ,97 17,19 281,90 Code3 200w rp ,97 155,51 516, ,93 107,10 252, ,73 81,47 416, ,67 70,96 426,90 Code411w rp ,00 0,00 22, ,00 0,00 5, ,00 0,00 5, ,00 0,00 7,90 Code411w rp ,00 0,00 117, ,00 0,00 49, ,00 0,00 53, ,00 0,00 48,80 Code411w rp ,73 16,24 298, ,00 0,00 92, ,00 0,00 89, ,00 0,00 39,60 Code4 150w rp ,33 98,75 290, ,20 66,09 56, ,43 77,20 128, ,00 0,00 38,30 Code4 150w rp ,00 0,00 285, ,43 24,88 71, ,00 0,00 124, ,00 0,00 71,30 Code4 150w rp ,93 7,44 276, ,43 8,52 79, ,50 5,69 221, ,50 2,74 251,30 Code4 200w rp ,40 43,37 191, ,70 66,08 50, ,87 15,15 271, ,47 14,39 115,60 Code4 200w rp ,43 87,24 403, ,30 108,36 120, ,63 52,72 217, ,03 32,68 241,30 Code4 200w rp ,67 113,20 502, ,77 118,92 253, ,37 97,49 362, ,70 89,41 388,50 Code511w rp ,00 0,00 39, ,00 0,00 16, ,00 0,00 9, ,00 0,00 8,90 Code511w rp ,90 7,40 332, ,47 4,03 114, ,80 3,99 141, ,00 0,00 63,40 Code511w rp ,33 9,94 101, ,00 0,00 95, ,00 0,00 89, ,00 0,00 76,00 Code5 150w rp ,73 10,59 329, ,83 6,43 153, ,00 0,00 162, ,00 0,00 32,90 Code5 150w rp ,93 34,91 392, ,20 39,38 205, ,87 27,57 273, ,97 26,56 214,60 Code5 150w rp ,77 8,91 343, ,83 14,82 108, ,90 3,19 344, ,50 3,29 227,30 Code5 200w rp ,13 66,25 338, ,77 60,06 70, ,40 66,03 208, ,10 27,45 268,20 Code5 200w rp ,60 71,37 413, ,97 84,84 118, ,77 86,14 262, ,03 42,10 320,90 Code5 200w rp ,13 90,25 499, ,90 96,86 201, ,43 108,54 340, ,10 42,91 345,90 Code611w rp ,73 1,46 110, ,00 0,00 22, ,00 0,00 17, ,00 0,00 17,70 Code611w rp ,00 0,00 74, ,00 0,00 17, ,00 0,00 16, ,00 0,00 15,70 Code611w rp ,53 18,58 248, ,13 3,30 95, ,00 0,00 120, ,00 0,00 96,00 Code6 150w rp ,83 64,84 242, ,13 4,75 51, ,00 0,00 73, ,00 0,00 36,90 Code6 150w rp ,53 32,51 319, ,47 69,57 152, ,00 0,00 112, ,00 0,00 71,60 Code6 150w rp ,23 39,25 368, ,77 52,27 262, ,53 8,03 258, ,00 0,00 133,90 Code6 200w rp ,17 130,57 207, ,73 54,01 227, ,83 46,47 340, ,53 5,58 197,50 Code6 200w rp ,27 150,55 442, ,50 115,47 131, ,40 53,01 253, ,23 27,71 326,70 Code6 200w rp ,63 116,02 570, ,83 100,37 229, ,20 82,03 366, ,53 91,67 452,50 Code711w rp ,00 0,00 79, ,00 0,00 34, ,00 0,00 7, ,00 0,00 8,70 5
6 Code711w rp ,00 0,00 83, ,00 0,00 56, ,00 0,00 21, ,00 0,00 31,60 Code711w rp ,00 0,00 73, ,00 0,00 20, ,00 0,00 22, ,00 0,00 29,80 Code7 150w rp ,90 44,98 293, ,07 17,08 216, ,17 38,36 316, ,10 0,55 190,10 Code7 150w rp ,00 0,00 231, ,97 21,41 44, ,00 0,00 59, ,00 0,00 82,90 Code7 150w rp ,87 42,85 290, ,63 39,41 201, ,77 6,76 143, ,83 14,02 203,10 Code7 200w rp ,37 149,21 274, ,57 80,24 264, ,70 57,39 234, ,30 20,44 222,80 Code7 200w rp ,73 61,94 518, ,13 52,77 127, ,93 23,12 367, ,30 35,03 283,90 Code7 200w rp ,63 58,28 476, ,93 61,18 251, ,77 39,99 363, ,10 33,88 361,90 Code811w rp ,20 14,09 301, ,00 0,00 116, ,00 0,00 91, ,00 0,00 21,60 Code811w rp ,77 11,42 180, ,20 22,13 102, ,00 0,00 66, ,00 0,00 41,60 Code811w rp ,00 0,00 77, ,00 0,00 39, ,00 0,00 25, ,00 0,00 24,40 Code8 150w rp ,33 14,61 217, ,00 0,00 41, ,00 0,00 68, ,00 0,00 28,70 Code8 150w rp ,73 8,45 340, ,20 5,16 155, ,00 0,00 139, ,00 0,00 103,10 Code8 150w rp ,13 19,77 285, ,67 30,79 83, ,33 9,94 174, ,73 11,06 188,20 Code8 200w rp ,83 122,64 375, ,20 63,40 149, ,57 2,37 149, ,57 2,37 170,60 Code8 200w rp ,57 81,04 530, ,17 119,21 165, ,40 35,42 429, ,10 41,76 357,90 Code8 200w rp ,93 97,88 512, ,63 95,46 236, ,53 66,63 445, ,90 23,35 484,30 Code911w rp ,00 0,00 21, ,00 0,00 5, ,00 0,00 5, ,00 0,00 7,50 Code911w rp ,07 6,15 339, ,07 20,95 220, ,43 1,48 325, ,93 0,25 220,60 Code911w rp ,00 2,03 239, ,07 1,72 109, ,00 0,00 203, ,00 0,00 92,50 Code9 150w rp ,70 39,05 220, ,00 0,00 46, ,00 0,00 41, ,00 0,00 55,50 Code9 150w rp ,93 15,49 274, ,30 49,77 179, ,70 12,07 136, ,40 0,93 148,40 Code9 150w rp ,23 63,63 365, ,77 64,64 99, ,27 44,37 382, ,40 41,30 299,90 Code9 200w rp ,73 119,21 204, ,87 143,78 78, ,43 103,98 238, ,40 8,76 182,90 Code9 200w rp ,87 75,56 445, ,30 81,41 117, ,33 44,68 312, ,20 23,40 335,40 Code9 200w rp ,13 62,21 539, ,93 74,78 231, ,47 16,11 382, ,57 16,55 416,80 Code1011w rp ,53 11,83 110, ,70 11,61 74, ,00 0,00 19, ,00 0,00 18,20 Code1011w rp ,00 0,00 254, ,00 0,00 78, ,00 0,00 54, ,00 0,00 29,20 Code1011w rp ,00 0,00 222, ,00 0,00 91, ,00 0,00 72, ,00 0,00 60,80 Code10 150w rp ,30 43,97 114, ,47 35,67 90, ,00 0,00 35, ,00 0,00 30,20 Code10 150w rp ,00 34,14 228, ,60 13,56 95, ,00 0,00 90, ,00 0,00 104,30 Code10 150w rp ,17 40,36 336, ,13 31,81 260, ,13 17,52 216, ,40 10,21 175,30 Code10 200w rp ,13 118,39 437, ,20 15,97 361, ,63 7,57 329, ,00 0,00 151,70 Code10 200w rp ,83 63,44 465, ,17 109,00 130, ,37 56,94 332, ,40 51,91 434,30 Code10 200w rp ,33 100,70 512, ,67 131,72 224, ,30 143,66 390, ,73 74,95 460,40 geometric mean 6995, , , ,16 #best results #unique best results
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