This file updates the content of the "mkcbres.txt" file from the Beasley OR Library with the results by CPLEX 12.6.2.0 run on NEOS platform (further: NEOS CPLEX); https://neos-server.org/neos/solvers/lp:CPLEX/LP.html . The first table below gives: 1. The first column - the problem size (m,n) and the problem orginal number; observe that in the original file "mkcbres.txt" Chu and Beasley numbered problems starting from zero; here we keep this convention, so e.g. problem 5.500-00 corresponds to the first problem in the "mknapcb4.txt" file in the OR Beasley Library, mknapcb section, and to the "mknapcb_3_1.txt" file in the set of problems with data converted to the LP format (http://www.ibspan.waw.pl/~kaliszew/main_page.html), 2. The second column - the best feasible solution value found by the algorithm given in P.C. Chu and J.E. Beasley "A genetic algorithm for the multidimensional knapsack problem". Journal of Heuristics, 4: 63–86 (1998). For problems marked by * Chu and Beasley derived either the optimal solution but without optimality proof or the same or a better incumbent than NEOS CPLEX. 3. The third column - the optimal value or, if in parentheses, incumbent found by NEOS CPLEX. 4. The forth column - the NEOS CPLEX asolute improvement over the results reported by Chu and Beasly. 5. The fifth column - the NEOS CPLEX relative improvement over the results reported by Chu and Beasly. The second table below gives: 1. The first column - the problem size (m,n) and the problem orginal number; here, as in the first table, the problems are numberd from zero. 2. The second column - LP optimal value obtained by Chu and Beasley. 3. The third column - the LP optimal value obtained by NEOS CPLEX. 4. The forth column - the absolute improvement over the results reported by Chu and Beasly. 5. The fifth column - the relative improvement over the results reported by Chu and Beasly. The results given in this file refer to the following combinations of (n-m): (5-500), (10-250), (10-500), (300-100), (300-250), (300-500). Problem Best CPLEX Improve- Improvement name feasible optimal ment % solution or obtained incum- by Chu bent and value Beasley obtained on NEOS 5.500-00 120130 120148 18 0.0150 5.500-01 117837 117879 42 0.0356 5.500-02 121109 121131 22 0.0182 5.500-03 120798 120804 6 0.0050 5.500-04 122319 * 122319 0 0.0000 5.500-05 122007 122024 17 0.0139 5.500-06 119113 119127 14 0.0118 5.500-07 120568 * 120568 0 0.0000 5.500-08 121575 121586 11 0.0090 5.500-09 120699 120717 18 0.0149 5.500-10 218422 218428 6 0.0027 5.500-11 221191 221202 11 0.0050 5.500-12 217534 * (217534) 0 0.0000 5.500-13 223558 223560 2 0.0009 5.500-14 218962 218966 4 0.0018 5.500-15 220514 220530 16 0.0073 5.500-16 219987 219989 2 0.0009 5.500-17 218194 218215 21 0.0096 5.500-18 216976 * 216976 0 0.0000 5.500-19 219693 219719 26 0.0118 5.500-20 295828 * 295828 0 0.0000 5.500-21 308077 308086 9 0.0029 5.500-22 299796 * 299796 0 0.0000 5.500-23 306476 306480 4 0.0013 5.500-24 300342 * 300342 0 0.0000 5.500-25 302560 302571 11 0.0036 5.500-26 301322 301339 17 0.0056 5.500-27 306430 306454 24 0.0078 5.500-28 302814 302828 14 0.0046 5.500-29 299904 * 299904 0 0.0000 10.250-00 59187 * (59187) 0 0.0000 10.250-01 58662 58781 119 0.2029 10.250-02 58094 58097 3 0.0052 10.250-03 61000 (60989) -11 -0.0180 10.250-04 58092 * (58092) 0 0.0000 10.250-05 58803 (58824) 21 0.0357 10.250-06 58607 58704 97 0.1655 10.250-07 58917 (58933) 16 0.0272 10.250-08 59384 (59387) 3 0.0051 10.250-09 59193 (59208) 15 0.0253 10.250-10 110863 (110913) 50 0.0451 10.250-11 108659 (108715) 56 0.0515 10.250-12 108932 (108932) 0 0.0000 10.250-13 110037 (110081) 44 0.0400 10.250-14 108423 108485 62 0.0572 10.250-15 110841 (110845) 4 0.0036 10.250-16 106075 (106077) 2 0.0019 10.250-17 106686 * (106686) 0 0.0000 10.250-18 109825 (109829) 4 0.0036 10.250-19 106723 * (106723) 0 0.0000 10.250-20 151790 151809 19 0.0125 10.250-21 148772 (148772) 0 0.0000 10.250-22 151900 151909 9 0.0059 10.250-23 151275 151324 49 0.0324 10.250-24 151948 151966 18 0.0118 10.250-25 152109 152109 0 0.0000 10.250-26 153131 * 153131 0 0.0000 10.250-27 153520 153578 58 0.0378 10.250-28 149155 149160 5 0.0034 10.250-29 149704 * 149704 0 0.0000 10.500-00 117726 (117809) 83 0.0705 10.500-01 119139 (119158) 19 0.0159 10.500-02 119159 (119211) 52 0.0436 10.500-03 118802 (118813) 11 0.0093 10.500-04 116434 (116469) 35 0.0301 10.500-05 119454 (119448) -6 -0.0050 10.500-06 119749 (119790) 41 0.0342 10.500-07 118288 (118297) 9 0.0076 10.500-08 117779 * (117750) -29 -0.0246 10.500-09 119125 (119191) 66 0.0554 10.500-10 217318 (217377) 59 0.0271 10.500-11 219022 (219051) 29 0.0132 10.500-12 217772 (217797) 25 0.0115 10.500-13 216802 (216868) 66 0.0304 10.500-14 213809 (213843) 34 0.0159 10.500-15 215013 (215040) 27 0.0126 10.500-16 217896 * (217889) -7 -0.0032 10.500-17 219949 (219984) 35 0.0159 10.500-18 214332 (214352) 20 0.0093 10.500-19 220833 (220855) 22 0.0100 10.500-20 304344 (304387) 43 0.0141 10.500-21 302332 (302356) 24 0.0079 10.500-22 302354 (302408) 54 0.0179 10.500-23 300743 (300747) 4 0.0013 10.500-24 304344 (304357) 13 0.0043 10.500-25 301730 (301764) 34 0.0113 10.500-26 304949 (304949) 0 0.0000 10.500-27 296437 (296456) 19 0.0064 10.500-28 301313 (301321) 8 0.0027 10.500-29 307014 (307049) 35 0.0114 30.100-00 21946 * 21946 0 0.0000 30.100-01 21716 * 21716 0 0.0000 30.100-02 20754 * 20754 0 0.0000 30.100-03 21464 * 21464 0 0.0000 30.100-04 21814 * 21844 30 0.1375 30.100-05 22176 * 22176 0 0.0000 30.100-06 21799 * 21799 0 0.0000 30.100-07 21397 * 21397 0 0.0000 30.100-08 22493 22525 32 0.1423 30.100-09 20983 * 20983 0 0.0000 30.100-10 40767 * 40767 0 0.0000 30.100-11 41304 41308 4 0.0097 30.100-12 41560 41630 70 0.1684 30.100-13 41041 * 41041 0 0.0000 30.100-14 40872 40889 17 0.0416 30.100-15 41058 * 41058 0 0.0000 30.100-16 41062 * 41062 0 0.0000 30.100-17 42719 * 42719 0 0.0000 30.100-18 42230 * 42230 0 0.0000 30.100-19 41700 41700 0 0.0000 30.100-20 57494 * 57494 0 0.0000 30.100-21 60027 * 60027 0 0.0000 30.100-22 58025 58052 27 0.0465 30.100-23 60776 * 60776 0 0.0000 30.100-24 58884 * 58884 0 0.0000 30.100-25 60011 * 60011 0 0.0000 30.100-26 58132 * 58132 0 0.0000 30.100-27 59064 * 59064 0 0.0000 30.100-28 58975 * 58975 0 0.0000 30.100-29 60603 * 60603 0 0.0000 30.250-00 56693 (56824) 131 0.2311 30.250-01 58318 (58520) 202 0.3464 30.250-02 56553 (56614) 61 0.1079 30.250-03 56863 (56930) 67 0.1178 30.250-04 56629 (56608) -21 -0.0371 30.250-05 57119 (57205) 86 0.1506 30.250-06 56292 (56348) 56 0.0995 30.250-07 56403 (56448) 45 0.0798 30.250-08 57442 * (57442) 0 0.0000 30.250-09 56447 * (56447) 0 0.0000 30.250-10 107689 (107770) 81 0.0752 30.250-11 108338 (108379) 41 0.0378 30.250-12 106385 (106442) 57 0.0536 30.250-13 106796 (106865) 69 0.0646 30.250-14 107396 (107414) 18 0.0168 30.250-15 107246 (107271) 25 0.0233 30.250-16 106308 (106372) 64 0.0602 30.250-17 103993 (104014) 21 0.0202 30.250-18 106835 * (106835) 0 0.0000 30.250-19 105751 (105780) 29 0.0274 30.250-20 150083 (150100) 17 0.0113 30.250-21 149907 (149958) 51 0.0340 30.250-22 152993 (153007) 14 0.0092 30.250-23 153169 (153234) 65 0.0424 30.250-24 150287 (150287) 0 0.0000 30.250-25 148544 (148574) 30 0.0202 30.250-26 147471 (147477) 6 0.0041 30.250-27 152841 (152912) 71 0.0465 30.250-28 149568 (149570) 2 0.0013 30.250-29 149572 (149668) 96 0.0642 30.500-00 115868 (115950) 82 0.0708 30.500-01 114667 (114780) 113 0.0985 30.500-02 116661 (116613) -48 -0.0411 30.500-03 115237 (116525) 172 0.1478 30.500-05 115604 (115694) 90 0.0779 30.500-06 113952 (114072) 120 0.1053 30.500-07 114199 (114232) 33 0.0289 30.500-08 115247 (115419) 172 0.1492 30.500-09 116947 (117019) 72 0.0616 30.500-10 217995 (218068) 73 0.0335 30.500-11 214534 (214626) 92 0.0429 30.500-12 215854 (215918) 64 0.0296 30.500-13 217836 (217863) 27 0.0124 30.500-14 215566 (215604) 38 0.0176 30.500-15 215762 (215788) 26 0.0121 30.500-16 215772 (215831) 59 0.0273 30.500-17 216336 (216425) 89 0.0411 30.500-18 217290 (217312) 22 0.0101 30.500-19 214624 (214739) 115 0.0536 30.500-20 301627 (301656) 29 0.0096 30.500-21 299985 (300020) 35 0.0117 30.500-22 304995 (305087) 92 0.0302 30.500-23 301935 (301982) 47 0.0156 30.500-24 304404 (304398) -6 -0.0020 30.500-25 296894 (296960) 66 0.0222 30.500-26 303233 (303304) 71 0.0234 30.500-27 306944 (306961) 17 0.0055 30.500-28 303057 (303178) 121 0.0399 30.500-29 300460 (300532) 72 0.0240 Problem LP optimal LP optimal Improv- Improvement name obtained by obtained on NEOS ement % Chu and Beasley 5.500-00 1.2023491673E+05 1.2016001480E+05 74.90193 0.0623 5.500-01 1.1795516424E+05 1.1789078788E+05 64.37636 0.0546 5.500-02 1.2121332587E+05 1.2114311310E+05 70.21277 0.0579 5.500-03 1.2088852459E+05 1.2081608040E+05 72.44419 0.0599 5.500-04 1.2242649395E+05 1.2233123189E+05 95.26206 0.0778 5.500-05 1.2212597055E+05 1.2203620239E+05 89.76816 0.0735 5.500-06 1.1921875799E+05 1.1913891270E+05 79.84529 0.0670 5.500-07 1.2064312783E+05 1.2058005677E+05 63.07106 0.0523 5.500-08 1.2166328076E+05 1.2159815859E+05 65.12217 0.0535 5.500-09 1.2080067536E+05 1.2072907170E+05 71.60366 0.0593 5.500-10 2.1850008325E+05 2.1844984279E+05 50.24046 0.0230 5.500-11 2.2127240550E+05 2.2122412020E+05 48.28530 0.0218 5.500-12 2.1761579702E+05 2.1756281391E+05 52.98311 0.0243 5.500-13 2.2365320947E+05 2.2358235600E+05 70.85347 0.0317 5.500-14 2.1906746667E+05 2.1898789639E+05 79.57028 0.0363 5.500-15 2.2061696224E+05 2.2055205298E+05 64.90926 0.0294 5.500-16 2.2007654782E+05 2.2001099888E+05 65.54894 0.0298 5.500-17 2.1828270591E+05 2.1823682149E+05 45.88442 0.0210 5.500-18 2.1705990360E+05 2.1699769759E+05 62.20601 0.0287 5.500-19 2.1981282298E+05 2.1974097188E+05 71.85110 0.0327 5.500-20 2.9589637697E+05 2.9585758255E+05 38.79442 0.0131 5.500-21 3.0815759683E+05 3.0811680855E+05 40.78828 0.0132 5.500-22 2.9987863506E+05 2.9982597956E+05 52.65550 0.0176 5.500-23 3.0655412944E+05 3.0651064799E+05 43.48145 0.0142 5.500-24 3.0041255797E+05 3.0037203395E+05 40.52402 0.0135 5.500-25 3.0266175013E+05 3.0260125709E+05 60.49304 0.0200 5.500-26 3.0140024536E+05 3.0136072202E+05 39.52334 0.0131 5.500-27 3.0651727306E+05 3.0647699758E+05 40.27548 0.0131 5.500-28 3.0289676134E+05 3.0285361455E+05 43.14679 0.0142 5.500-29 2.9997371776E+05 2.9993399039E+05 39.72737 0.0132 10.250-00 5.9489339237E+04 5.9320368035E+04 168.97120 0.2840 10.250-01 5.9024301618E+04 5.8786877934E+04 237.42368 0.4022 10.250-02 5.8413150128E+04 5.8102809672E+04 310.34046 0.5313 10.250-03 6.1262996954E+04 6.1127487728E+04 135.50923 0.2212 10.250-04 5.8363341572E+04 5.8224552586E+04 138.78899 0.2378 10.250-05 5.9052327288E+04 5.8894391541E+04 157.93575 0.2675 10.250-06 5.8894666665E+04 5.8709870394E+04 184.79627 0.3138 10.250-07 5.9204526838E+04 5.9087310075E+04 117.21676 0.1980 10.250-08 5.9701693112E+04 5.9087310075E+04 614.38304 1.0291 10.250-09 5.9495159378E+04 5.9483319764E+04 11.83961 0.0199 10.250-10 1.1114715301E+05 1.1098736745E+05 159.78556 0.1438 10.250-11 1.0894761747E+05 1.0880543296E+05 142.18451 0.1305 10.250-12 1.0921136647E+05 1.0901754621E+05 193.82026 0.1775 10.250-13 1.1030649459E+05 1.1020022940E+05 106.26519 0.0963 10.250-14 1.0872851736E+05 1.0849584846E+05 232.66890 0.2140 10.250-15 1.1110679918E+05 1.1094376308E+05 163.03610 0.1467 10.250-16 1.0637133258E+05 1.0618357981E+05 187.75277 0.1765 10.250-17 1.0692273460E+05 1.0677875055E+05 143.98405 0.1347 10.250-18 1.1009444234E+05 1.0992080110E+05 173.64124 0.1577 10.250-19 1.0697307190E+05 1.0673367227E+05 239.39963 0.2238 10.250-20 1.5203138663E+05 1.5182418089E+05 207.20574 0.1363 10.250-21 1.4902161650E+05 1.4884569972E+05 175.91678 0.1180 10.250-22 1.5214125987E+05 1.5192419086E+05 217.06901 0.1427 10.250-23 1.5149002143E+05 1.5133913232E+05 150.88911 0.0996 10.250-24 1.5216955171E+05 1.5198119660E+05 188.35511 0.1238 10.250-25 1.5232675542E+05 1.5212421083E+05 202.54459 0.1330 10.250-26 1.5336543619E+05 1.5314631294E+05 219.12325 0.1429 10.250-27 1.5376516339E+05 1.5365732115E+05 107.84224 0.0701 10.250-28 1.4937282630E+05 1.4917491592E+05 197.91038 0.1325 10.250-29 1.4991672245E+05 1.4971897036E+05 197.75209 0.1319 10.500-00 1.1801947688E+05 1.1796077557E+05 58.70131 0.0497 10.500-01 1.1943728755E+05 1.1938110860E+05 56.17895 0.0470 10.500-02 1.1940570001E+05 1.1935288443E+05 52.81558 0.0442 10.500-03 1.1906609340E+05 1.1897813996E+05 87.95344 0.0739 10.500-04 1.1669795500E+05 1.1665657672E+05 41.37828 0.0355 10.500-05 1.1970995427E+05 1.1964288826E+05 67.06601 0.0560 10.500-06 1.2003331236E+05 1.1995731077E+05 76.00159 0.0633 10.500-07 1.1854570561E+05 1.1847468181E+05 71.02380 0.0599 10.500-08 1.1800159642E+05 1.1793762890E+05 63.96752 0.0542 10.500-09 1.1944064466E+05 1.1938492947E+05 55.71519 0.0466 10.500-10 2.1755291667E+05 2.1749356576E+05 59.35091 0.0273 10.500-11 2.1925519173E+05 2.1920077835E+05 54.41338 0.0248 10.500-12 2.1798778166E+05 2.1793308394E+05 54.69772 0.0251 10.500-13 2.1704066999E+05 2.1698871445E+05 51.95554 0.0239 10.500-14 2.1401031384E+05 2.1397520400E+05 35.10984 0.0164 10.500-15 2.1526133241E+05 2.1520514992E+05 56.18249 0.0261 10.500-16 2.1810919852E+05 2.1804666324E+05 62.53528 0.0287 10.500-17 2.2017555900E+05 2.2011480451E+05 60.75449 0.0276 10.500-18 2.1456104137E+05 2.1449739381E+05 63.64756 0.0297 10.500-19 2.2108363678E+05 2.2102147428E+05 62.16250 0.0281 10.500-20 3.0455503161E+05 3.0447905151E+05 75.98010 0.0249 10.500-21 3.0255296929E+05 3.0248352350E+05 69.44579 0.0230 10.500-22 3.0258154377E+05 3.0252448633E+05 57.05744 0.0189 10.500-23 3.0095672281E+05 3.0087821459E+05 78.50822 0.0261 10.500-24 3.0458473485E+05 3.0450106771E+05 83.66714 0.0275 10.500-25 3.0195251570E+05 3.0190305227E+05 49.46343 0.0164 10.500-26 3.0513972652E+05 3.0507436771E+05 65.35881 0.0214 10.500-27 2.9663657338E+05 2.9657370328E+05 62.87010 0.0212 10.500-28 3.0154762738E+05 3.0147719788E+05 70.42950 0.0234 10.500-29 3.0724999467E+05 3.0718336793E+05 66.62674 0.0217 30.100-00 2.2579069212E+04 2.1948192737E+04 630.87647 2.7941 30.100-01 2.2367844631E+04 2.1718171025E+04 649.67361 2.9045 30.100-02 2.1270501365E+04 2.0756073497E+04 514.42787 2.4185 30.100-03 2.2049634468E+04 2.1466146183E+04 583.48828 2.6462 30.100-04 2.2531454669E+04 2.1846184078E+04 685.27059 3.0414 30.100-05 2.2910072356E+04 2.2178217031E+04 731.85533 3.1945 30.100-06 2.2530091561E+04 2.1801178040E+04 728.91352 3.2353 30.100-07 2.2088758696E+04 2.1399138794E+04 689.61990 3.1220 30.100-08 2.3201206906E+04 2.2527252191E+04 673.95471 2.9048 30.100-09 2.1524818140E+04 2.0985084966E+04 539.73317 2.5075 30.100-10 4.1276362342E+04 4.0771076668E+04 505.28567 1.2242 30.100-11 4.1866733659E+04 4.1312129955E+04 554.60370 1.3247 30.100-12 4.2232960640E+04 4.1634162892E+04 598.79775 1.4178 30.100-13 4.1634875036E+04 4.1045101939E+04 589.77310 1.4165 30.100-14 4.1410884850E+04 4.0893088141E+04 517.79671 1.2504 30.100-15 4.1603163557E+04 4.1062105592E+04 541.05797 1.3005 30.100-16 4.1616130334E+04 4.1066105881E+04 550.02445 1.3217 30.100-17 4.3388049309E+04 4.2723268506E+04 664.78080 1.5322 30.100-18 4.2656562926E+04 4.2234221137E+04 422.34179 0.9901 30.100-19 4.2262702368E+04 4.1704167183E+04 558.53519 1.3216 30.100-20 5.7987771072E+04 5.7499737479E+04 488.03359 0.8416 30.100-21 6.0486824869E+04 6.0033001945E+04 453.82292 0.7503 30.100-22 5.8541843041E+04 5.8057802627E+04 484.04041 0.8268 30.100-23 6.1239524289E+04 6.0782058849E+04 457.46544 0.7470 30.100-24 5.9380820171E+04 5.8889872961E+04 490.94721 0.8268 30.100-25 6.0452579964E+04 6.0017000276E+04 435.57969 0.7205 30.100-26 5.8635340471E+04 5.8137802609E+04 497.53786 0.8485 30.100-27 5.9550708673E+04 5.9069898678E+04 480.81000 0.8074 30.100-28 5.9520220087E+04 5.8980897254E+04 539.32283 0.9061 30.100-29 6.1140159137E+04 6.0609060176E+04 531.09896 0.8687 30.250-00 5.7430148056E+04 5.7112229231E+04 317.91883 0.5536 30.250-01 5.9080031355E+04 5.8786296220E+04 293.73514 0.4972 30.250-02 5.7176741169E+04 5.6896402111E+04 280.33906 0.4903 30.250-03 5.7568920302E+04 5.7237714704E+04 331.20560 0.5753 30.250-04 5.7277695761E+04 5.6968769946E+04 308.92582 0.5393 30.250-05 5.7844080772E+04 5.7537920729E+04 306.16004 0.5293 30.250-06 5.6922694564E+04 5.6715247222E+04 207.44734 0.3644 30.250-07 5.7106212879E+04 5.6773684770E+04 332.52811 0.5823 30.250-08 5.8097727984E+04 5.7836556135E+04 261.17185 0.4495 30.250-09 5.7036642112E+04 5.6738337492E+04 298.30462 0.5230 30.250-10 1.0825806939E+05 1.0800967896E+05 248.39043 0.2294 30.250-11 1.0889980003E+05 1.0865404773E+05 245.75230 0.2257 30.250-12 1.0690571505E+05 1.0667289355E+05 232.82150 0.2178 30.250-13 1.0739661415E+05 1.0718414892E+05 212.46523 0.1978 30.250-14 1.0795409221E+05 1.0770798524E+05 246.10697 0.2280 30.250-15 1.0776320907E+05 1.0752509925E+05 238.10982 0.2210 30.250-16 1.0685085514E+05 1.0662377084E+05 227.08430 0.2125 30.250-17 1.0457408643E+05 1.0430910125E+05 264.98518 0.2534 30.250-18 1.0737384099E+05 1.0712085752E+05 252.98347 0.2356 30.250-19 1.0632177906E+05 1.0608634873E+05 235.43033 0.2214 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