2908:
2447:
523:
refers to the inheritance of characteristics of one generation by the next. For example, a schema is propagated if individuals in the current generation match it and so do those in the next generation. Those in the next generation may be (but do not have to be) children of parents who matched it.
1120:
2315:
2848:
984:
539:
Two basic operators are defined for schema: expansion and compression. The expansion maps a schema onto a set of words which it represents, while the compression maps a set of words on to a schema.
377:
is the average fitness of all strings matching the schema. The fitness of a string is a measure of the value of the encoded problem solution, as computed by a problem-specific evaluation function.
331:
For example, consider binary strings of length 6. The schema 1**0*1 describes the set of all words of length 6 with 1's at the first and sixth positions and a 0 at the fourth position. The * is a
2310:
2219:
2580:
1985:
2998:
2898:
1474:
1226:
2535:
2157:
1510:
2686:
2442:{\displaystyle {\uparrow }\epsilon _{*}\subseteq {\uparrow }11\subseteq {\uparrow }1*\subseteq {\uparrow }**=\emptyset \subseteq \{11\}\subseteq \{11,10\}\subseteq \{11,10,01,00\}}
1665:
841:
2711:
2106:
2953:
2633:
2069:
1696:
1537:
1376:
1195:
726:
800:
1947:
1251:
866:
2474:
1888:
1816:
1587:
1278:
977:
773:
654:
587:
371:
2494:
910:
1848:
2183:
1921:
1338:
674:
627:
560:
2239:
1431:
461:
432:
1402:
2706:
2600:
2025:
2005:
1776:
1756:
1736:
1716:
1627:
1607:
1318:
1298:
1162:
1142:
950:
930:
746:
694:
607:
481:
403:
3149:
270:
3405:
93:
3142:
229:
17:
263:
3400:
3192:
3187:
3182:
98:
373:
is the distance between the first and last specific positions. The order of 1**0*1 is 3 and its defining length is 5. The
2264:
2188:
3438:
1670:
3135:
3057:
2540:
1115:{\displaystyle {\uparrow }s:=\{b\in \Sigma ^{l}|b_{i}=s_{i}{\mbox{ or }}s_{i}=*{\mbox{ for each }}i\in \{1,...,l\}\}}
176:
256:
123:
31:
1952:
3210:
58:
2958:
2858:
156:
1436:
3306:
1200:
209:
186:
166:
128:
2507:
2118:
1482:
3464:
2641:
224:
171:
1632:
808:
3459:
3301:
3245:
3021:
103:
2074:
3265:
3255:
2914:
2605:
2246:
2030:
214:
161:
113:
1515:
1343:
1167:
699:
3110:
Jack McKay
Fletcher and Thomas Wennkers (2017). "A natural approach to studying schema processing".
3230:
3177:
3158:
778:
78:
1926:
1231:
846:
3360:
3286:
3026:
3009:
2459:
1853:
1781:
1542:
1256:
955:
751:
632:
565:
347:
3355:
3225:
3172:
2479:
871:
508:
68:
48:
39:
1821:
3390:
3375:
2162:
1893:
1323:
659:
612:
545:
219:
181:
2843:{\displaystyle {\mathcal {S}}(A)=\{001,100,000,110,00*,*00,1*0,**0,*0*,***,\epsilon _{*}\}}
2224:
1407:
437:
408:
8:
3334:
3240:
2254:
1381:
516:
307:
of strings with similarities at certain string positions. Schemata are a special case of
200:
133:
88:
3281:
3250:
3220:
3111:
2691:
2585:
2010:
1990:
1761:
1741:
1721:
1701:
1612:
1592:
1303:
1283:
1147:
1127:
935:
915:
731:
679:
592:
512:
466:
388:
332:
83:
63:
3420:
3395:
3385:
3339:
3324:
3235:
3053:
2453:
2112:
335:
symbol, which means that positions 2, 3 and 5 can have a value of either 1 or 0. The
320:
300:
147:
108:
73:
3430:
3410:
3380:
3370:
2901:
2242:
316:
296:
244:
138:
2537:, we call the process of calculating the compression on each subset of A, that is
3365:
3047:
341:
312:
53:
3083:
3329:
3291:
3260:
2007:
and if all elements in a column are equivalent, the symbol at that position in
118:
3453:
3316:
3296:
3001:
191:
3127:
2250:
533:
308:
2027:
takes this value, otherwise there is a wild card symbol. For example, let
3415:
3109:
339:
is defined as the number of fixed positions in the template, while the
2911:
The
Schematic lattice formed from the schematic completion on the set
3202:
2499:
2907:
3116:
3008:
The schematic lattice is similar to the concept lattice found in
1987:. One can think of this operator as stacking up all the items in
239:
3215:
2258:
319:
on strings. In other words, schemata can be used to generate a
304:
463:
is also equal to the number of nodes in the programs matching
2853:
491:
If the child of an individual that matches schema H does not
527:
434:, is defined as the total number of nodes in the schema.
3216:
Covariance Matrix
Adaptation Evolution Strategy (CMA-ES)
1070:
1047:
2961:
2917:
2861:
2714:
2694:
2644:
2608:
2588:
2543:
2510:
2482:
2462:
2318:
2267:
2227:
2191:
2165:
2121:
2077:
2033:
2013:
1993:
1955:
1929:
1896:
1856:
1824:
1784:
1764:
1744:
1724:
1704:
1673:
1635:
1615:
1595:
1545:
1518:
1485:
1439:
1410:
1384:
1346:
1326:
1306:
1286:
1259:
1234:
1203:
1170:
1150:
1130:
987:
958:
938:
918:
874:
849:
811:
781:
754:
734:
702:
682:
662:
635:
615:
595:
568:
548:
469:
440:
411:
391:
350:
3045:
2992:
2947:
2892:
2842:
2700:
2680:
2627:
2594:
2574:
2529:
2500:The Schematic Completion and The Schematic Lattice
2488:
2468:
2441:
2305:{\displaystyle \epsilon _{*}\leq 11\leq 1*\leq **}
2304:
2233:
2214:{\displaystyle {\uparrow }a\subseteq {\uparrow }b}
2213:
2177:
2151:
2100:
2063:
2019:
1999:
1979:
1941:
1915:
1882:
1842:
1810:
1770:
1750:
1730:
1710:
1690:
1659:
1621:
1601:
1581:
1531:
1504:
1468:
1425:
1396:
1370:
1332:
1312:
1292:
1272:
1245:
1220:
1189:
1156:
1136:
1114:
971:
944:
924:
904:
860:
835:
794:
767:
740:
720:
688:
668:
648:
621:
601:
581:
554:
475:
455:
426:
397:
365:
3451:
2575:{\displaystyle \{{\downarrow }X|X\subseteq A\}}
2452:The compression and expansion operators form a
3143:
264:
3157:
3049:Adaptation in Natural and Artificial Systems
2942:
2924:
2837:
2734:
2675:
2651:
2569:
2544:
2436:
2412:
2406:
2394:
2388:
2382:
2058:
2040:
1980:{\displaystyle {\downarrow }A=\epsilon _{*}}
1463:
1451:
1365:
1353:
1109:
1106:
1082:
999:
3150:
3136:
3105:
3103:
3101:
271:
257:
3115:
2993:{\displaystyle ({\mathcal {S}}(A),\leq )}
2893:{\displaystyle ({\mathcal {S}}(A),\leq )}
495:match H, the schema is said to have been
3406:No free lunch in search and optimization
2906:
1469:{\displaystyle {\uparrow }s=\{100,101\}}
532:Recently schema have been studied using
502:
3098:
3039:
1778:is determined in the following way: if
1221:{\displaystyle {\uparrow }s=\emptyset }
528:The Expansion and Compression Operators
14:
3452:
3078:
3076:
2530:{\displaystyle A\subseteq \Sigma ^{l}}
2152:{\displaystyle a,b\in \Sigma _{*}^{l}}
1505:{\displaystyle A\subseteq \Sigma ^{l}}
3131:
2681:{\displaystyle A=\{110,100,001,000\}}
3401:Interactive evolutionary computation
3193:Interactive evolutionary computation
3188:Human-based evolutionary computation
3183:Evolutionary multimodal optimization
3084:"Foundations of Genetic Programming"
1660:{\displaystyle s\in \Sigma _{*}^{l}}
836:{\displaystyle s\in \Sigma _{*}^{l}}
99:Evolutionary multimodal optimization
3073:
3052:(reprint ed.). The MIT Press.
1280:that can be made by exchanging the
288:
24:
3439:Evolutionary Computation (journal)
2967:
2867:
2717:
2708:, results in the following set:
2611:
2518:
2376:
2135:
2101:{\displaystyle {\downarrow }A=**0}
1936:
1643:
1493:
1347:
1327:
1261:
1215:
1144:denotes the character at position
1009:
960:
819:
756:
704:
663:
637:
616:
570:
549:
25:
3476:
2948:{\displaystyle A=\{111,011,001\}}
2628:{\displaystyle {\mathcal {S}}(A)}
2064:{\displaystyle A=\{100,000,010\}}
1738:such that the symbol at position
1691:{\displaystyle {\downarrow }A:=s}
1532:{\displaystyle {\downarrow }{A}}
124:Promoter based genetic algorithm
3211:Cellular evolutionary algorithm
2904:called the schematic lattice.
1371:{\displaystyle \Sigma =\{0,1\}}
1190:{\displaystyle s=\epsilon _{*}}
721:{\displaystyle \Sigma _{*}^{l}}
59:Cellular evolutionary algorithm
2987:
2978:
2972:
2962:
2887:
2878:
2872:
2862:
2728:
2722:
2688:. The schematic completion of
2622:
2616:
2582:, the schematic completion of
2556:
2548:
2483:
2463:
2363:
2349:
2338:
2320:
2245:on a set of schemata from the
2204:
2193:
2079:
1957:
1675:
1520:
1441:
1236:
1205:
1019:
989:
851:
450:
444:
421:
415:
360:
354:
326:
13:
1:
3307:Bacterial Colony Optimization
3032:
2955:. Here the schematic lattice
795:{\displaystyle \epsilon _{*}}
728:denotes all schema of length
542:In the following definitions
486:
210:Cartesian genetic programming
129:Spiral optimization algorithm
3046:Holland, John Henry (1992).
1942:{\displaystyle A=\emptyset }
1246:{\displaystyle {\uparrow }s}
861:{\displaystyle {\uparrow }s}
775:as well as the empty schema
589:denotes all words of length
225:Multi expression programming
7:
3302:Particle swarm optimization
3246:Gene expression programming
3015:
2469:{\displaystyle \downarrow }
1883:{\displaystyle s_{i}=x_{i}}
1811:{\displaystyle x_{i}=y_{i}}
1582:{\displaystyle compression}
1273:{\displaystyle \Sigma ^{l}}
1253:is the set of all words in
1164:in a word or schema. When
972:{\displaystyle \Sigma ^{l}}
768:{\displaystyle \Sigma _{*}}
649:{\displaystyle \Sigma _{*}}
582:{\displaystyle \Sigma ^{l}}
104:Particle swarm optimization
10:
3481:
3266:Learning classifier system
3256:Natural evolution strategy
366:{\displaystyle \delta (H)}
215:Linear genetic programming
162:Clonal selection algorithm
114:Natural evolution strategy
3429:
3348:
3315:
3274:
3201:
3165:
2489:{\displaystyle \uparrow }
2476:is the lower adjoint and
905:{\displaystyle expansion}
380:
3231:Evolutionary programming
3178:Evolutionary data mining
3159:Evolutionary computation
3022:Holland's schema theorem
1843:{\displaystyle x,y\in A}
952:to a subset of words in
79:Evolutionary computation
3361:Artificial intelligence
3287:Ant colony optimization
3027:Formal concept analysis
3010:Formal concept analysis
2261:relation. For example,
2178:{\displaystyle a\leq b}
1916:{\displaystyle s_{i}=*}
1333:{\displaystyle \Sigma }
843:the following operator
669:{\displaystyle \Sigma }
622:{\displaystyle \Sigma }
555:{\displaystyle \Sigma }
385:The length of a schema
323:on a space of strings.
3356:Artificial development
3226:Differential evolution
3173:Evolutionary algorithm
3005:
2994:
2949:
2894:
2844:
2702:
2682:
2629:
2596:
2576:
2531:
2490:
2470:
2443:
2306:
2235:
2215:
2179:
2153:
2102:
2065:
2021:
2001:
1981:
1943:
1917:
1884:
1844:
1812:
1772:
1752:
1732:
1718:is a schema of length
1712:
1692:
1661:
1623:
1603:
1583:
1533:
1506:
1470:
1427:
1398:
1372:
1334:
1314:
1294:
1274:
1247:
1222:
1191:
1158:
1138:
1116:
973:
946:
926:
906:
862:
837:
796:
769:
742:
722:
690:
676:with the extra symbol
670:
650:
623:
603:
583:
556:
509:evolutionary computing
477:
457:
428:
399:
367:
69:Differential evolution
49:Artificial development
40:Evolutionary algorithm
18:Disruption (of schema)
3391:Fitness approximation
3376:Evolutionary robotics
3317:Metaheuristic methods
2995:
2950:
2910:
2895:
2845:
2703:
2683:
2630:
2597:
2577:
2532:
2491:
2471:
2444:
2307:
2236:
2234:{\displaystyle \leq }
2216:
2180:
2154:
2103:
2066:
2022:
2002:
1982:
1944:
1918:
1885:
1845:
1813:
1773:
1753:
1733:
1713:
1693:
1662:
1624:
1604:
1584:
1534:
1507:
1471:
1428:
1426:{\displaystyle s=10*}
1399:
1373:
1335:
1315:
1295:
1275:
1248:
1223:
1192:
1159:
1139:
1117:
974:
947:
927:
907:
863:
838:
797:
770:
743:
723:
691:
671:
656:denotes the alphabet
651:
624:
604:
584:
562:denotes an alphabet,
557:
503:Propagation of schema
478:
458:
429:
400:
368:
299:used in the field of
220:Grammatical evolution
182:Genetic fuzzy systems
2959:
2915:
2859:
2712:
2692:
2642:
2606:
2586:
2541:
2508:
2480:
2460:
2316:
2265:
2225:
2189:
2163:
2119:
2075:
2031:
2011:
1991:
1953:
1927:
1894:
1854:
1822:
1782:
1762:
1742:
1722:
1702:
1671:
1633:
1613:
1593:
1543:
1516:
1483:
1479:Conversely, for any
1437:
1408:
1382:
1344:
1324:
1304:
1284:
1257:
1232:
1228:. More simply put,
1201:
1168:
1148:
1128:
1072: for each
985:
956:
936:
916:
872:
847:
809:
779:
752:
732:
700:
680:
660:
633:
613:
593:
566:
546:
467:
456:{\displaystyle N(H)}
438:
427:{\displaystyle N(H)}
409:
389:
348:
3465:Genetic programming
3335:Gaussian adaptation
3241:Genetic programming
2496:the upper adjoint.
2148:
1656:
1397:{\displaystyle l=3}
832:
717:
517:genetic programming
375:fitness of a schema
295:) is a template in
230:Genetic Improvement
201:Genetic programming
134:Self-modifying code
89:Gaussian adaptation
3460:Genetic algorithms
3282:Swarm intelligence
3275:Related techniques
3251:Evolution strategy
3221:Cultural algorithm
3006:
2990:
2945:
2890:
2840:
2698:
2678:
2625:
2592:
2572:
2527:
2486:
2466:
2439:
2312:. This is because
2302:
2231:
2221:. It follows that
2211:
2175:
2149:
2134:
2098:
2061:
2017:
1997:
1977:
1939:
1913:
1880:
1840:
1808:
1768:
1748:
1728:
1708:
1688:
1657:
1642:
1619:
1599:
1579:
1529:
1502:
1466:
1423:
1394:
1368:
1340:. For example, if
1330:
1320:with symbols from
1310:
1290:
1270:
1243:
1218:
1187:
1154:
1134:
1112:
1074:
1051:
969:
942:
922:
902:
858:
833:
818:
792:
765:
748:over the alphabet
738:
718:
703:
686:
666:
646:
619:
609:over the alphabet
599:
579:
552:
513:genetic algorithms
473:
453:
424:
395:
363:
303:that identifies a
301:genetic algorithms
84:Evolution strategy
64:Cultural algorithm
3447:
3446:
3421:Program synthesis
3396:Genetic operators
3386:Fitness landscape
3340:Memetic algorithm
3325:Firefly algorithm
3236:Genetic algorithm
2701:{\displaystyle A}
2638:For example, let
2595:{\displaystyle A}
2454:Galois connection
2113:partially ordered
2020:{\displaystyle s}
2000:{\displaystyle A}
1771:{\displaystyle s}
1751:{\displaystyle i}
1731:{\displaystyle l}
1711:{\displaystyle s}
1622:{\displaystyle A}
1602:{\displaystyle A}
1313:{\displaystyle s}
1293:{\displaystyle *}
1157:{\displaystyle i}
1137:{\displaystyle i}
1073:
1050:
945:{\displaystyle s}
925:{\displaystyle s}
741:{\displaystyle l}
689:{\displaystyle *}
602:{\displaystyle l}
476:{\displaystyle H}
398:{\displaystyle H}
337:order of a schema
281:
280:
148:Genetic algorithm
109:Memetic algorithm
94:Grammar induction
74:Effective fitness
16:(Redirected from
3472:
3411:Machine learning
3381:Fitness function
3371:Digital organism
3152:
3145:
3138:
3129:
3128:
3122:
3121:
3119:
3107:
3096:
3095:
3093:
3091:
3080:
3071:
3070:
3068:
3066:
3043:
2999:
2997:
2996:
2991:
2971:
2970:
2954:
2952:
2951:
2946:
2902:complete lattice
2899:
2897:
2896:
2891:
2871:
2870:
2849:
2847:
2846:
2841:
2836:
2835:
2721:
2720:
2707:
2705:
2704:
2699:
2687:
2685:
2684:
2679:
2634:
2632:
2631:
2626:
2615:
2614:
2601:
2599:
2598:
2593:
2581:
2579:
2578:
2573:
2559:
2551:
2536:
2534:
2533:
2528:
2526:
2525:
2495:
2493:
2492:
2487:
2475:
2473:
2472:
2467:
2448:
2446:
2445:
2440:
2366:
2352:
2341:
2333:
2332:
2323:
2311:
2309:
2308:
2303:
2277:
2276:
2243:partial ordering
2240:
2238:
2237:
2232:
2220:
2218:
2217:
2212:
2207:
2196:
2184:
2182:
2181:
2176:
2158:
2156:
2155:
2150:
2147:
2142:
2111:Schemata can be
2107:
2105:
2104:
2099:
2082:
2070:
2068:
2067:
2062:
2026:
2024:
2023:
2018:
2006:
2004:
2003:
1998:
1986:
1984:
1983:
1978:
1976:
1975:
1960:
1948:
1946:
1945:
1940:
1922:
1920:
1919:
1914:
1906:
1905:
1889:
1887:
1886:
1881:
1879:
1878:
1866:
1865:
1849:
1847:
1846:
1841:
1817:
1815:
1814:
1809:
1807:
1806:
1794:
1793:
1777:
1775:
1774:
1769:
1757:
1755:
1754:
1749:
1737:
1735:
1734:
1729:
1717:
1715:
1714:
1709:
1697:
1695:
1694:
1689:
1678:
1666:
1664:
1663:
1658:
1655:
1650:
1628:
1626:
1625:
1620:
1608:
1606:
1605:
1600:
1588:
1586:
1585:
1580:
1538:
1536:
1535:
1530:
1528:
1523:
1511:
1509:
1508:
1503:
1501:
1500:
1475:
1473:
1472:
1467:
1444:
1432:
1430:
1429:
1424:
1403:
1401:
1400:
1395:
1377:
1375:
1374:
1369:
1339:
1337:
1336:
1331:
1319:
1317:
1316:
1311:
1299:
1297:
1296:
1291:
1279:
1277:
1276:
1271:
1269:
1268:
1252:
1250:
1249:
1244:
1239:
1227:
1225:
1224:
1219:
1208:
1196:
1194:
1193:
1188:
1186:
1185:
1163:
1161:
1160:
1155:
1143:
1141:
1140:
1135:
1124:Where subscript
1121:
1119:
1118:
1113:
1075:
1071:
1062:
1061:
1052:
1048:
1045:
1044:
1032:
1031:
1022:
1017:
1016:
992:
978:
976:
975:
970:
968:
967:
951:
949:
948:
943:
931:
929:
928:
923:
911:
909:
908:
903:
867:
865:
864:
859:
854:
842:
840:
839:
834:
831:
826:
801:
799:
798:
793:
791:
790:
774:
772:
771:
766:
764:
763:
747:
745:
744:
739:
727:
725:
724:
719:
716:
711:
695:
693:
692:
687:
675:
673:
672:
667:
655:
653:
652:
647:
645:
644:
628:
626:
625:
620:
608:
606:
605:
600:
588:
586:
585:
580:
578:
577:
561:
559:
558:
553:
482:
480:
479:
474:
462:
460:
459:
454:
433:
431:
430:
425:
404:
402:
401:
396:
372:
370:
369:
364:
317:product topology
297:computer science
290:
273:
266:
259:
245:Parity benchmark
139:Polymorphic code
27:
26:
21:
3480:
3479:
3475:
3474:
3473:
3471:
3470:
3469:
3450:
3449:
3448:
3443:
3425:
3366:Artificial life
3344:
3311:
3270:
3197:
3161:
3156:
3126:
3125:
3108:
3099:
3089:
3087:
3082:
3081:
3074:
3064:
3062:
3060:
3044:
3040:
3035:
3018:
2966:
2965:
2960:
2957:
2956:
2916:
2913:
2912:
2900:always forms a
2866:
2865:
2860:
2857:
2856:
2831:
2827:
2716:
2715:
2713:
2710:
2709:
2693:
2690:
2689:
2643:
2640:
2639:
2610:
2609:
2607:
2604:
2603:
2587:
2584:
2583:
2555:
2547:
2542:
2539:
2538:
2521:
2517:
2509:
2506:
2505:
2502:
2481:
2478:
2477:
2461:
2458:
2457:
2362:
2348:
2337:
2328:
2324:
2319:
2317:
2314:
2313:
2272:
2268:
2266:
2263:
2262:
2226:
2223:
2222:
2203:
2192:
2190:
2187:
2186:
2185:if and only if
2164:
2161:
2160:
2143:
2138:
2120:
2117:
2116:
2078:
2076:
2073:
2072:
2032:
2029:
2028:
2012:
2009:
2008:
1992:
1989:
1988:
1971:
1967:
1956:
1954:
1951:
1950:
1928:
1925:
1924:
1901:
1897:
1895:
1892:
1891:
1874:
1870:
1861:
1857:
1855:
1852:
1851:
1823:
1820:
1819:
1802:
1798:
1789:
1785:
1783:
1780:
1779:
1763:
1760:
1759:
1743:
1740:
1739:
1723:
1720:
1719:
1703:
1700:
1699:
1674:
1672:
1669:
1668:
1651:
1646:
1634:
1631:
1630:
1629:on to a schema
1614:
1611:
1610:
1594:
1591:
1590:
1544:
1541:
1540:
1524:
1519:
1517:
1514:
1513:
1496:
1492:
1484:
1481:
1480:
1440:
1438:
1435:
1434:
1409:
1406:
1405:
1383:
1380:
1379:
1345:
1342:
1341:
1325:
1322:
1321:
1305:
1302:
1301:
1285:
1282:
1281:
1264:
1260:
1258:
1255:
1254:
1235:
1233:
1230:
1229:
1204:
1202:
1199:
1198:
1181:
1177:
1169:
1166:
1165:
1149:
1146:
1145:
1129:
1126:
1125:
1069:
1057:
1053:
1046:
1040:
1036:
1027:
1023:
1018:
1012:
1008:
988:
986:
983:
982:
963:
959:
957:
954:
953:
937:
934:
933:
917:
914:
913:
873:
870:
869:
850:
848:
845:
844:
827:
822:
810:
807:
806:
805:For any schema
786:
782:
780:
777:
776:
759:
755:
753:
750:
749:
733:
730:
729:
712:
707:
701:
698:
697:
681:
678:
677:
661:
658:
657:
640:
636:
634:
631:
630:
614:
611:
610:
594:
591:
590:
573:
569:
567:
564:
563:
547:
544:
543:
530:
505:
489:
468:
465:
464:
439:
436:
435:
410:
407:
406:
390:
387:
386:
383:
349:
346:
345:
342:defining length
329:
277:
54:Artificial life
23:
22:
15:
12:
11:
5:
3478:
3468:
3467:
3462:
3445:
3444:
3442:
3441:
3435:
3433:
3427:
3426:
3424:
3423:
3418:
3413:
3408:
3403:
3398:
3393:
3388:
3383:
3378:
3373:
3368:
3363:
3358:
3352:
3350:
3349:Related topics
3346:
3345:
3343:
3342:
3337:
3332:
3330:Harmony search
3327:
3321:
3319:
3313:
3312:
3310:
3309:
3304:
3299:
3294:
3292:Bees algorithm
3289:
3284:
3278:
3276:
3272:
3271:
3269:
3268:
3263:
3261:Neuroevolution
3258:
3253:
3248:
3243:
3238:
3233:
3228:
3223:
3218:
3213:
3207:
3205:
3199:
3198:
3196:
3195:
3190:
3185:
3180:
3175:
3169:
3167:
3163:
3162:
3155:
3154:
3147:
3140:
3132:
3124:
3123:
3097:
3072:
3058:
3037:
3036:
3034:
3031:
3030:
3029:
3024:
3017:
3014:
3000:is shown as a
2989:
2986:
2983:
2980:
2977:
2974:
2969:
2964:
2944:
2941:
2938:
2935:
2932:
2929:
2926:
2923:
2920:
2889:
2886:
2883:
2880:
2877:
2874:
2869:
2864:
2839:
2834:
2830:
2826:
2823:
2820:
2817:
2814:
2811:
2808:
2805:
2802:
2799:
2796:
2793:
2790:
2787:
2784:
2781:
2778:
2775:
2772:
2769:
2766:
2763:
2760:
2757:
2754:
2751:
2748:
2745:
2742:
2739:
2736:
2733:
2730:
2727:
2724:
2719:
2697:
2677:
2674:
2671:
2668:
2665:
2662:
2659:
2656:
2653:
2650:
2647:
2624:
2621:
2618:
2613:
2591:
2571:
2568:
2565:
2562:
2558:
2554:
2550:
2546:
2524:
2520:
2516:
2513:
2501:
2498:
2485:
2465:
2438:
2435:
2432:
2429:
2426:
2423:
2420:
2417:
2414:
2411:
2408:
2405:
2402:
2399:
2396:
2393:
2390:
2387:
2384:
2381:
2378:
2375:
2372:
2369:
2365:
2361:
2358:
2355:
2351:
2347:
2344:
2340:
2336:
2331:
2327:
2322:
2301:
2298:
2295:
2292:
2289:
2286:
2283:
2280:
2275:
2271:
2230:
2210:
2206:
2202:
2199:
2195:
2174:
2171:
2168:
2146:
2141:
2137:
2133:
2130:
2127:
2124:
2097:
2094:
2091:
2088:
2085:
2081:
2060:
2057:
2054:
2051:
2048:
2045:
2042:
2039:
2036:
2016:
1996:
1974:
1970:
1966:
1963:
1959:
1938:
1935:
1932:
1912:
1909:
1904:
1900:
1877:
1873:
1869:
1864:
1860:
1839:
1836:
1833:
1830:
1827:
1805:
1801:
1797:
1792:
1788:
1767:
1747:
1727:
1707:
1687:
1684:
1681:
1677:
1654:
1649:
1645:
1641:
1638:
1618:
1609:, which maps
1598:
1578:
1575:
1572:
1569:
1566:
1563:
1560:
1557:
1554:
1551:
1548:
1527:
1522:
1499:
1495:
1491:
1488:
1465:
1462:
1459:
1456:
1453:
1450:
1447:
1443:
1422:
1419:
1416:
1413:
1393:
1390:
1387:
1367:
1364:
1361:
1358:
1355:
1352:
1349:
1329:
1309:
1289:
1267:
1263:
1242:
1238:
1217:
1214:
1211:
1207:
1184:
1180:
1176:
1173:
1153:
1133:
1111:
1108:
1105:
1102:
1099:
1096:
1093:
1090:
1087:
1084:
1081:
1078:
1068:
1065:
1060:
1056:
1049: or
1043:
1039:
1035:
1030:
1026:
1021:
1015:
1011:
1007:
1004:
1001:
998:
995:
991:
966:
962:
941:
921:
901:
898:
895:
892:
889:
886:
883:
880:
877:
857:
853:
830:
825:
821:
817:
814:
789:
785:
762:
758:
737:
715:
710:
706:
685:
665:
643:
639:
618:
598:
576:
572:
551:
529:
526:
504:
501:
488:
485:
472:
452:
449:
446:
443:
423:
420:
417:
414:
394:
382:
379:
362:
359:
356:
353:
328:
325:
279:
278:
276:
275:
268:
261:
253:
250:
249:
248:
247:
242:
237:
232:
227:
222:
217:
212:
204:
203:
197:
196:
195:
194:
189:
184:
179:
177:Genetic memory
174:
169:
164:
159:
151:
150:
144:
143:
142:
141:
136:
131:
126:
121:
119:Neuroevolution
116:
111:
106:
101:
96:
91:
86:
81:
76:
71:
66:
61:
56:
51:
43:
42:
36:
35:
9:
6:
4:
3:
2:
3477:
3466:
3463:
3461:
3458:
3457:
3455:
3440:
3437:
3436:
3434:
3432:
3428:
3422:
3419:
3417:
3414:
3412:
3409:
3407:
3404:
3402:
3399:
3397:
3394:
3392:
3389:
3387:
3384:
3382:
3379:
3377:
3374:
3372:
3369:
3367:
3364:
3362:
3359:
3357:
3354:
3353:
3351:
3347:
3341:
3338:
3336:
3333:
3331:
3328:
3326:
3323:
3322:
3320:
3318:
3314:
3308:
3305:
3303:
3300:
3298:
3297:Cuckoo search
3295:
3293:
3290:
3288:
3285:
3283:
3280:
3279:
3277:
3273:
3267:
3264:
3262:
3259:
3257:
3254:
3252:
3249:
3247:
3244:
3242:
3239:
3237:
3234:
3232:
3229:
3227:
3224:
3222:
3219:
3217:
3214:
3212:
3209:
3208:
3206:
3204:
3200:
3194:
3191:
3189:
3186:
3184:
3181:
3179:
3176:
3174:
3171:
3170:
3168:
3164:
3160:
3153:
3148:
3146:
3141:
3139:
3134:
3133:
3130:
3118:
3113:
3106:
3104:
3102:
3085:
3079:
3077:
3061:
3059:9780472084609
3055:
3051:
3050:
3042:
3038:
3028:
3025:
3023:
3020:
3019:
3013:
3011:
3003:
3002:Hasse diagram
2984:
2981:
2975:
2939:
2936:
2933:
2930:
2927:
2921:
2918:
2909:
2905:
2903:
2884:
2881:
2875:
2855:
2850:
2832:
2828:
2824:
2821:
2818:
2815:
2812:
2809:
2806:
2803:
2800:
2797:
2794:
2791:
2788:
2785:
2782:
2779:
2776:
2773:
2770:
2767:
2764:
2761:
2758:
2755:
2752:
2749:
2746:
2743:
2740:
2737:
2731:
2725:
2695:
2672:
2669:
2666:
2663:
2660:
2657:
2654:
2648:
2645:
2636:
2619:
2589:
2566:
2563:
2560:
2552:
2522:
2514:
2511:
2497:
2455:
2450:
2433:
2430:
2427:
2424:
2421:
2418:
2415:
2409:
2403:
2400:
2397:
2391:
2385:
2379:
2373:
2370:
2367:
2359:
2356:
2353:
2345:
2342:
2334:
2329:
2325:
2299:
2296:
2293:
2290:
2287:
2284:
2281:
2278:
2273:
2269:
2260:
2256:
2252:
2248:
2244:
2228:
2208:
2200:
2197:
2172:
2169:
2166:
2144:
2139:
2131:
2128:
2125:
2122:
2114:
2109:
2095:
2092:
2089:
2086:
2083:
2055:
2052:
2049:
2046:
2043:
2037:
2034:
2014:
1994:
1972:
1968:
1964:
1961:
1933:
1930:
1910:
1907:
1902:
1898:
1875:
1871:
1867:
1862:
1858:
1837:
1834:
1831:
1828:
1825:
1803:
1799:
1795:
1790:
1786:
1765:
1745:
1725:
1705:
1685:
1682:
1679:
1652:
1647:
1639:
1636:
1616:
1596:
1576:
1573:
1570:
1567:
1564:
1561:
1558:
1555:
1552:
1549:
1546:
1539:, called the
1525:
1497:
1489:
1486:
1477:
1460:
1457:
1454:
1448:
1445:
1420:
1417:
1414:
1411:
1391:
1388:
1385:
1362:
1359:
1356:
1350:
1307:
1287:
1265:
1240:
1212:
1209:
1182:
1178:
1174:
1171:
1151:
1131:
1122:
1103:
1100:
1097:
1094:
1091:
1088:
1085:
1079:
1076:
1066:
1063:
1058:
1054:
1041:
1037:
1033:
1028:
1024:
1013:
1005:
1002:
996:
993:
980:
964:
939:
932:, which maps
919:
899:
896:
893:
890:
887:
884:
881:
878:
875:
868:, called the
855:
828:
823:
815:
812:
803:
787:
783:
760:
735:
713:
708:
683:
641:
596:
574:
540:
537:
535:
525:
522:
518:
514:
510:
500:
498:
494:
484:
470:
447:
441:
418:
412:
392:
378:
376:
357:
351:
344:
343:
338:
334:
324:
322:
318:
314:
310:
309:cylinder sets
306:
302:
298:
294:
286:
274:
269:
267:
262:
260:
255:
254:
252:
251:
246:
243:
241:
238:
236:
233:
231:
228:
226:
223:
221:
218:
216:
213:
211:
208:
207:
206:
205:
202:
199:
198:
193:
192:Fly algorithm
190:
188:
185:
183:
180:
178:
175:
173:
170:
168:
165:
163:
160:
158:
155:
154:
153:
152:
149:
146:
145:
140:
137:
135:
132:
130:
127:
125:
122:
120:
117:
115:
112:
110:
107:
105:
102:
100:
97:
95:
92:
90:
87:
85:
82:
80:
77:
75:
72:
70:
67:
65:
62:
60:
57:
55:
52:
50:
47:
46:
45:
44:
41:
38:
37:
33:
29:
28:
19:
3088:. Retrieved
3063:. Retrieved
3048:
3041:
3007:
2851:
2637:
2503:
2451:
2255:transitivity
2251:antisymmetry
2110:
1478:
1123:
981:
804:
541:
538:
534:order theory
531:
520:
506:
496:
492:
490:
384:
374:
340:
336:
330:
311:, forming a
292:
284:
282:
234:
3416:Mating pool
3166:Main Topics
2247:reflexivity
1300:symbols in
521:propagation
327:Description
3454:Categories
3203:Algorithms
3117:1705.04536
3033:References
2602:, denoted
2504:For a set
2115:. For any
1890:otherwise
1512:we define
487:Disruption
157:Chromosome
2985:≤
2885:≤
2833:∗
2829:ϵ
2822:∗
2819:∗
2816:∗
2810:∗
2804:∗
2795:∗
2792:∗
2783:∗
2771:∗
2765:∗
2564:⊆
2549:↓
2519:Σ
2515:⊆
2484:↑
2464:↓
2410:⊆
2392:⊆
2380:⊆
2377:∅
2371:∗
2368:∗
2364:↑
2360:⊆
2357:∗
2350:↑
2346:⊆
2339:↑
2335:⊆
2330:∗
2326:ϵ
2321:↑
2300:∗
2297:∗
2294:≤
2291:∗
2285:≤
2279:≤
2274:∗
2270:ϵ
2229:≤
2205:↑
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2194:↑
2170:≤
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2132:∈
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2080:↓
1973:∗
1969:ϵ
1958:↓
1937:∅
1911:∗
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1640:∈
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1490:⊆
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1237:↑
1216:∅
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1080:∈
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1006:∈
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761:∗
757:Σ
709:∗
705:Σ
684:∗
664:Σ
642:∗
638:Σ
617:Σ
571:Σ
550:Σ
497:disrupted
405:, called
352:δ
187:Selection
167:Crossover
3431:Journals
3086:. UCL UK
3065:22 April
3016:See also
2456:, where
1818:for all
511:such as
333:wildcard
321:topology
293:schemata
172:Mutation
32:a series
30:Part of
3090:13 July
2257:of the
2159:we say
240:Eurisko
3056:
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1698:where
493:itself
381:Length
315:for a
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285:schema
235:Schema
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3112:arXiv
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313:basis
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3067:2014
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