鎽樿锛氭湰鏂囬鍏堥棥杩颁簡閬哄偝绠楁硶鐨勮捣婧愶紝闅ㄥ悗灏嶉伜鍌崇畻娉曢€�(j矛n)琛屼簡绨¤姒傝堪銆傛湰鏂囬噸榛�(di菐n)浠嬬垂浜嗛伜鍌崇畻娉曠殑鍩烘湰宸ヤ綔鍘熺悊锛岃◣璜栦簡閬哄偝绠楁硶鐞嗚珫瀛樺湪鐨勫晱椤屽強鏀归€�(j矛n)鏂规硶锛屾彁鍑轰簡閬哄偝绠楁硶鍦ㄨ嚜鍕曟帶鍒朵腑鐨勭爺绌跺強鍏舵噳(y墨ng)鐢�銆傛渶鍚�锛屾湰鏂囩郸鍑轰簡鍦∕atlab涓伜鍌崇畻娉曠殑涓€鑸▼搴�銆�

闂�(gu膩n)閸靛瓧锛氶伜鍌崇畻娉曪紝鑷嫊鎺у埗锛孧atlab

涓湒鍒嗛铏燂細TP301.6

The Theory and Application of Genetic Algorithm  

Li Shanshan, He Yinzhou

School of Control Science and Engineering

Shandong University 250061

Abstract: This paper introduces the origin of genetic algorithm, and then gives a shot introduction of genetic algorithm. This paper underlines the basic working theory, discusses the problems and improving methods in genetic algorithm and then proposes the research and application of genetic algorithm in automatic control. At last, this paper gives the codes of genetic algorithm in Matlab.

Keywords: Genetic algorithm, Automatic control, Matlab

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1.閬哄偝绠楁硶璧锋簮

鑷緸閬�(d谩)鐖炬枃鐨勯€�(j矛n)鍖栬珫寰楀埌浜哄€戠殑鎺ュ彈涔嬪悗锛岀敓鐗╁(xu茅)瀹跺€戝氨灏嶉€�(j矛n)鍖栨(j墨)鍒剁敘(ch菐n)鐢熶簡妤靛ぇ鐨勮垐瓒�?锛涱嚳顖堟稐娲风牷榄戣鍏媱^瀵熷埌鐨勫京(f霉)闆滅祼(ji茅)妲�(g貌u)鐨勭敓鍛芥槸鍦ㄧ浉灏嶇煭鐨勬檪闁撻€�(j矛n)鍖栬€屼締鐨�锛屽皪閫欎竴榛�(di菐n)鍖呮嫭鐢熺墿瀛�(xu茅)瀹跺湪鍏�(n猫i)鐨勮ū澶氫汉閮芥劅鍒伴濂囥€傞洊鐒剁洰鍓嶉棞(gu膩n)浜庢帹鍕曢€欏€嬮€�(j矛n)鍖栫殑姗�(j墨)鍒堕倓娌掓湁瀹屽叏寮勬竻妤�锛屼絾瀹冨€戠殑鏌愪簺鐗瑰緛宸辩偤浜烘墍鐭�銆傞€�(j矛n)鍖栨槸鐧�(f膩)鐢熷湪浣滅偤鐢熺墿绲�(ji茅)妲�(g貌u)绶ㄧ⒓鐨勬煋鑹查珨涓�锛岄€氶亷灏嶆煋鑹查珨鐨勮纰奸儴鍒嗗湴鐢熸垚鐢熺墿銆備笅闈㈡槸闂�(gu膩n)浜庨€�(j矛n)鍖栫悊璜栦腑鐨勫凡寤ｇ偤浜哄€戞墍鎺ュ彈涓€鑸壒鎬э細

(1)閫�(j矛n)鍖栭亷绋嬬櫦(f膩)鐢熷湪鏌撹壊楂斾笂锛岃€屼笉鏄櫦(f膩)鐢熷湪瀹冨€戞墍绶ㄧ⒓鐨勭敓鐗╁€嬮珨涓�銆�

(2)鑷劧閬告搰鎶婃煋鑹查珨浠ュ強鐢卞畠鍊戞墍璀垚鐨勭祼(ji茅)妲�(g貌u)鐨勮〃鐝�(xi脿n)鑱�(li谩n)绯诲湪涓€璧�锛岄偅浜涢仼鎳�(y墨ng)鎬уソ鐨勫€嬮珨鐨勬煋鑹查珨缍�(j墨ng)甯告瘮宸殑鍊嬮珨鐨勬煋鑹查珨鏈夋洿澶氱殑绻佹畺姗�(j墨)鏈�銆�

(3)绻佹畺閬庣▼鏄€�(j矛n)鍖栫櫦(f膩)鐢熺殑閭ｄ竴鍒伙紝璁婄暟鍙互浣跨敓璨ㄧ墿瀛愪唬鐨勬煋鑹查珨涓嶅悓浜庡畠鍊戠埗浠ｇ殑鏌撹壊楂�锛岄€氶亷绲�(ji茅)鍚堝叐鍊嬬埗浠ｆ煋鑹查珨涓殑鐗╄唱(zh矛)锛岄噸绲勯亷绋嬪彲浠ュ湪瀛愪唬涓敘(ch菐n)鐢熸湁寰堝ぇ宸暟鐨勬煋鑹查珨銆�

(4)鐢熺墿閫�(j矛n)鍖栨矑鏈夎鎲�銆傛湁闂�(gu膩n)鐢�(ch菐n)鐢熷€嬮珨鐨勪俊鎭寘鍚湪鍊嬮珨鎵€鏀滃付鐨勬煋鑹查珨鐨勯泦鍚堜互鍙婃煋鑹查珨绶ㄧ⒓鐨勭祼(ji茅)妲�(g貌u)涔嬩腑锛岄€欎簺鍊嬮珨鏈冨緢濂界殑閬╂噳(y墨ng)瀹冨€戠殑鐠�(hu谩n)澧�銆�

澶у鏁�(sh霉)鐢熺墿鏄€氶亷鑷劧閬告搰鍜屾湁鎬х敓娈栭€欏叐绋熀鏈亷绋嬮€�(j矛n)琛屾紨鍖栫殑銆傝嚜鐒堕伕鎿囩殑鍘熷墖鏄仼鎳�(y墨ng)鑰呯敓瀛橈紝涓嶉仼鎳�(y墨ng)鑰呮窐姹�銆傝嚜鐒堕伕鎿囨焙瀹氫簡缇ら珨涓摢浜涘€嬪€嬮珨鑳藉瀛樻椿骞剁箒娈�锛涙湁鎬х敓娈栦繚璀変簡鍚庝唬鍩哄洜涓殑娣峰悎鑸囬噸绲勩€傛瘮璧烽偅浜涘儏鍖呭惈鍠€嬭Κ鏈殑鍩哄洜鎷疯矟鍜屼緷闈犲伓鐒惰畩鐣颁締鏀归€�(j矛n)鐨勫悗浠�锛岄€欑ó鐢卞熀鍥犻噸绲勭敘(ch菐n)鐢熺殑鍚庝唬閫�(j矛n)鍖栬蹇緱澶氥€�60骞翠唬缇庡湅Michigan澶у(xu茅)鐨凧ohn Holland鍦ㄥ緸浜嬪浣曡兘寤虹珛鑳藉(xu茅)缈�(x铆)鐨勬(j墨)鍣ㄧ殑鐮旂┒涓敞鎰忓埌瀛�(xu茅)缈�(x铆)涓嶅儏鍙互閫氶亷鍠€嬬敓璨ㄧ墿鐨勯仼鎳�(y墨ng)鑰屼笖閫氶亷涓€鍊嬬兢楂旂殑瑷卞浠ｇ殑閫�(j矛n)鍖栦篃鑳界櫦(f膩)鐢�銆傚彈閬�(d谩)鐖炬枃閫�(j矛n)鍖栬珫鐨勫暉鐧�(f膩)锛屼粬閫愭几瑾�(r猫n)璀樺埌锛屽湪姗�(j墨)鍣ㄥ(xu茅)缈�(x铆)鐨勭爺绌朵腑锛岀偤浜嗙嵅寰椾竴鍊嬪ソ鐨勫(xu茅)缈�(x铆)绠楁硶锛屽儏闈犲柈鍊嬬瓥鐣ョ殑寤虹珛鏄笉澶犵殑锛岄倓瑕佷緷璩翠簬涓€鍊嬪寘鍚ū澶氬€欓伕绛栫暐鐨勭兢楂旂殑绻佹畺銆傚畠鍊戠殑鎬濇兂璧锋簮浜庨伜鍌抽€�(j矛n)鍖�锛孒olland灏卞皣閫欏€嬬爺绌堕牁(l菒ng)鍩熷懡鍚嶇偤閬哄偝绠楁硶[4]銆�

2.閬哄偝绠楁硶姒傝堪

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鍒濅唬绋兢鐢�(ch菐n)鐢熶箣鍚�锛屾寜鐓ч仼鑰呯敓瀛樺拰鍎�(y艒u)鍕濆姡姹扮殑鍘熺悊锛岄€愪唬婕斿寲鐢�(ch菐n)鐢熷嚭閬╂噳(y墨ng)搴﹁秺渚嗚秺濂界殑鍊嬮珨銆傚湪姣忎竴浠ｄ腑锛屾牴鎿�(j霉)鍟忛鍩熶腑鍊嬮珨鐨勯仼鎳�(y墨ng)搴︾殑鍎�(y艒u)鍔�锛岄伕鎿囦竴浜涢仼鎳�(y墨ng)搴﹂珮鐨勫€嬮珨锛屽熀浜庨€欎簺閬稿嚭鐨勯仼鎳�(y墨ng)搴﹂珮鐨勫€嬮珨锛屽苟鍊熷姪浜庤嚜鐒堕伜鍌冲(xu茅)鐨勪氦鍙�銆佽畩鐣扮畻瀛�锛岀敘(ch菐n)鐢熷嚭浠ｈ〃鏂拌В闆嗙殑涓嬩竴浠ｇó缇�銆傞€欏€嬮亷绋嬪皣灏�(d菐o)鑷寸ó缇ゅ儚鑷劧閫�(j矛n)鍖栦竴妯�锛屼娇鍚庣敓浠ｇó缇ゆ瘮鍓嶄唬绋兢鍏锋湁鏇撮珮鐨勯仼鎳�(y墨ng)搴�锛屾洿鍔犻仼鎳�(y墨ng)浜庣挵(hu谩n)澧�銆傚湪鍎�(y艒u)鍖栭亷绋嬬祼(ji茅)鏉熷悗锛屾湯浠ｇó缇や腑鐨勬渶鍎�(y艒u)鍊嬮珨缍�(j墨ng)閬庤В纰�锛屽嵆鍙互浣滅偤鍟忛鐨勮繎浼兼渶鍎�(y艒u)瑙7]銆�

3.閬哄偝绠楁硶鐨勫師鐞�

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3.1鍩烘湰鍘熺悊

鍦ㄨ嚜鐒剁晫锛岀敱浜庣祫鎴愮敓鐗╃兢楂斾腑鍚勫€嬮珨涔嬮枔鐨勫樊鐣帮紝灏嶆墍铏曠挵(hu谩n)澧冩湁涓嶅悓鐨勯仼鎳�(y墨ng)鍜岀敓瀛樿兘鍔�锛岄伒鐓ц嚜鐒剁晫鐢熺墿閫�(j矛n)鍖栫殑鍩烘湰鍘熷墖锛岄仼鑰呯敓瀛�锛屽劒(y艒u)鍕濆姡姹�锛屽皣瑕佹窐姹板摢浜涙渶宸€嬮珨锛岄€氶亷浜ら厤灏囩埗鏈劒(y艒u)绉€鐨勬煋鑹查珨鍜屽熀鍥犻伜鍌崇郸瀛愪唬锛岄€氶亷鏌撹壊楂旀牳鍩哄洜鐨勯噸鏂扮祫鍚堢敘(ch菐n)鐢熺敓鍛藉姏鏇村挤(qi谩ng)鐨勬柊鐨勫€嬮珨鑸囦粬鍊戠祫鎴愮殑鏂扮兢楂�銆傚湪鐗瑰畾鐨勬浠朵笅锛屽熀鍥犳渻鐧�(f膩)鐢熺獊璁�锛岀敘(ch菐n)鐢熸柊鍩哄洜鍜岀敓鍛藉姏鏇村挤(qi谩ng)鐨勬柊鍊嬮珨锛涗絾绐佽畩鏄潪閬哄偝鐨�锛岄毃钁楀€嬮珨涓嶆柗鏇存柊锛岀兢楂斾笉鏂锋湞钁楁渶鍎�(y艒u)鏂瑰悜閫�(j矛n)鍖�锛岄伜鍌崇畻娉曟槸鐪熷(sh铆)妯℃摤鑷劧鐣岀敓鐗╅€�(j矛n)鍖栨(j墨)鍒堕€�(j矛n)琛屽皨鍎�(y艒u)鐨�銆�

鑸囧偝绲�(t菕ng)鎼滅储绠楁硶涓嶅悓锛岄伜鍌崇畻娉曞緸涓€绲勯毃姗�(j墨)鐢�(ch菐n)鐢熺殑鍒濆瑙�锛岀ū鐐虹兢楂�锛岄枊濮嬫悳绱㈤亷绋�銆傜兢楂斾腑鐨勬瘡鍊嬪€嬮珨鏄晱椤岀殑涓€鍊嬭В锛岀ū鐐烘煋鑹查珨銆傞€欎簺鏌撹壊楂斿湪鍚庣簩(x霉)杩唬涓笉鏂烽€�(j矛n)鍖栵紝绋辩偤閬哄偝銆傞伜鍌崇畻娉曚富瑕侀€氶亷浜ゅ弶锛岃畩鐣�锛岄伕鎿囬亱(y霉n)绠楀(sh铆)鐝�(xi脿n)銆備氦鍙夋垨渚垮疁閬�(y霉n)绠楃敓鎴愪笅涓€浠ｆ煋鑹查珨锛岀ū鐐哄悗浠ｃ€傛煋鑹查珨鐨勫ソ澹炵敤閬╂噳(y墨ng)搴︿締琛￠噺銆傛牴鎿�(j霉)閬╂噳(y墨ng)搴︾殑澶у皬寰炰笂涓€浠ｅ拰鍚庝唬涓伕鎿囦竴瀹氭暩(sh霉)閲忕殑鍊嬮珨锛屼綔鐐轰笅涓€浠ｇ兢楂�锛屽啀绻肩簩(x霉)閫�(j矛n)鍖栵紝閫欐ǎ缍�(j墨ng)閬庤嫢骞蹭唬涔嬪悗锛岀畻娉曟敹鏂備簬鏈€濂界殑鏌撹壊楂旓紝瀹冨緢鍙兘灏辨槸鍟忛鐨勬渶鍎�(y艒u)瑙ｆ垨娆″劒(y艒u)瑙�銆傞伜鍌崇畻娉曚腑浣跨敤閬╂噳(y墨ng)搴﹂€欏€嬫蹇典締搴﹂噺缇ら珨涓殑鍚勫€嬪€嬮珨鐨勬偁蹇借▓(j矛)绠椾腑鏈夊彲鑳介仈(d谩)鍒版渶鍎�(y艒u)瑙ｇ殑鍎�(y艒u)鑹▼搴�銆傚害閲忓€嬮珨閬╂噳(y墨ng)搴︾殑鍑芥暩(sh霉)绋辩偤閬╂噳(y墨ng)搴﹀嚱鏁�(sh霉)銆傞仼鎳�(y墨ng)搴﹀嚱鏁�(sh霉)鐨勫畾缇╀竴鑸垏鍏烽珨姹傝В鍟忛鏈夐棞(gu膩n)[9]銆�

3.2鍏稿瀷绠楁硶鑸囨椹�

閬哄偝绠楁硶鐨勪竴鑸椹熺偤锛�

锛�1锛夐毃姗�(j墨)鐢�(ch菐n)鐢熷垵濮嬬ó缇�锛屽垵濮嬪寲绋兢锛�

锛�2锛夎▓(j矛)绠楃ó缇や笂姣忓€嬪€嬮珨鐨勯仼鎳�(y墨ng)搴�锛屾槸鍚︽豢瓒虫敹鏂傛簴(zh菙n)鍓囷紱

锛�3锛夋寜鐢卞€嬮珨閬╂噳(y墨ng)搴﹀€兼墍姹哄畾鐨勬煇鍊嬭(gu墨)鍓囬伕鎿囧皣閫�(j矛n)鍏ヤ笅涓€浠ｇ殑鍊嬮珨锛�

锛�4锛夋寜姒傜巼Pc閫�(j矛n)琛屼氦鍙夋搷浣�锛�

锛�5锛夋寜姒傜巼Pm閫�(j矛n)琛岃畩鐣版搷浣滐紱

锛�6锛夎嫢娌掓湁婊胯冻鏌愮ó鍋滄姊濅欢锛屽墖杞�(zhu菐n)鍏ワ紙3锛�锛屽惁鍓囬€�(j矛n)鍏ヤ笅涓€姝�锛�

锛�7锛夎几鍑虹ó缇や腑閬╂噳(y墨ng)搴︽渶鍎�(y艒u)鐨勬煋鑹查珨浣滅偤鍟忛鐨勬豢鎰忚В鎴栨渶鍎�(y艒u)瑙ｃ€�

閬哄偝绠楁硶鐨勪竴鑸亷绋媅10]濡傚湒1鎵€绀�銆�

3.3绶ㄧ⒓鍟忛

绶ㄧ⒓鏄伜鍌崇畻娉曡瑙ｆ焙鐨勯瑕佸晱椤屻€傚父鐢ㄧ殑绶ㄧ⒓鏂规硶鏈変簩閫�(j矛n)鍒剁法纰�锛屾牸闆风⒓绶ㄧ⒓锛屽(sh铆)鏁�(sh霉)绶ㄧ⒓锛岀铏熺法纰肩瓑銆傞嚌灏嶄笉鍚岀殑鍟忛瑕侀噰鐢ㄤ笉鍚岀殑绶ㄧ⒓鏂规硶銆�

3.4缇ら珨瑷�(sh猫)瀹�

閬哄偝鎿嶄綔鏄皪鐪惧鍊嬮珨鍚屾檪閫�(j矛n)琛岀殑锛岄€欑溇澶氬€嬮珨绲勬垚浜嗙兢楂�銆傚湪閬哄偝绠楁硶铏曠悊娴佺▼涓�锛岀辜绶ㄧ⒓瑷�(sh猫)瑷�(j矛)鍚庣殑浠诲嫏(w霉)鏄垵濮嬬兢楂旂殑瑷�(sh猫)瀹�锛屽苟浠ユ鐐鸿捣榛�(di菐n)涓€浠ｄ唬閫�(j矛n)鍖栫煡閬撴寜鏌愮ó閫�(j矛n)鍖栧仠姝㈡簴(zh菙n)鍓囩祩姝㈤€�(j矛n)鍖栭亷绋�锛岀敱姝ゅ緱鍒版渶鍚庝竴浠�銆傞棞(gu膩n)閸靛晱椤屾槸锛岀兢楂旇(gu墨)妯�锛屽嵆缇ら珨涓寘鎷殑鍊嬮珨鏁�(sh霉)鐩浣曠⒑瀹氥€傚叾涓湁鍏╁€嬮渶瑕佽€冩叜鐨勫洜绱狅細a.鍒濆缇ら珨鐨勮ō(sh猫)瀹�锛涢鍏堟牴鎿�(j霉)鍟忛鍥烘湁鐭ヨ瓨锛岃ō(sh猫)娉曟妸鎻℃渶鍎�(y艒u)瑙ｆ墍鍗犵┖闁撳湪鏁村€嬪晱椤岀┖闁撶殑鍒嗗竷鑼冨湇锛岀劧鍚庡湪姝ゅ垎甯冭寖鍦嶅収(n猫i)瑷�(sh猫)瀹氬垵濮嬬兢楂�銆傜劧鍚庡厛闅ㄦ(j墨)鐢熸垚涓€瀹氭暩(sh霉)鐩殑鍊嬮珨锛岀劧鍚庡緸涓寫鍑烘渶濂界殑鍊嬮珨鍔犲埌鍒濆缇ら珨涓�銆傞€欑ó閬庣▼涓嶆柗杩唬锛岀洿鍒板垵濮嬬兢楂斾腑鍊嬮珨鏁�(sh霉)閬�(d谩)鍒颁簡闋�(y霉)鍏堢⒑瀹氱殑瑕�(gu墨)妯�銆俠.閫�(j矛n)鍖栭亷绋嬪懆鍚勪唬鐨勮(gu墨)妯″浣曠董鎸�銆傜兢楂旇(gu墨)妯＄殑纰哄畾鍙楅伜鍌虫搷浣滀腑閬告搰鎿嶄綔鐨勫奖闊垮緢澶�銆備竴鑸€岃█锛岀兢楂旇(gu墨)妯¤秺澶�锛岀兢楂斾腑鍊嬮珨鐨勫妯ｆ€ц秺楂�锛岀畻娉曢櫡鍏ュ眬閮ㄨВ鐨勫嵄闅氨瓒婂皬銆傛墍浠�锛屽緸鑰冩叜缇ら珨澶氭ǎ鎬у嚭鐧�(f膩)锛岀兢楂旇(gu墨)妯℃噳(y墨ng)杓冨ぇ銆備絾鏄�锛岀兢楂旇(gu墨)妯″お澶ф渻甯朵締鑻ュ共寮婄梾銆備竴鏄▓(j矛)绠楁晥鐜�锛岀兢楂旇秺澶э紝鍏堕仼鎳�(y墨ng)鍊艰⿻浼版鏁�(sh霉)澧炲姞锛屾墍浠ヨ▓(j矛)绠楅噺涔熷鍔狅紝寰炶€屽奖闊跨畻娉曟晥鑳�锛涗簩鏄兢楂斾腑鍊嬮珨鐢熷瓨涓嬩締姒傜巼澶у閲囩敤鍜岄仼鎳�(y墨ng)鍊兼垚姣斾緥鐨勬柟娉曪紝鐣�(d膩ng)缇ら珨涓€嬮珨闈炲父澶氭檪锛屽皯閲忛仼鎳�(y墨ng)鍊煎緢楂樼殑鍊嬮珨鏈冭閬告搰鑰岀敓瀛樹笅渚嗭紝浣嗗ぇ澶氭暩(sh霉)鍊嬮珨鍗昏娣樻卑锛岄€欐渻褰遍熆閰嶅皪搴殑褰㈡垚锛屽緸鑰屽奖闊夸氦鍙夋搷浣�銆傚彟涓€鏂归潰锛岀兢楂旇(gu墨)妯″お灏�锛屾渻浣块伜鍌崇畻娉曠殑鎼滅储绌洪枔涓垎甯冭寖鍦嶆湁闄愶紝鍥犺€屾悳绱㈡湁鍙兘鍋滄鍦ㄦ湭鎴愮啛闅庢锛屽紩璧锋湭鎴愮啛鏀舵杺鐝�(xi脿n)璞°€�

閬╂噳(y墨ng)搴﹀嚱鏁�(sh霉)锛氶伜鍌崇畻娉曞湪閫�(j矛n)鍖栨悳绱腑鍩烘湰涓婁笉鐢ㄥ閮ㄤ俊鎭�锛屽儏鐢ㄩ仼鎳�(y墨ng)搴﹀嚱鏁�(sh霉)浣滅偤渚濇摎(j霉)銆傞伜鍌崇畻娉曠殑鐩(bi膩o)鍑芥暩(sh霉)涓嶅彈閫ｇ簩(x霉)鍙井鐨勭磩鏉熶笖瀹氱京鍩熷彲浠ョ偤浠绘剰闆嗗悎銆傚皪鐩(bi膩o)鍑芥暩(sh霉)鐨勫敮涓€瑕佹眰鏄嚌灏嶈几鍏ュ€�锛屽彲瑷�(j矛)绠楀嚭鑳藉姞浠ユ瘮杓冪殑闈炶矤(f霉)绲�(ji茅)鏋溿€傞€欎竴鐗归粸(di菐n)浣垮緱閬哄偝绠楁硶鎳�(y墨ng)鐢ㄨ寖鍦嶅緢寤11]銆�

3.5閬哄偝鎿嶄綔

閬哄偝鎿嶄綔鍖呮嫭3鍊嬪熀鏈伜鍌崇畻瀛�锛屼氦鍙�锛岃畩鐣帮紝閬告搰[12]銆傞€�3鍊嬬畻瀛愭湁浠ヤ笅鐗归粸(di菐n)锛歛.閫�3鍊嬮伜鍌崇畻瀛愮殑鎿嶄綔閮芥槸闅ㄦ(j墨)鍖栨搷浣滐紝鍥犳锛屽€嬮珨鍚戞渶鍎�(y艒u)瑙ｇ殑閬风Щ涔熸槸闅ㄦ(j墨)鐨�銆俠.閬哄偝鎿嶄綔鐨勬晥鏋滃拰涓婅堪3鍊嬮伜鍌崇畻瀛愭墍鍙栫殑鎿嶄綔姒傜巼锛岀法纰兼柟娉�锛岀兢楂斿ぇ灏忥紝鍒濆缇ら珨浠ュ強閬╂噳(y墨ng)搴﹀嚱鏁�(sh霉)鐨勮ō(sh猫)瀹氬瘑鍒囩浉闂�(gu膩n)銆俢.3鍊嬪熀鏈伜鍌崇畻瀛愮殑鎿嶄綔鏂规硶鎴栨搷浣滅瓥鐣ュ拰鍊嬮珨鐨勭法纰兼柟寮忕洿鎺ユ湁闂�(gu膩n)銆�

3.5.1浜ゅ弶閬�(y霉n)绠�

鎵€璎備氦鍙夐亱(y霉n)绠�锛屾槸鎸囧叐鍊嬬浉浜掗厤灏嶇殑鏌撹壊楂旀寜鏌愮ó鏂瑰紡鐩镐簰浜ゆ彌鍏堕儴鍒嗗熀鍥�锛屽緸鑰屽舰鎴愬叐鍊嬫柊鐨勫€嬮珨銆備氦鍙夐亱(y霉n)绠楁槸閬哄偝绠楁硶鍗€(q奴)鍒ヤ簬鍏朵粬閫�(j矛n)鍖栫畻娉曠殑閲嶈鐗瑰緛锛屽畠姹哄畾浜嗛伜鍌崇畻娉曠殑鍏ㄥ眬鎼滅储鑳藉姏锛屾槸鐢�(ch菐n)鐢熸柊鍊嬮珨鐨勪富瑕佹柟娉曘€傚父鐢ㄧ殑浜ゅ弶绠楀瓙鏈夛細a.鍠粸(di菐n)浜ゅ弶銆傚張绋辩啊鍠氦鍙夛紝瀹冩槸鎸囧湪鍊嬮珨绶ㄧ⒓涓蹭腑闅ㄦ(j墨)瑷�(sh猫)缃竴鍊嬩氦鍙夐粸(di菐n)锛岀劧鍚庡湪瑭查粸(di菐n)鐩镐簰浜ゆ彌鍏╁€嬮厤灏嶅€嬮珨鐨勯儴鍒嗗熀鍥�銆俠.闆欓粸(di菐n)浜ゅ弶銆傚畠鐨勫叿楂旀搷浣滈亷绋嬫槸1鍦ㄧ浉浜掗厤灏嶇殑鍏╁€嬪€嬮珨涓法纰间覆涓ō(sh猫)缃叐鍊嬩氦鍙夐粸(di菐n)锛�2浜ゆ彌鍏╁€嬩氦鍙夐粸(di菐n)涔嬮枔鐨勯儴鍒嗗熀鍥�銆俢.鍧囧嫽浜ゅ弶銆傚畠鏄寚鍏╁€嬮厤灏嶅€嬮珨鐨勬瘡涓€浣嶅熀鍥犻兘浠ョ浉鍚岀殑姒傜巼閫�(j矛n)琛屼氦鎻涳紝寰炶€屽舰鎴愬叐鍊嬫柊鍊嬮珨銆傚叿楂旀搷浣滈亷绋嬫槸1闅ㄦ(j墨)鐢�(ch菐n)鐢熶竴鍊嬭垏鍊嬮珨绶ㄧ⒓闀峰害鐩稿悓鐨勪簩閫�(j矛n)鍒跺睆钄藉瓧w=w1w2…..wx銆�2鎸変笅鍒楄(gu墨)鍓囧緸A,B鍏╁€嬬埗浠ｅ€嬮珨涓敘(ch菐n)鐢熷叐鍊嬫柊鍊嬮珨X,Y锛涜嫢wi=0,鍓嘪鐨勭i鍊嬪熀鍥犵辜鎵緼鐨勫皪鎳�(y墨ng)鍩哄洜锛孻鐨勭i鍊嬪熀鍥犵辜鎵緽鐨勫皪鎳�(y墨ng)鍩哄洜锛涜嫢wi=1锛屽墖A,B鐨勭i鍊嬪熀鍥犵浉浜掍氦鎻�锛屽緸鑰岀敓鎴怷,Y鐨勭i鍊嬪熀鍥燵13]銆�

3.5.2璁婄暟閬�(y霉n)绠�

鎵€璎傝畩鐣伴亱(y霉n)绠�锛屾槸鎸囧皣鍊嬮珨绶ㄧ⒓涓蹭腑鐨勬煇浜涘熀鍥犲€肩敤鍏朵粬鍩哄洜鍊间締鏇挎彌锛屽緸鑰屽舰鎴愪竴鍊嬫柊鐨勫€嬮珨锛岄伜鍌崇畻娉曚腑鐨勮畩鐣伴亱(y霉n)绠楁槸鐢�(ch菐n)鐢熸柊鍊嬮珨鐨勮紨鍔╂柟娉�锛屼絾蹇呬笉鍙皯锛屽洜?y脿n)妯楅吉Q瀹氫簡閬哄偝绠楁硶鐨勫眬閮ㄦ悳绱㈣兘鍔�銆傚父鐢ㄧ殑鏂规硶鏈夛細a.鍩烘湰浣嶈畩鐣板畠鏄寚灏嶅€嬮珨绶ㄧ⒓涓蹭互璁婄暟姒傜巼p闅ㄦ(j墨)鍒跺畾鏌愪竴浣嶆垨鏌愬咕浣嶅熀鍥犱綔璁婄暟閬�(y霉n)绠�銆俠.鍧囧嫽璁婄暟銆傚畠鏄寚鍒嗗垾鐢ㄧ鍚堟煇涓€鑼冨湇鍏�(n猫i)鍧囧嫽鍒嗗竷鐨勯毃姗�(j墨)鏁�(sh霉)锛屼互鏌愪竴杓冨皬鐨勬鐜囦締鏇挎彌鍊嬮珨涓殑姣忓€嬪熀鍥�銆俢.浜屽厓璁婄暟銆傚畠鐨勬搷浣滈渶瑕佸叐姊濇煋鑹查珨鍙冭垏锛屽叐姊濇煋鑹查珨閫氶亷浜屽厓璁婄暟鎿嶄綔鍚庣敓鎴愬叐姊濇柊鍊嬮珨锛屾柊鍊嬮珨涓殑鍚勫€嬪熀鍥犲垎鍒ュ彇鍘熸煋鑹查珨灏嶆噳(y墨ng)鍩哄洜鍊肩殑鍚屾垨/鐣版垨銆�

3.5.3閬告搰閬�(y霉n)绠�

閬告搰閬�(y霉n)绠楀氨鏄皪缇ら珨涓殑鍊嬮珨閫�(j矛n)琛屽劒(y艒u)鍕濆姡姹版搷浣滐細閬╂噳(y墨ng)搴﹂珮鐨勫€嬮珨琚伜鍌冲埌涓嬩竴浠ｇ兢楂斾腑鐨勬鐜囧ぇ锛涢仼鎳�(y墨ng)搴︿綆鐨勫€嬮珨锛岃閬哄偝鍒颁笅涓€浠ｇ兢楂斾腑鐨勬鐜囧皬銆傚畠鐨勪换鍕�(w霉)灏辨槸鎸夋煇绋柟娉曞緸鐖朵唬缇ら珨涓伕鍙栦竴浜涘€嬮珨锛岄伜鍌冲埌涓嬩竴浠ｇ兢楂斻€�

4.閬哄偝绠楁硶鍦ㄦ帶鍒堕牁(l菒ng)鍩熶腑鐨勭爺绌惰垏鎳�(y墨ng)鐢�

閬哄偝绠楁硶鎻愪緵浜嗕竴绋眰瑙ｅ京(f霉)闆滅郴绲�(t菕ng)鍎�(y艒u)鍖栧晱椤岀殑閫氱敤妗嗘灦锛屽畠涓嶄緷璩翠簬鍟忛鐨勫叿楂旈牁(l菒ng)鍩�锛屽皪鍟忛鐨勭ó椤炴湁寰堝挤(qi谩ng)鐨勯妫掓€�锛屾墍浠ュ唬娉涙噳(y墨ng)鐢ㄤ簬寰堝瀛�(xu茅)绉�銆傜洰鍓嶄富瑕佹噳(y墨ng)鐢ㄧ殑闋�(l菒ng)鍩熸湁鍑芥暩(sh霉)鍎�(y艒u)鍖�銆佺敓鐢�(ch菐n)瑾�(di脿o)搴﹀晱椤�銆佽嚜鍕曟帶鍒躲€佹(j墨)鍣ㄥ(xu茅)缈�(x铆)銆佸湒鍍忚檿鐞嗐€佷汉宸ョ敓鍛�銆侀伜鍌崇法绋�锛屾(j墨)鍣ㄥ(xu茅)缈�(x铆)銆佹暩(sh霉)鎿�(j霉)鎸栨帢绛夌瓑[14]銆傛湰鏂囦富瑕佹帰瑷庨伜鍌崇畻娉曞湪鎺у埗闋�(l菒ng)鍩熶腑鐨勭爺绌惰垏鎳�(y墨ng)鐢�銆�

4.1绯荤当(t菕ng)杈ㄨ瓨鍜屾ā鍨嬮檷鍍�

绯荤当(t菕ng)杈ㄨ瓨鏄帶鍒剁郴绲�(t菕ng)瑷�(sh猫)瑷�(j矛)鐨勫熀绀�(ch菙)锛屾湁瑷卞鏈夋晥鐨勬柟娉曪紝浣嗘槸閫欎簺鎶€琛�(sh霉)绲曞ぇ閮ㄥ垎铏曠悊鐨勯兘鏄弮鏁�(sh霉)鐨勭窔鎬фā鍨�,骞朵笖鍩轰簬鎼滅储绌洪枔鏄€ｇ簩(x霉)鍜屽彲寰殑鍋囪ō(sh猫)銆傜洰鍓嶇殑鍦ㄧ窔杈ㄨ瓨鏂规硶閮芥槸闆㈢窔鏂规硶鐨勯仦姝稿(sh铆)鐝�(xi脿n)銆傞€欎簺閬炴鏂规硶鏈唱(zh矛)涓婇兘鏄娇鐢ㄦ搴︽妧琛�(sh霉)鐨勫眬閮ㄦ悳绱㈡柟娉�,鍦ㄦ悳绱㈢┖闁撲笉鍙井鎴栧弮鏁�(sh霉)闈炵窔鎬ф檪锛岄€欎簺鏂规硶閮戒笉瀹规槗鎵惧埌鍏ㄥ眬鏈€鍎�(y艒u)瑙�锛岃€岄伜鍌崇畻娉曠殑鎼滅储涓嶄緷璩存搴︿俊鎭�锛屼篃涓嶉渶瑕佹眰瑙ｅ嚱鏁�(sh霉)鍙井锛屽彧闇€瑕佹眰瑙ｅ嚱鏁�(sh霉)鑷磩鏉熸浠朵笅鐨勫彲琛岃В锛屽苟涓旈伜鍌崇畻娉曞叿鏈夊叏灞€鎼滅储鐨勭壒鎬�銆侴A鐐洪潪绶氭€х郴绲�(t菕ng)鐨勮鲸璀樻彁渚涗簡涓€绋啊鍠€屾湁鏁堢殑鏂规硶[15]銆�

4.2闈炵窔鎬х郴绲�(t菕ng)鎺у埗

鍦ㄦ帶鍒剁郴绲�(t菕ng)瑷�(sh猫)瑷�(j矛)涓�锛岀敱浜庡(sh铆)闅涘晱椤屽線寰€甯舵湁鍤�(y谩n)鏍肩殑绱勬潫鍜岄潪绶氭€�锛屽悓鏅傛寚妯�(bi膩o)鍑芥暩(sh霉)鍙兘鏃笉閫ｇ簩(x霉)鍙堜笉鍙井锛屼笉鍚岀殑鍙冩暩(sh霉)绲勫悎鍙兘寰楀埌鐩稿悓鐨勬帶鍒朵綔鐢�銆傚偝绲�(t菕ng)鍎�(y艒u)鍖栨柟娉曞皪鍒濆鍊肩殑閬稿彇閮藉緢鏁忔劅锛屽緢瀹规槗闄峰叆鍒濆瑙ｉ檮杩戠殑灞€閮ㄦサ鍊�銆傞伜鍌崇畻娉曠偤闈炵窔鎬ф帶鍒剁郴绲�(t菕ng)鐨勫劒(y艒u)鍖栨彁渚涗簡涓€绋湁鏁堥€斿緫銆傚洜?y脿n)闀欰涓嶉渶瑕佹寚妯�(bi膩o)鍑芥暩(sh霉)鐨勫井鍒嗭紝鎵€浠ュ熀浜庨伜鍌崇畻娉曞拰鎬ц兘鍒嗘瀽鐨勮ō(sh猫)瑷�(j矛)鑷嫊鍖栨柟娉曡兘澶犺€冩叜瀵�(sh铆)闅涚郴绲�(t菕ng)鐨勮ū澶氭€ц兘瑕佹眰,骞跺彲浠ョ洿鎺ヨō(sh猫)瑷�(j矛)闈炵窔鎬у皪璞＄殑绶氭€ф帶鍒跺櫒锛岃€屼笉闇€瑕佸厛灏囧皪璞￠€�(j矛n)琛岀窔鎬у寲锛屽(sh铆)韪愯瓑鏄庨€欐槸鎺у埗绯荤当(t菕ng)瑷�(sh猫)瑷�(j矛)鐨勪竴绋湁鏁堟柟娉�銆傚緪婊囩敓瑷庤珫浜嗗埄鐢℅A閫�(j矛n)琛屾帶鍒跺櫒鍙冩暩(sh霉)鍎�(y艒u)鍖栧晱椤�,鐮旂┒浜嗗埄鐢℅A纰哄畾鍏锋湁鐗瑰畾绲�(ji茅)妲�(g貌u)鐨勯潪绶氭€х郴绲�(t菕ng)鐨勫弮鏁�(sh霉)鍊�锛屾寚鍑哄湪瀵�(sh铆)鐝�(xi脿n)绲﹀畾鐨勬€ц兘鎸囨(bi膩o)涓�,鍙嵅寰楀叏灞€鏈€鍎�(y艒u)鐨勬帶鍒跺櫒鍙冩暩(sh霉)[16]銆�

4.3妯＄硦閭忚集鎺у埗绯荤当(t菕ng)

鍦ㄥ(sh铆)闅涘伐绋嬫噳(y墨ng)鐢ㄤ腑锛岀敱浜庣己涔忛棞(gu膩n)浜庡皪璞″嫊鎱�(t脿i)銆侀潪绶氭€у拰鏅傝畩鐗规€х殑瑭崇窗(x矛)鍏堥(y脿n)鐭ヨ瓨锛屽緱鍒拌鎺у皪璞＄殑绮剧⒑妯″瀷鏄潪甯稿洶闆ｇ殑鎴栦笉鍙兘鐨�?锛涱媱璇冲垈钁″埌y(t菕ng)鐒℃ā鍨嬩及瑷�(j矛)鐨勬ā绯婃帹鐞嗘柟娉曟槸鎺у埗绯荤当(t菕ng)瑷�(sh猫)瑷�(j矛)鐨勬湁鍔涘伐鍏蜂箣涓€銆傞€欑ó鍩轰簬瑕�(gu墨)鍓囩殑绯荤当(t菕ng)灏囨ā绯婅獮瑷€璁婇噺寮曞叆瑕�(gu墨)鍓囬泦鍚堜腑锛岀敤浠ュ皪浜虹殑缍�(j墨ng)椹�(y脿n)鏂规硶寤烘ā銆備絾鏄ā绯婃帶鍒跺櫒鐨勮(gu墨)鍓囧拰闅稿爆搴﹀嚱鏁�(sh霉)鐨勯伕鍙栧叿鏈夊緢澶х▼搴︾殑涓昏鎬�锛岀暥(d膩ng)杓稿叆銆佽几鍑烘暩(sh霉)鐩拰瑾炶█璁婇噺鍔冨垎鐨勭瓑绱氬澶ф檪锛屾ā绯婅(gu墨)鍓囩殑鏁�(sh霉)鐩槸浠ョ礆鏁�(sh霉)鐨勫钩鏂归棞(gu膩n)绯昏繀閫熷鍔�銆傞€欎簺閮界郸妯＄硦鎺у埗鍣ㄧ殑瑷�(sh猫)瑷�(j矛)甯朵締浜嗗洶闆�銆傜偤浜嗚В姹烘ā绯婃帶鍒跺櫒瑷�(sh猫)瑷�(j矛)鐨勫洶闆�锛屽緢澶氬(xu茅)鑰呯爺绌跺埄鐢℅A閫�(j矛n)琛屾ā绯婄郴绲�(t菕ng)鐨勮紨鍔╄ō(sh猫)瑷�(j矛)鍜岃嚜鍕曞寲瑷�(sh猫)瑷�(j矛)銆俈arsek[17]鎻愬嚭浜嗗(xu茅)缈�(x铆)鍕曟厠(t脿i)绯荤当(t菕ng)鎺у埗鐨勪笁闅庢妗嗘灦锛涘嵆鍏堥€氶亷GA鐛插緱姹虹瓥琛�锛屽啀閫氶亷姗�(j墨)鍣ㄥ(xu茅)缈�(x铆)灏囨帶鍒惰(gu墨)鍓囪綁(zhu菐n)鎻涙垚鍙互鐞嗚В鐨勫舰寮忥紝鏈€鍚庡啀鐢℅A鍎�(y艒u)鍖栬(gu墨)鍓囩殑鏁�(sh霉)鍊煎弮鏁�(sh霉)銆俛rk鐮旂┒浜嗕竴绋柊鐨勫熀浜庨伜鍌崇殑妯＄硦鎺ㄧ悊绯荤当(t菕ng)锛岀敤浜庣敘(ch菐n)鐢熷劒(y艒u)鍖栧弮鏁�(sh霉)闆�锛岀嵅寰椾簡鑹ソ鐨勬€ц兘[18]銆�

4.4绁炵稉(j墨ng)缍�(w菐ng)绲�(lu貌)鎺у埗绯荤当(t菕ng)

浜哄伐绁炵稉(j墨ng)缍�(w菐ng)绲�(lu貌)鏄緸寰绲�(ji茅)妲�(g貌u)鑸囧姛鑳戒笂灏嶄汉鑵︾缍�(j墨ng)绯荤当(t菕ng)鐨勬ā鎿€屽缓绔嬭捣渚嗙殑涓€椤炴ā鍨�锛屽叿鏈夋ā鎿汉鐨勯儴鍒嗗舰璞℃€濈董鐨勮兘鍔涳紝鍏剁壒榛�(di菐n)鏄叿鏈夐潪绶氭€х壒鎬�銆佸(xu茅)缈�(x铆)鑳藉姏鍜岃嚜閬╂噳(y墨ng)鎬э紝鏄ā鎿汉鐨勬櫤鑳界殑涓€绋噸瑕侀€斿緫锛屽畠鍦ㄨū澶氭柟闈㈠彇寰椾簡寤ｆ硾鎳�(y墨ng)鐢�銆備絾鏄缍�(j墨ng)缍�(w菐ng)绲�(lu貌)鐨勫垵濮嬫瑠(qu谩n)鍊笺€侀柧鍊煎拰楂樻柉鍑芥暩(sh霉)涓績鐭㈤噺涓嶈兘寰堝ソ鐨勭⒑瀹�锛岃€岄毐鍚堡鍠厓鐨勫偝杓稿嚱鏁�(sh霉)鏄笉閫ｇ簩(x霉)鍜屼笉鍙井鐨�锛屽洜姝ら噰鐢ㄥ偝绲�(t菕ng)鐨勫劒(y艒u)鍖栨柟娉曞彲鑳介櫡鍏ュ眬閮ㄦサ灏忓€糩19]銆傝€岄伜鍌崇畻娉曠殑鎼滅储涓嶄緷璩存搴︿俊鎭�锛屼篃涓嶉渶瑕佹眰瑙ｅ嚱鏁�(sh霉)鍙井锛屽彧闇€瑕佹眰瑙ｅ嚱鏁�(sh霉)鑷磩鏉熸浠朵笅鐨勫彲琛岃В锛屽苟涓旈伜鍌崇畻娉曞叿鏈夊叏灞€鎼滅储鐨勭壒鎬�锛岀敤閬哄偝绠楁硶鍎�(y艒u)鍖栫缍�(j墨ng)缍�(w菐ng)绲�(lu貌)鐨勯€ｆ帴娆�(qu谩n)銆佺恫(w菐ng)绲�(lu貌)绲�(ji茅)妲�(g貌u)銆佸垵濮嬫瑠(qu谩n)鍊�銆侀柧鍊煎拰楂樻柉鍑芥暩(sh霉)涓績鐭㈤噺涓嶅儏瀹规槗鐛插緱鍏ㄥ眬鏈€鍎�(y艒u)瑙�锛岄倓鍙互鎻愰珮绁炵稉(j墨ng)缍�(w菐ng)绲�(lu貌)鐨勬硾鍖栨€ц兘锛屽ぇ澶ф彁楂樼郴绲�(t菕ng)鐨勭簿搴�銆侀妫掓€у拰鑷仼鎳�(y墨ng)銆傛枃鐛�(xi脿n)[20]鎻愬嚭浜嗙敤閬哄偝绠楁硶渚嗕唬鏇挎渶灏忎簩涔樻硶渚嗚〒(x霉n)绶碦BF绁炵稉(j墨ng)缍�(w菐ng)绲�(lu貌)鐨勬瑠(qu谩n)鍊�銆侀柧鍊煎拰楂樻柉鍑芥暩(sh霉)涓績鐭㈤噺锛屽緱鍑轰簡婊挎剰鐨勪豢鐪熺祼(ji茅)鏋�銆�

5.閬哄偝绠楁硶鐨凪ATLAB瀵�(sh铆)鐝�(xi脿n)

闇€瑕佸涓嬩富鍑芥暩(sh霉)锛�

锛�1锛夌法纰煎拰绋兢鐢熸垚

function [pop] = initializega(num,bounds,evalFN,evalOps,options)

% pop    - the initial, evaluated, random population 

% num    - the size of the population, i.e. the number to create

% bounds - the number of permutations in an individual (e.g., number of cities in a tsp

% evalFN - the evaluation fn, usually the name of the .m file for evaluation

% evalOps- any options to be passed to the eval function defaults [ ]

% options- options to the initialize function, ie. [eps, float/binary, prec] where eps is the epsilon value and the second option is 1 for orderOps, prec is the precision of the variables defaults [1e-6 1]

锛�2锛変氦鍙�

function [c1,c2] = arithXover(p1,p2,bounds,Ops)

% Arith crossover takes two parents P1,P2 and performs an interpolation along the line formed by the two parents.

% function [c1,c2] = arithXover(p1,p2,bounds,Ops)

% p1 - the first parent ( [solution string function value] )

% p2      - the second parent ( [solution string function value] )

% bounds  - the bounds matrix for the solution space

% Ops     - Options matrix for arith crossover [gen #ArithXovers]

锛�3锛夐伕鎿�

normGeomSelect锛歂ormGeomSelect is a ranking selection function based on the normalized geometric distribution.

锛堝熀浜庢鎱�(t脿i)鍒嗗竷鐨勫簭鍒楅伕鎿囧嚱鏁�(sh霉)锛�

锛�4锛夎畩鐣�

function[newPop] = normGeomSelect(oldPop,options)

% NormGeomSelect is a ranking selection function based onthe normalized geometric distribution.  

% function[newPop] = normGeomSelect(oldPop,options)

% newPop  - the new population selected from the oldPop

% oldPop  - the current population

% options - options to normGeomSelect [gen probability_of_selecting_best]

锛�5锛変竴浜涜紨鍔╁嚱鏁�(sh霉)锛�

f2b 锛歊eturn the binary representation of the float number fval锛堝皣娴粸(di菐n)鏁�(sh霉)杞�(zhu菐n)鍖栫偤浜岄€�(j矛n)鍒舵暩(sh霉)锛�

b2f锛歊eturn the float number corresponing to the binary representation of bval. 锛堝皣浜岄€�(j矛n)鍒舵暩(sh霉)杞�(zhu菐n)鍖栫偤娴粸(di菐n)鏁�(sh霉)锛�

nonUnifMutation锛� Non uniform mutation changes one of the parameters of the parent based on a non-uniform probability distribution.  This Gaussian distribution starts wide, and narrows to a point distribution as the current generation approaches the maximum generation.锛堝熀浜庨潪鍧囦竴姒傜巼鍒嗗竷閫�(j矛n)琛岄潪鍧囦竴璁婄暟锛�

maxGenTerm锛歊eturns 1, i.e. terminates the GA when the 

maximal_generation is reached.锛堢暥(d膩ng)?sh霉)顜款寖铻�?sh霉)澶т簬鏈€澶ц凯浠ｆ鏁�(sh霉)鏅�锛岀祩姝㈤伜鍌崇畻娉�锛岃繑鍥炵偤1锛屽惁鍓囪繑鍥炵偤0銆傦級

roulette锛歳oulette is the traditional selection function with the probability of surviving equal to the fitness of i / sum of the fitness of all individuals

6.绲�(ji茅)璜�

閬哄偝绠楁硶鏄竴绋潪甯告湁鏁堢殑鍎�(y艒u)鍖栨眰瑙ｆ柟娉曪紝灏嶄簬鎺у埗闋�(l菒ng)鍩熶腑鐨勬煇浜涙帶鍒剁祼(ji茅)妲�(g貌u)鍜屾帶鍒朵綔鐢ㄧ殑姹傚彇锛屽彲浠ユ彁渚涙瘮鍌崇当(t菕ng)鍎�(y艒u)鍖栨柟娉曟洿蹇洿濂界殑绲�(ji茅)鏋�?锛熸ⅱ鍝塮灏嘒A鑸嘋AD杌熶欢鍖呮櫤鑳介€ｆ帴鑰岄€�(j矛n)琛岄珮绮惧害绯荤当(t菕ng)寤烘ā鍜屾帶鍒跺櫒鑷嫊鍖栬ō(sh猫)瑷�(j矛)鍙婂弮鏁�(sh霉)鍎�(y艒u)鍖栧皣鏄竴绋涔嬫湁鏁堢殑鏂版柟娉�銆備絾瀹冨绲傛湭鑳藉皪鑷韩婕斿寲鏈韩鐨勭爺绌剁櫦(f膩)鐢熶綔鐢ㄣ€傝€屼笖灏卞叾瀵�(sh铆)璩�(zh矛)渚嗚瑳锛岀洰鍓嶇殑GA瀛�(xu茅)缈�(x铆)浜洪婕斿寲閬庣▼閭勫彧鏄舰寮忕殑锛屽皻鏈兘鍒荤暙浜洪鑷韩鐨勬紨鍖栭亷绋�锛屾洿鏈兘鍒荤暙绁炵稉(j墨ng)鍏冩€濈董鐪熷(sh铆)瀛�(xu茅)缈�(x铆)閬庣▼銆傚洜姝A灏卞叾妯″瀷鏈韩渚嗚瑳闇€瑕佹洿鍔犳繁鍏ョ殑鎺㈣◣銆�

鍙冭€冩枃鐛�(xi脿n)

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