The　multi-objective　optimization　problem　is　difficult　to　solve　with　conventional　optimization　methods　and　algorithms　because　there　are　conflicts　among　several　optimization　objectives　and　functions.　Through　the　efforts　of　researchers　and　experts　from　different　fields　for　the　last　30　years,　the　research　and　application　of　multi-objective　evolutionary　algorithms　(MOEA)　have　made　excellent　progress　in　solving　such　problems.　MOEA　has　become　one　of　the　primary　used　methods　and　technologies　in　the　realm　of　multi-objective　optimization.　It　is　also　a　hotspot　in　the　evolutionary　computation　research　community.　This　survey　provides　a　comprehensive　investigation　of　MOEA　algorithms　that　have　emerged　in　recent　decades　and　summarizes　and　classifies　the　classical　MOEAs　by　evolutionary　mechanism　from　the　viewpoint　of　the　search　strategy.　This　paper　divides　them　into　three　categories　considering　the　search　strategy　of　MOEA,　i.e.,　decomposition-based　MOEA　algorithms,　dominant　relation-based　MOEA　algorithms,　and　evaluation　index-based　MOEA　algorithms.　This　paper　selects　the　relevant　representative　algorithms　for　a　detailed　summary　and　analysis.　As　a　prospective　research　direction,　we　propose　to　combine　the　chaotic　evolution　algorithm　with　these　representative　search　strategies　for　improving　the　search　capability　of　multi-objective　optimization　algorithms.　The　capability　of　the　new　multi-objective　evolutionary　algorithm　has　been　discussed,　which　further　proposes　the　future　research　direction　of　MOEA.　It　also　lays　a　foundation　for　the　application　and　development　of　MOEA　with　these　prospective　works　in　the　future.