Heat　conduction　optimization　benefits　many　important　applications　and　attracts　researchers’　interest　unceasingly.　Here　we　present　an　alternative　heat　conduction　optimization　algorithm　on　the　basis　of　generalized　Benders　decomposition　technique.　In　this　algorithm,　the　heat　conduction　optimization　problem　is　first　decomposed　to　a　subproblem　and　a　master　problem.　The　subproblem　calculates　the　temperature　field　with　the　given　thermal　conductivity　distribution,　updates　the　upper　boundary　of　objective,　and　constructs　an　optimality　cut　at　the　current　point.　The　master　problem　updates　the　lower　boundary　of　objective　from　solving　the　programming　problem　formed　by　all　optimality　cuts　generated.　The　subproblem　and　master　problem　are　solved　alternately,　the　two　boundaries　approach　mutually,　and　the　optimal　solution　can　be　reached.　The　proposed　algorithm　is　validated　by　applying　it　on　the　classic　“volume-to-point”　problem.　Results　show　that　the　average　and　maximum　temperature　in　the　domain　can　be　effectively　reduced.　It　is　further　extended　to　the　topology　optimization　to　obtain　discrete　material　distribution,　and　numerical　studies　are　also　conducted　for　validation.　Finally,　the　inverse　design　of　thermal　cloak　is　studied　by　using　the　proposed　algorithm,　and　square　and　circular　thermal　cloaks　are　numerically　designed　and　verified.　All　cases　studied　demonstrate　the　efficacy　and　flexibility　of　the　proposed　algorithm.　©　2023　Elsevier　Ltd