Existing　heuristic　attribute　reduction　algorithms　generally　fail　to　get　a　minimum　entropy-based　attribute　reduction　of　a　decision　table.　Some　stochastic　optimization　algorithms　are　discussed　to　solve　the　problem　of　entropy-based　attribute　reduction.　Firstly,　a　proper　fitness　function　is　defined　to　transform　the　minimum　attribute　reduction　problem　into　a　fitness　optimization　problem　without　additional　constraints　and　the　equivalence　of　transformation　is　proved.　Then,　the　solving　efficiency　and　the　solution　quality　of　some　stochastic　optimization　algorithms　are　studied　such　as　Genetic　Algorithm,　Particle　Swarm　Optimization,　Tabu　search　and　Ant　Colony　Optimization.　Some　UCI　datasets　are　applied　to　test　those　performances.　The　experimental　results　show　that　the　fully　informed　PSO　based　attribute　reduction　algorithm　with　refine　scheme　has　a　higher　probability　to　find　a　minimum　entropy-based　attribute　reduction　and　good　performance.