An　improved　food　chain　algorithm　was　proposed　for　permutation　flow　shop　scheduling　with　multiple　objectives　of　minimizing　makespan　and　total　tardiness.　Fast　non-dominated　sorting　and　crowded　distance　estimation　were　introduced　into　the　food　chain　algorithm　to　improve　the　optimization　ability　based　on　Pareto　optimal　solutions.　Three　typical　OR-Library　examples　were　selected　to　conduct　comparison.　Numerical　results　show　that　the　designed　algorithm　can　obtain　much　better　solutions　than　NSGA-II.　©,　2015,　China　Mechanical　Engineering　Magazine　Office.　All　right　reserved.