We consider two bicriteria scheduling problems on a single machine: minimizing flowtime and number of tardy jobs, and minimizing flowtime and maximum earliness. Both problems are known to be NP-hard. For the first problem, we developed a heuristic that produces an approximately efficient solution (AES) for each possible value the number of tardy jobs can take over the set of efficient solutions. We developed a genetic algorithm (GA) that further improves the AESs. We then adapted the GA for the second problem by exploiting its special structure. We present computational experiments that show that the GAs perform well. Many aspects of the developed GAs are quite general and can be adapted to other multiple criteria scheduling problems. (C) 2002 Elsevier Science B.V. All rights reserved.