complex and hard problem. For different QoS
requirements, many heuristics have been proposed [4-8].
Ref. [4] introduced a dynamic time and cost reduction
in grid workflows, in which cost is optimized with the
expectation to minimize workflow duration. Jin et al [5]
presented a multidimensional QoS model for service
composition represented by DAG(Directed Acrylic
Graph ) , and two heuristics were established to
minimize duration and cost under deadline and budget
constraints. Yu Jia [6] proposed a genetic algorithm for
workflows to minimize workflow duration with the
budget constraints. Two different Leveling algorithms
[7, 8] were developed for cost optimization with
deadline constraints. Activities are partitioned into
levels by their top-depth (bottom-depth) in DAG. The
whole deadline is segmented to level deadlines. In each
level, the most appropriate service for each activity is
selected. Then the workflow cost is optimized by
minimizing level costs with level deadlines. Although
the leveling algorithms are simple and relatively
effective, partial DAG structure is partially destroyed.