Research on bi-objective scheduling problems subjected to special process constraint on parallel machines

The study presents a bi-objective scheduling model on parallel machines(BOSP), and proposes a new genetic algorithm (VIGA) based on the vector group encoding method and the immune method. Compared with other scheduling problems on parallel machines, The BOSP is distinct for the following characteristics: (1) parallel machines are non-identical; (2) the sort of jobs processed on every machine can be restricted; (3) take minimizing the total tardiness penalty and minimizing the total completion time into account as a bi-objective problem. For VIGA, its two distinct characteristics are described as follows. On one hand, individuals are represented by a vector group, which can effectively reflect the virtual scheduling policy; On the other hand, an immune operator is adopted and studied in order to guarantee diversity of the population and improve quality of the population. Numerical experiments show that it is efficient, and is superior to the genetic algorithm which is the same as VIGA without the immune operator. A much better prospect of application can be optimistically expected.