Constrained optimization via quantum genetic algorithm for task scheduling problem

Task scheduling is one of the most important issues on heterogeneous multiprocessor systems. In this paper, the problem is defined as performance-constrained energy optimization. It is a commonly used constrained optimization problem (COP) in practice. Task scheduling for constrained optimization problem is NP problem. It is usually handled by heuristics or meta-heuristics method. Classic quantum genetic algorithm is an excellent meta-heuristics algorithm, but they are hardly ever used to handle COPs because quantum rotation gate can only deal with single objective problem. Moreover, it is difficult to model the task scheduling problems so as to be handled by quantum genetic algorithm. To handles COPs in task scheduling on heterogeneous multiprocessor systems, we propose a new quantum genetic algorithm. In our algorithm, the chromosome consists of task sequence part and mapping part. Task sequence part is generated by list scheduling algorithm which can improve the parallel of the tasks. The mapping part indicates the correspondence between the tasks and the processors which they will run on. The mapping part will be transferred to quantum bits and take part in the evolve-ment guided by quantum genetic algorithm. Beside, we adopt an adaptive penalty method which belongs to constraint-handling technique to transfer COP into single objective problem. The results in simulations show the superiority of our method compared with state-of-the-art algorithms.