multi-objective scheduling problem in a three-stage production system

a three stage production system is considered in this paper. there are two stages to fabricate and ready the parts and an assembly stage to assembly the parts and complete the products in this system. suppose that a number of products of different kinds are ordered. each product is assembled with a set of several parts. at first the parts are produced in the first stage with parallel machines and then they are controlled and ready in the second stage and finally the parts are assembled in an assembly stage to produce the products. two objective functions are considered that are: (1) to minimizing the completion time of all products (makespan), and (2) minimizing the sum of earliness and tardiness of all products (∑_i▒(e_i∕t_i ) . since this type of problem is np-hard, a new multi-objective algorithm is designed for searching locally pareto-optimal frontier for the problem. to validate the performance of the proposed algorithm, in terms of solution quality and diversity level, various test problems are made and the reliability of the proposed algorithm, based on some comparison metrics, is compared with two prominent multi-objective genetic algorithms, i.e. nsga-ii and spea-ii. the computational results show that performance of the proposed algorithms is good in both efficiency and effectiveness criterions.