A multi-start path-relinking algorithm for the flexible job-shop scheduling problem

Scheduling is a well-known NP-hard problem. The flexible job-shop scheduling problem (FJSP) is an extention of the classical job-shop scheduling problem(JSP). FJSP allows an operation of each job to be performed by any machine out of a set of available machines. FJSP consists two sub-problems which are assigning each operation to a machine out of a set of capable machines and sequencing the assigned operations on the machines. This paper proposes a path-relinking(PR) algorithm that solves the FJSP to minimize makespan. Also, a GRASP method has been used for creating the initial solutions. The proposed algorithm is evaluated by testing on a set of 15 benchmark problems. The computational results show that the proposed algorithm is an effective approach to solve the FJSP.