Multi-objective optimization Model for Flexible Job Shop Scheduling Problem Considering Transportation Constraints: A Comparative Study

Flexible job shop scheduling problem (FJSP) has long been a complex problem due to the resource flexibility and strong constraints, generating a mixed-integer non-linear optimization problem. The problem becomes more complex with the increasing demand of energy reduction and the corresponding environmental impacts. Proper production scheduling is of significant potential in saving energy in the manufacturing system. In this paper, a multi-objective FJSP model is formulated with the objectives of minimizing the makespan and energy consumption considering strong transportation constraints. Two popular multi-objective optimization solver including Non-dominated Sorting Genetic Algorithm-II (NSGA-II) and A Multiobjective Evolutionary Algorithm Based on Decomposition (MOEA/D) are employed and compared in a real-world instance of the FJSP, associated with novel coding schemes. The results show that the proposed model is well solved by the two solvers and NSGA-II get the better solutions.