Mathematical model and genetic optimization for hybrid flow shop scheduling problem based on energy consumption

Hybrid flow shop scheduling problem (HFSP) is characterized as the scheduling of jobs in a flow shop environment where, at any stage, there may exist multiple machines. Besides the finishing time of the last job, energy consumption is another important factor affecting economy benefit of hybrid flow shop. A mixed-integer nonlinear programming model is established for the HFSP with minimizing the energy consumption, according to the characteristic of HFSP in practice. It is a typical NP-hard combinatorial optimization problem. For solving it efficiently, an improved genetic algorithm is presented. The fitness based on the ranking of the energy consumption of every individual and the self-adaptive mutation operation based on the fitness are adopted. The numerical experiment is carried out on the three-two-three HFSP, and the result indicates that the model is right and the improved algorithm is efficient.