A Mutualism Quantum Genetic Algorithm to Optimize the Flow Shop Scheduling with Pickup and Delivery Considerations

A mutualism quantum genetic algorithm(MQGA) is proposed for an integrated supply chain scheduling with the materials pickup, flow shop scheduling, and the finished products delivery. The objective is to minimize the makespan, that is, the arrival time of the last finished product to the customer. In MQGA, a new symbiosis strategy named mutualism is proposed to adjust the size of each population dynamically by regarding the mutual influence relation of the two subpopulations. A hybrid Q-bit coding method and a local speeding-up method are designed to increase the diversity of genes, and a checking routine is carried out to ensure the feasibility of each solution; that is, the total physical space of each delivery batch could not exceed the capacity of the vehicle. Compared with the modified genetic algorithm (MGA) and the quantum-inspired genetic algorithm (QGA), the effectiveness and efficiency of the MQGA are validated by numerical experiments.