A new optimization approach for nozzle selection and component allocation in multi-head beam-type SMD placement machines

This paper addresses a highly challenging scheduling problem faced in multi-head beam-type surface mounting devices (SMD) machines. An integrated mathematical model is formulated aiming to balance workloads over multiple heads as well as improving the traveling speed of the robotic arm by incorporating the appropriateness factors in the model to evaluate the compatibility of component-nozzle pairs. The proposed model is a bi-objective mixed integer nonlinear programming one, which is first converted into a linearized model and then directly solved by using the augmented epsilon constraint method for small problem instances. As the model is turned out to be NP-hard, we also develop a Multi-Objective Particle Swarm Optimization (MOPSO) algorithm to solve the model for medium and large-sized problem instances. The parameters of the proposed MOPSO are tuned by using the Taguchi Method and corresponding numerical results are provided.