Sustainable production automation - energy optimization of robot cells

This paper concerns the reduction of energy use in manufacturing industry. If individual robot movements in a system are preprocessed using Dynamic Programming, one can attain a Mixed Integer Nonlinear Program (MINLP) which models the energy consumption of the complete system. This model can then be solved to optimality using mathematical programming. We have previously shown proof of concept for this energy reduction method. In this paper, we apply state of the art MINLP methods to a number of problems in order benchmark their effectiveness. Algorithms used are Nonlinear Programming based Branch and Bound (NLP-BB), Outer Approximation (OA), LP/NLP based Branch and Bound (LP/NLP-BB) and Extended Cutting Plane (ECP). Benchmarks show that the NLP-BB does not perform well for nonlinear scheduling problems. This is due to the weak lower bounds of the integer relaxations. For scheduling problems with nonlinear costs, ECP and in particular LP/NLP-BB are shown to outperform both NLP-BB and OA. The resulting energy optimal schedules for the examples show a significant decrease in energy consumption.