Integrated OR/CP optimization for Discrete Event Systems with nonlinear cost

Towards integrated OR/CP energy optimization for robot cells

“…The LP/NLP-BB algorithm uses successive linearization and will either solve an NLP or an LP depending on which ruleset is selected. Our implementation of the integrated algorithm in [21] mimics this behaviour; it solves linearized problems in branch nodes and NLPs in terminal nodes. An imporAlgorithm 1 Integrated Algorithm 1: UB ← ∞ 2: NodeSet ← Top node 3: while 0 < |NodeSet| do While any nodes left 4: n ← NodeSet Get the next node 5: n ← Inference(n) Use CP for inference 6: if n is feasible then 7: s ← GenerateSubproblem(n) 8: cost ← Solve(s) Solve LP or NLP 9: if cost < UB then 10: if n is branch node then 11:…”

“…Even though an initial guess may be quickly determined by heuristics, including initial guess heuristics into "out of the box" MINLP algorithms is not always straight forward. This, in combination with the remarks in the previous paragraph leads us to suggest extending the integrated framework presented in [21] such as to solve the scheduling problem with collocated dynamics. The following will outline the structure of such an integrated algorithm.…”

“…As in [21], we propose extending an existing CP solver by adding the OR parts by means of a custom constraint propagator.…”

“…When the size of the node subproblems (NLPs) grow, this becomes a large problem; especially when optimality is to be proven. In [21], inspired by [22], [23], we showed how OR methods can be integrated with CP such as to eliminate infeasible branches at an early stage in MINLP problems.…”

Energy Optimization of Robotic Cells

“…Such parallelism is analogous with the cyclic scheduling of the processor pipeline (see, e.g., [17] and [18]). However, Wigström and Lennartson [10] presumed that the whole robotic cell is dedicated to one workpiece during the entire processing time, which the authors called the work cycle time; hence, the overall throughput may be limited because there is no parallelism. This different view of time distinguishes the problem in the present work.…”