Speedup Techniques for Multiobjective Integer Programs in Designing Optimal and Structurally Simple Supervisors of AMS

This paper investigates several speedup techniques for a multiobjective integer linear program (ILP) used to obtain an optimal Petri net supervisor with a compressed structure for automated manufacturing systems (AMSs). An optimal supervisor can be obtained by forbidding all first-met bad markings and no legal markings of a plant net via place invariants. An iterative method to perform lexicographic multiobjective ILP is proposed to design such supervisor with a simple structure in terms of the numbers of control places and added arcs. Instead of a single ILP, several much smaller ILPs are formulated in the iterative method, and they can be solved much faster. To further reduce the ILP solution time, an efficient redundancy identification method is used. Finally, some AMS examples are provided to demonstrate the proposed speedup techniques and approaches.