Reductions and Abstractions for Optimization of Modular Timed Automata

Abstract

Time optimization of concurrent sequences of operations is in this paper solved by timed automata. To reduce the complexity of this classical problem, including applications such as planning and scheduling, an abstraction method has recently been proposed based on local optimization (Hage-bring and Lennartson, 2019). In a modular subsystem, local paths without any communication with other subsystems are optimized with respect to time, and when subsystems are synchronized more local behavior appears. The proposed method has shown to be successful, drastically reducing computational complexity for important classes of planning problems. The only drawback is that the synchronous composition includes a heuristic non-standard synchronous composition procedure to achieve true concurrency. In this paper a simple solution to this problem is presented based on the original synchronous composition of timed automata. In the transformation of the timed automaton to an ordinary automaton, where time weights are generated, it is first observed that the state space often increases dramatically in this transformation. To solve this complexity problem, an efficient reduction is proposed as a complement to local optimization, and both methods are demonstrated to be very efficient when they are applied to realistic benchmark examples.