Stressing Symbolic Scheduling Techniques within Aircraft Maintenance Optimization

Abstract

Scheduling, or planning, is widely recognized as a very important step in several domains such as high level synthesis, real-time systems, and everyday applications. Given a problem described by a number of actions and their relationships, finding a schedule, or a plan, means to find a way to perform all the actions minimizing a specific cost function. The goal of this paper is to develop, analyze and compare different scheduling techniques on a new scheduling/planning problem. The new application domain is aircraft maintenance. It shares with previous ones the underlying problem definition, but it also unveils brand new challenging characteristics, and a different optimization target. We show how to model the problem in a suitable way, and how to solve it with different methodologies going from Satisfiability solvers and Binary Decision Diagrams, to Timed Automata and Coloured Petri Nets. New ideas are put forward in the different domains having efficiency and scalability as main targets. Experimental results stress the different techniques, showing their application range and limits, and defining advantages and disadvantages of the underlying models. Overall, general-purpose tools have been easily applied to our problem, but failed as far as efficiency was concerned. The satisfiability-based approach proved to be faster and more scalable, being able to solve instances 3 − 4 times larger. To sum up, our contributions range from modeling the aircraft maintenance problem as a scheduling instance, to coding this problem with home-made and general-purpose tools, to dovetailing exact and heuristic techniques, and comparing these techniques in terms of efficiency and scalability.

A Novel SAT-Based Approach to the Task Graph Cost-Optimal Scheduling Problem

“…In most of the cases, a few MB are enough to complete the experiments with our method, whereas several hundred MB are usually required by UPPAAL CORA. 9 The previous results can be further appreciated when considering the overall statistics. Our tool was able to solve a total of 2026 benchmarks, i.e., more than 90% of all instances, while hitting 113 overflows on time and 21 overflows on memory.…”

“…The resulting automaton, further restricted by several constraints, incorporates all the allowed system behaviors, and can indeed be used for solving the scheduling problem. Following [8] and [9], the overall formulation is…”

“…Example 7: Let us consider once more the task graph scheduling problem presented in Example 3. Following (9) and 10 However, by running the ASAP algorithm, we find the schedule trace depicted in Fig. 10, which is characterized by a cost equal to 81.…”

“…cently attained interesting results in the framework of hardware scheduling [4]- [9], as an alternative to integer linear programming [10] and heuristic techniques [11], [12]. The key idea of the symbolic approach is to use a set of nondeterministic finite automata to describe the behavior of each operation in the system.…”

“…In [6], [8], [14], and [9] Cabodi et al adapted the previous model to support conventional model checking procedures for control-dependent systems. More specifically, alternative sub-traces were transformed into concurrent behaviors, subsequently followed in parallel.…”