Anytime heuristic search for scheduling flexible manufacturing systems: a timed colored Petri net approach

Abstract

Given the fluctuations in demand, diversity in products, production flexibility requirements, and tight customer due dates, obtaining optimal production schedules is considered a complex research problem. This can drastically affect the survival of some manufacturing companies in today's fiercely competitive global market. In a very demanding decision-making environment, scheduling problems are dealt with in a short-term horizon, in which computation time is a critical factor. Producing optimal solutions is practically impossible given the time limitations and the nondeterministic polynomial (NP)-hard nature of scheduling problems. This paper presents an anytime-heuristic search approach based on a simulation-optimization framework that combines evaluation methods (simulation) and search methods (optimization) through the reachability analysis (or state space) of timed colored Petri net models to schedule flexible manufacturing systems (FMS). The anytime search algorithm is capable of finding a first suboptimal solution very quickly and continuously improves the solution quality over time. If given enough computation time, the algorithm eventually converges to an optimal solution. The proposed approach is aimed at obtaining optimal or near-optimal solutions to FMS scheduling problems in relatively short computation times with the objective of minimizing the makespan. Its effectiveness is highlighted with excellent results that outperform previous methods on benchmark examples with flexible material handling systems, machine, and routing configurations. The approach can also serve as a decision support tool to assist production schedulers that require rapid and almost real-time responses to time-critical production scheduling on the shop floor.

Deadlock-Free Scheduling Method for Flexible Manufacturing Systems Based on Timed Colored Petri Nets and Anytime Heuristic Search

“…Owing to the limitations of RSS, this paper considers the ESS. It has been used in TCPN-based scheduling methods proposed in [50], [60], and [61].…”

“…As such, they will be listed as two unique nodes. Exploring the duplicate marking will lead to the same future behavior with differing time evolutions and could even lead to an infinite exploration in some systems [50].…”

“…We consider the CSS method [50], [61], [62] that explores the state space in a compact form by separating the evaluation of the untimed marking from the time stamps. The CSS factors out the notion of time for duplicate detection.…”

“…This process may become time-consuming if the number of tokens involved is quite large. We use the criterion described in [50] that employs the actual path cost to reach a marking M from the initial marking M 0 denoted as g (M).…”

“…Anytime algorithms guarantee that the search produces the best solution obtained so far within the allotted computation time and they are expected to return better solutions when given more time. A recent study [50] adapted the anytime column search [51] to schedule FMS without considering DL situations. The proposed approach called anytime layered search (ALS) combines breadth-first iterative deepening A * search (BFIDA * ) with suboptimal breadth-first heuristic search (sBFHS) [52] and backtracking to provide a sequence of improving solutions.…”