Abstract
The aim of the paper is to present a heuristic method for decision-making regarding an NP-hard scheduling problem with limitations related to tasks and the resources dependent on the current state of the process. The presented approach is based on the algebraic-logical meta-model (ALMM), which enables making collective decisions in successive process stages, not separately for individual objects or executors. Moreover, taking into account the limitations of the problem, it involves constructing only an acceptable solution and significantly reduces the amount of calculations. A general algorithm based on the presented method is composed of the following elements: preliminary analysis of the problem, techniques for the choice of decision at a given state, the pruning non-perspective trajectory, selection technique of the initial state for the trajectory final part, and the trajectory generation parameters modification. The paper includes applications of the presented approach to scheduling problems on unrelated parallel machines with a deadline and machine setup time dependent on the process state, where the relationship between tasks is defined by the graph. The article also presents the results of computational experiments.
Highlights
Scheduling problems are very widely presented and studied in the literature [1,2]
There are areas related to the specific features of scheduling problems
The purpose of this paper is to present a heuristic method for a common decision-making problem, where there are limitations related to the task and the resources needed to perform the tasks are not fixed and dependent on the current state of the process
Summary
There are many different solutions for known problems (travelling salesman problem TSP [3], basic and different versions of Vehicle routing problem VRP) [4,5,6,7,8]. There are many different approaches used to solve scheduling problems, mathematical methods (e.g., Petri net, branch and bound, integer programming, constraint programming) [16,17,18], and heuristic methods (genetic algorithms, Tabu search, simulated annealing, and swarm intelligence method) [19,20,21,22]. The adaptation of cellular automata to solve scheduling problems is becoming more and more popular [24,25,26]
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