SMT solvers for flexible job-shop scheduling problems: A computational analysis
Paper in proceedings, 2019

In this paper we evaluate different formulations for solving the Flexible Job-shop Scheduling Problem (FJSP) to optimality. Heuristic methods resulting in sub-optimal solutions are traditionally used to solve this problem since it is a known NP-hard problem. Since industrial problems often have additional constraints that need to be considered during optimization, the heuristic methods need to be adapted to deal efficiently with the additional constraints. For this reason general-purpose solvers that are often used in industrial applications. There are different approaches to formulate FJSPs as Mixed-Integer Linear Programming problems (MILP) that can be solved using generic MILP-solvers. In recent years, satisfiability solvers, i.e. SAT- and SMT-solvers, have evolved within the formal verification community and shown to be able to efficiently solve large instances of well-known NP-hard problems. In our previous work we have shown that SMT-solvers extended with optimization techniques can be a competitive alternative to commercial MILP-solvers on traditional job-shop scheduling problems. In this work we have adapted three formulations used for formulating FJSPs for MILP solvers into SMT-formulations. The three formulations are used to solve benchmark FJSPs using the open-source Z3 SMT-solver. We show that the a formulation based on the Manne formulation adapted for SMT-formulations for FJSPs is a competitive alternative for solving large-scale FJSPs, and might be considered as a viable alternative for solving industrial problems.

Author

Sabino Francesco Roselli

Chalmers, Electrical Engineering, Systems and control, Automation

Kristofer Bengtsson

Chalmers, Electrical Engineering, Systems and control, Automation

Knut Åkesson

Chalmers, Electrical Engineering, Systems and control, Automation

IEEE International Conference on Automation Science and Engineering

21618070 (ISSN) 21618089 (eISSN)

Vol. 2019-August 673-678 8843025

15th IEEE International Conference on Automation Science and Engineering, CASE 2019
Vancouver, Canada,

Engineering Tool Chain for Efficient and Iterative Development of Smart Factories (ENTOC)

VINNOVA, 2016-09-01 -- 2019-08-31.

Subject Categories

Computational Mathematics

Control Engineering

Computer Science

DOI

10.1109/COASE.2019.8843025

More information

Latest update

9/18/2020