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Adaptive Bias Generalized Rollout Policy Adaptation on the Flexible Job-Shop Scheduling Problem

Lotfi Kobrosly, Marc-Emmanuel Coupvent des Graviers, Christophe Guettier, Tristan Cazenave

TL;DR

This work proposes a novel algorithm derived from the Generalized Nested Rollout Policy Adaptation, developed to solve the FJSSP, and reports encouraging experimental results, as the algorithm performs better than other MCTS-based approaches, even if makespans obtained on large instances are still far from known upper bounds.

Abstract

The Flexible Job-Shop Scheduling Problem (FJSSP) is an NP-hard combinatorial optimization problem, with several application domains, especially for manufacturing purposes. The objective is to efficiently schedule multiple operations on dissimilar machines. These operations are gathered into jobs, and operations pertaining to the same job need to be scheduled sequentially. Different methods have been previously tested to solve this problem, such as Constraint Solving, Tabu Search, Genetic Algorithms, or Monte Carlo Tree Search (MCTS). We propose a novel algorithm derived from the Generalized Nested Rollout Policy Adaptation, developed to solve the FJSSP. We report encouraging experimental results, as our algorithm performs better than other MCTS-based approaches, even if makespans obtained on large instances are still far from known upper bounds.

Adaptive Bias Generalized Rollout Policy Adaptation on the Flexible Job-Shop Scheduling Problem

TL;DR

This work proposes a novel algorithm derived from the Generalized Nested Rollout Policy Adaptation, developed to solve the FJSSP, and reports encouraging experimental results, as the algorithm performs better than other MCTS-based approaches, even if makespans obtained on large instances are still far from known upper bounds.

Abstract

The Flexible Job-Shop Scheduling Problem (FJSSP) is an NP-hard combinatorial optimization problem, with several application domains, especially for manufacturing purposes. The objective is to efficiently schedule multiple operations on dissimilar machines. These operations are gathered into jobs, and operations pertaining to the same job need to be scheduled sequentially. Different methods have been previously tested to solve this problem, such as Constraint Solving, Tabu Search, Genetic Algorithms, or Monte Carlo Tree Search (MCTS). We propose a novel algorithm derived from the Generalized Nested Rollout Policy Adaptation, developed to solve the FJSSP. We report encouraging experimental results, as our algorithm performs better than other MCTS-based approaches, even if makespans obtained on large instances are still far from known upper bounds.
Paper Structure (30 sections, 6 equations, 3 figures, 24 tables, 1 algorithm)

This paper contains 30 sections, 6 equations, 3 figures, 24 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Background and motivation
  3. The Job-Shop Scheduling Problem
  4. The Flexible Job-Shop Scheduling Problem
  5. Generalized Nested Rollout Policy Adaptation
  6. Motivation
  7. Disclaimer
  8. The Adaptive Bias Generalized Nested Rollout Policy Adaptation (ABGNRPA)
  9. Experiments and results
  10. Model description and implementation
  11. Datasets
  12. Baseline algorithms
  13. Experimental Results
  14. Observations and discussion
  15. Conclusion
  16. ...and 15 more sections

Figures (3)

  • Figure 1: Gantt's diagram of an example of a JSSP instance. The operations denoted by $O_{ij}$ are assigned to machines $M_l$ while respecting the constraints of order of operations in a job, of compatibility with machines and no interruption of the processing of operations. Blank spaces in a machine's line of processing represent inactivity.
  • Figure 2: Representation of a Nested Rollout Policy Adaptation, also compatible with GNRPA. The figure on the left represents a rollout, and arcs in green represent the chosen actions at each step. In this figure, the sequence obtained is the best one found so far. We use it to adapt the policy, as described in \ref{['gnrpa']}. Otherwise, we use the last best sequence for the policy update. Then we run the next rollout shown on the right. The values in bold are the ones that were updated, the incremented ones have their arcs in red, belonging to the best sequence and the decremented ones are in blue.
  • Figure 3: Correlation between mean and minimal makespans for each branch for the reduced mfjs04 instance.