Solving the Fuzzy Job Shop Scheduling Problem via Learning Approaches

My primary concern about this paper is regarding its novelty. While using neural combinatorial optimization (NCO) techniques to solve FJSSP problems might be novel, the high-level graph representation of the FJSSP problem adopted in this paper is very similar to many existing studies. It seems that the key difference is the introduction of fuzzy model related features and feature vectors. However, the technical novelty associated with these features has not been properly highlighted and justified.

Meanwhile, the training strategy does not seem to be new. Perhaps random solution selection is a novel element of the training algorithm. Nevertheless, the effectiveness of this selection mechanism is only discussed intuitively. More thorough theoretical and empirical analysis may be necessary to clearly quantify its importance for the newly proposed NCO system to find near-optimal solutions. To my understanding, the analogy with genetic algorithms does not reveal the true advantages of using random solution selection techniques, since the proposed NCO system is not closely related to genetic algorithms.

The baseline algorithms adopted in this paper were published about 8 to 9 years ago. It is important to include more recent baselines in the experimental comparison to truly understand the technical advancement introduced by the new approach. In particular, to clearly demonstrate the advantages of the newly developed encoder-decoder network architecture, several existing approaches using different GNN architecture designs should be experimentally examined and compared in this paper.

The authors just compared their method with one method, which is not enough to verify the effectiveness of the proposed method. There are state-of-the-art evolutionary computation algorithms for FJSSP. What is the advantage of the proposed method over them? The comparison between the proposed method and them should be implemented to analyze the difference. Meanwhile, the proposed algorithm is not very competitive in items of FMS, and its performance is poorer than that of the comparison algorithm in some problems. The paper lacks parameter analysis and ablation study, making a gap between the results and the conclusion.

There are two major issues with the paper that right now prevent me from being more positive about it.

1. The new perturbation strategy is not experimentally validated at all. First note that it is said that "Corsini et al. (2024) ... select the optimal solution as the pseudo-label". My understanding of the Corsini paper is that they use the best solution from the sample. I assume that this is just a typo though. More importantly, where does P_p come from and who sets it? Why is this value not experimentally validated? The experimental section says that it is set to 0.05 and that's all. First, turning it off is an important ablation step, and showing the sensitivity is also very interesting. I also wonder why the authors do not try this technique out on the original JSSP? It would improve the generalizability of this paper, which is rather sharply focused on the FJSSP right now and, in all honesty, ICLR is not an applications conference. The reviewers need to at least believe there is a chance of generalization here, but right now there is no evidence.
2. The experimental results are not complete. They compare the approach with a CP model, mostly lose, and then claim victory because it is faster. First, CP is proving optimality and this method is not, so it is a completely apples to oranges comparison. Second, where do these results even come from in the Afsar et al. (2023) paper? I do not see these runtimes; on the contrary, Table 5 in the Afsar paper indicate that S6.1-4 only need 0.1 seconds to solve to optimality and the heuristic approach HTS only 0.2 seconds. On S10.1-4 on average 76 seconds are needed for the CP model and 1.0 for HTS. This brings me to a question: where is HTS in this work? How does HTS compare to the SS-FJSSP approach? I note that this comparison is quite important as SS-FJSSP has many domain specific components in it, so the method is not interesting in and of itself -- it ought to be as good as the current techniques available. One more note here: the authors make note that they do not re-implement the CP model because the source code is not available... but we are talking about a model with 5 constraints, this would not be much of a challenge...

I note that I am also a bit wary about the FJSSP in general. The fuzzy literature makes rather simplifying assumptions (triangular distribution), thus avoiding any of the hard parts of modeling stochastic optimization problems while still claiming to be more realistic. While I agree that it is more realistic than a standard JSSP, the question is whether it is really worth the trouble compared to just modeling a two-stage, robust or chance constrained problem. My opinion is that it is not because the triangular distribution is unrealistic for a variety of reasons (real distributions are often shifted, can have long tails, etc.). Thus, I think the authors are betting all their money here on a rather weak application that is not at the level of top conferences.

Some other notes about the paper for the authors to improve:

1. The references in the introduction about the FJSSP are not terribly convincing that it is an important problem. For a paper at a top conference, I would expect papers at top conferences (or an argument why those venues have overlooked this important problem)
2. The second paragraph of the introduction is not well written; it is very long and just meanders through the literature.
3. Page 3: Additional should be addition
4. The explanation about the arrow operator in 2.2 is unclear (namely i->x or x->j) -- I think this can be interpreted (incorrectly) as banning chains of operations.
5. The mathematical model ought to have a min before the max so it is more clear. Also the math model does not use the max operator in the constraints, which seems like it ought to be necessary? I admit I am not so familiar with modeling with fuzzy variables, so maybe there is a convention there I am not aware of.
6. The jobs numbers ought to be more clear in Figure 1 so it is easier to understand the scheduling scheme.

1. The experiments are not sufficient to show the contributions of the proposed method without comparing other methods.

2. The novelty is limited since the fuzzy job shop scheduling problem has been investigated and the paper looks like an extension of existing work by adding the fuzzy processing time.