A Memetic Decomposition-Based Multi-Objective Evolutionary Algorithm Applied to a Constrained Menu Planning Problem
Round 1
Reviewer 1 Report
The problem is rather interesting and the formulation and layout are sufficiently rich in detail. However the authors may consider the following minor changes:
1. What is the motivation to involve the ILS and ad-hoc crossovers in MOEA/D? It is understandable that the crossover resulted in speedup however a more detailed explanation about how a practitioner can assume certain combinations will work and others will not, may be made.
2.The authors need to elaborate and emphasize why for increased problem sizes (i.e. n=40, n=60 and so on) ILS-MOEA/D renders worse results than MA. On a high level, what kinds of improvements on ILS-MOEA/D would produce competitive results (possibly better) and why?
Author Response
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Author Response File: 
Author Response.pdf
Reviewer 2 Report
This paper is concerned with the multi-objective formulation of the menu planning problem (MPP). For solving the MPP, the authors develop a decomposition-based multi-objective evolutionary algorithm, which is enhanced by incorporating an iterated local search technique. The results of computational experiments are provided for several instances of the MPP. They are compared with the results obtained by a memetic algorithm (MA) proposed earlier in the literature. The experimental comparison demonstrates that the new algorithm can produce much more balanced menu plans than those yielded by MA, and the cost of menu plans in both cases is quite close.
The paper, in general, is well structured and also well written. I have only a few minor remarks, as follows.
1. On page 4, line 134, the letter c with subscripts is selected to represent the cost of the courses. However, on the same page, line 138, exactly the same notation is used to denote courses themselves, which is not correct.
2. In order to indicate which exactly terms are summed up in (1) and (2), I suggest to use parentheses. Also, the parentheses in (4) should be placed correctly.
3. The right-hand side of (10) is not fully clear. Specifically, λi is assumed to be a scalar in (10). However, in line 184, λi is defined as being a vector. An explanation or correction is needed.
4. The input to Algorithm 2 includes T. Is T the same as in Eq. (4)? I guess that not. If indeed not, then a different letter must be used.
5. It is not immediate to see where 'Population' is updated in Algorithm 2. Probably, 'Population' could be added as a parameter to the procedure UpdateNeighbouringSolutions(Offspring) in line 10.
Author Response
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Author Response File: Author Response.pdf
Reviewer 3 Report
Authors present a novel multi-objective memetic approach based on the well-known Multi-objective Evolutionary Algorithm based on Decomposition (MOEA/D).
The background section lacks in describing the disadvantages of existing solving methods of the meal planning problem. There are various algorithms under the umbrella of evolutionary algorithms. Why other algorithms are not chosen to solve this problem.
The proposed algorithm has been compared with only one algorithm. What about other algorithms like Differential Evolution, Particle Swarm Optimizer, BAT etc?
What about the computational complexity and time complexity of the proposed algorithm?
How the authors are sure that the proposed algorithm does not suffer for local optima problem?
Author Response
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Author Response File: Author Response.pdf
Reviewer 4 Report
The paper is well written and well structured. However, there are some issues that the authors should take care of:
1. At the end of related work, the authors should remind the reader how their work differentiates compared to the previous approaches.
2. Please discuss why is the proposed method suitable for Constrained Menu Planning Problem? Why is this exemplary application used? Does the method contain domain-specific steps that are addressed here? Can the method be applied to other domains?
3. The authors should check the taxonomies and communicate to the potential reader the characteristics of Constrained Menu Planning Problem and especially if and how their system can mitigate them. Maybe a subsection should fit that purpose.
4. No technical details are given about the testbed environment, such as the physical machine used for the experiments.
Author Response
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Author Response File: Author Response.pdf
Round 2
Reviewer 3 Report
Authors explain my comments nicely and made necessary changes to the manuscript. Thanks to the authors for the nice work.
