Application of Multi-Objective Evolutionary Algorithms for Planning Healthy and Balanced School Lunches

Round 1

Reviewer 1 Report

The Authors presented a method that utilizes well known MOEAs to plan meals in schools. The objective functions take into account:

• cost of the menu
• degree of repetition of courses
• degree of repetition of food groups
• intake of of nutrients in the examinated time

Intake norms are taken from the White Book on Child Nutrition.

The authors described MPP, objective functions and conducted several experiments. The results are promising. The conclusions are correct. The detailed review is presented below.

Section 2

Menu planning is clearly described in section 2. Authors provided comprehensive review of current methods and noticed that most of them uses a single objective function in the optimization process. The multiobjective nature of MPP was clearly introduced and justified.

On the other hard, in Table 1. there are numerous optimization methods presented, but they may be a novelty for some readers. I think that the Authors should provide literature references for these methods. For example, Decision Trees are not mentioned in the article text at all, but are present in the Table 1.

I know, that the purpose of the article is not a description of numerous optimization methods, but still I think, that they should be introduced somehow.

 

Section 3

In the section 3, the Authors introduce the objective functions for the optimization methods. They are clearly introduced and discussed sufficiently.

The first drawback in this section is that a solution in section 3.1. is called an individual. Individual is actually a term specific to evolutionary algoritms which were not introduced sufficently in the previous chapters. Actual description of EA is in the section 4. The Authors should note that some readers can be unfamiliar with EAs. The target audience can be either people who worked with other methods (i.e. decision trees mentioned before) or people who want to prepare a meal plan. I think that section 3.1. can be entitled "Solution encoding" or "Individual solution encoding".

Please also note that the term "individual" in the Introduction described rather a person than a solution:

• line 84: "If a meal plan has to be designed for an individual..."
• lines 37-38: "At the same time, our formulation is intended for groups of people, rather than individuals"

The second drawback is the lack of consistency in line 158 and Equation 5. Line 158 states that: "Each integer value in the vector, i.e., i_q=1,...,3*n". Note that in Eq. 5, there is also "i" but in this case it denotes a day. Maybe subsitute "i" to "d" in Eq. 5?

 

Section 4

Section 4 is very good. Authors provided a good experiment plan, performed calculations and discussed the results. The results of all three experiments are presented clearly and discussed sufficiently.

Remarks:

• I think that hypervolume and nadir-point should be presented as Equations. (lines 279-281)

 

Section 5

Conclusions are correct. The Authors justified the hypotheses stated in the Introduction.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Reviewer comments were placed in PDF file "Review_2020_Mathematics.pdf"

Comments for author File: Comments.pdf

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

The authors prepared a very interesting article on a multi-objective formulation of the Menu Planning Problem. In this article, the authors proposed a multi-purpose problem of menu planning, which is very interesting in the field of health due to the importance of proper nutrition in today's society, especially at school canteens. In particular (which should be considered of high value), the authors wanted to minimize the degree of repeatability of the dishes and food groups that make up a given meal plan.

The article is very interesting for me for two reasons:

- I try to eat rationally myself, I am a vegetarian and an active athlete (mainly running and karate sport). Therefore, meal planning is very important. In addition, resignation from meat forces a rich (diverse) arrangement of meals to cover the demand for all micro and macro elements as well as vitamins and minerals.I admit that it is not an easy task.

- The second reason is the need to constantly modify the diet, especially for children. Because currently there is a continuous trend of reduced sports activity of children and adolescents and the consumption of more and more highly processed foods. Unhealthy foods in children's nutrition are becoming more common.

 Additionally:

"The State of the World’s Children 2019: Children, food and nutrition" finds that at least 1 in 3 children under five – or over 200 million – is either undernourished or overweight. Almost 2 in 3 children between six months and two years of age are not fed food that supports their rapidly growing bodies and brains. This puts them at risk of poor brain development, weak learning, low immunity, increased infections and, in many cases, death.

[Poor diets damaging children’s health worldwide, warns UNICEF]

The article is written at a high level.

Clear and legible introduction to the issue. The authors sufficiently referred to the previous literature on the subject. Perhaps the only missing publications are from the UNICEF organization I mentioned earlier.

The authors described the scope of the research very well, including: they presented quantitative and qualitative analyzes of the resulting meal plans, which show their suitability in terms of nutritional value. The multi-purpose nature of the proposed MMPP has been demonstrated.

Do the authors plan to make a similar analysis for adult nutrition? In particular, they take into account individual nutritional characteristics, such as: intermittent fasting, one meal a day (OMAD) or a ketogenic diet (consisting mainly of fats?

The authors presented a very interesting article that perfectly fits the scope of the of the Mathematics journal.

Author Response

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Reviewer 4 Report

Although the manuscript is very well done both formally and linguistically, its subject does not, in my opinion, correspond to the focus of the journal Mathematics, to which it was sent. The authors describe in detail the application and results of three selected optimization algorithms for generating a menu for a school canteen, but the contribution from the point of view of mathematical theory/practice is negligible. I recommend considering offering the manuscript for publication in a more relevant journal, such as Children, Foods, Nutrients, or similar.

Author Response

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Reviewer 5 Report

This paper proposes a multi-objective formulation, but the purpose is not clear. 

 

It seems the goal of this paper is to present a well-balanced diet menu using MPP. It would be a good idea to indicate the purpose of this paper in the abstract and introduction sections.

 

The authors have indicated that a mixed-method approach is adopted for this study.

 

In addition, section 4.3 indicates that the main goal is to analyse the solutions attained by the MOEAs considered in this paper from both a quantitative and qualitative point of view. However, these views are not elaborated anywhere in the paper (or what they mean by "both a quantitative and qualitative point of view").

 

The introduction section highlights the problem and the need to address this problem. The second section outlines earlier research, which is good. However, there is no clear indication on what is going to be achieved and how. The authors would be able to do this by outlining the aims/goals of this paper and how the aims will be achieved (in a sequential manner).

 

Although information relating to the algorithms has been presented in section three, it would be important to summarise the reasons for selecting the three algorithms, probably at the beginning of section four.

 

Also, include limitations in section five.

 

Overall, the authors have made valid contributions and presented an interesting topic.

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 4 Report

In the case of SI - no comments.

Just a small cosmetic note - the titles of similar articles usually begin with the naming of the method followed by a description of the application domain (eg "Multi-Objective Evolutionary Algorithms for (in) Planning Healthy and Balanced School Lunches").

Author Response

Taking into account the reviewer's suggestion, we propose to change the title of the article to "Application of Multi-Objective Evolutionary Algorithms for Planning Healthy and Balanced School Lunches".