Binary Programming for Primary School Diet Among Autism Children in Malaysia

Fairuz B. Baharom, Natasha A. M. Zailani, and Suliadi F. Sufahani

Abstract Parents of children diagnosed with autism or autism spectrum disorder (ASD) often deal with many kinds of food-related challenges. These can include many things, like allergies or may be the child has a hard time swallowing. The children may be picky eaters or hate certain foods and refuse to eat any of them. Autism is a complex brain disorder. While it may seem that cutting out certain foods could relieve autism child’s symptoms, it might cause more harm. In Malaysia, the use of mathematical modeling in creating a healthy menu for autism children is limited. Moreover, manually planning a menu is complicated, inefficient, and inac- curate, lacks variety, no consumer preferences, and flexibility, no local recipes incom- plete number of nutrient and food groups, does not meet the nutrient’s boundaries and is time-consuming. This study proposes a new mathematical model for solving menu planning issues using the optimization method that increases the necessary nutrient intake. Balanced nutrients are required by the autism children. Minimizing the budget will also help to overcome all the problems mentioned. Three optimiza- tion methods will be used, namely, Linear Programming, Integer Programming, and Binary Programming as a proposal to solve the diet problem for Autism children aged 7–12 years old.

Keywords Autism · Diet problem · Integer programming · Operational research

1 Introduction

According to the National Autism Society ofMalaysia (NASOM) to recent statistics, there are 300,000 people on the autism spectrum inMalaysia [26, 27].Autismpatients faced their problems in choosing the diet that meets the nutrition requirements.

F. B. Baharom · N. A. M. Zailani · S. F. Sufahani (B) Faculty of Applied Sciences and Technology, Universiti Tun Hussein Onn Malaysia, 84600 Pagoh, Johor, Malaysia e-mail: [email protected]

S. F. Sufahani Oasis Integrated Group, Universiti Tun Hussein Onn Malaysia, 86400 Parit RajaJohor, Malaysia

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 M. S. Kaiser et al. (eds.), Proceedings of the Third International Conference on Trends in Computational and Cognitive Engineering, Lecture Notes in Networks and Systems 348, https://doi.org/10.1007/978-981-16-7597-3_15

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190 F. B. Baharom et al.

There is no research about conducting an optimization approach in solving diet for autism patients. Planning adequate menus involves consideration of several types of constraints: the desired nutritional content, the amount of food to be consumed, and their food should be avoided [29].

A balanced diet is vital for every humankind to maintain good health and body condition. This diet includes a variety of foods to provide essential nutrients such as carbohydrates, proteins, vitamins, minerals, fat, and fibers to our body. Autism or Autism Spectrum Disorders (ASD) is a complex biological disorder character- ized by difficulties with speech, abnormalities of posture or gesture, problems with understanding the feelings of others, sensory and visual misperceptions, fears and anxieties, and behavioral abnormalities such as compulsive/obsessive behavior and ritualistic movements [5, 8, 10]. The National Autistic Society estimates that more than half a million people have autism in the United Kingdom with four times more boys than girls affected.

The word “autism” is originated from the Greek language “autos”, which means “self”. It describes the conditions in which a person is removed from social interac- tion. In other words, he becomes an “isolated self’. Eugen Bleuler, a Swiss psychi- atrist, was the first person to use the term. He started using it around 1911 to refer to one group of symptoms related to schizophrenia. In the 1940s, researchers in the United States began to use “autism” to describe children with emotional or social problems. Children with ASD often repeat behaviors and have narrow, obsessive interests. These types of attitudes can affect eating habits and food choices, which can lead to the following health things [2]:

• Limited food selection or strong food dislikes • Not eating enough food • Constipation • Medication interactions.

Dairy, gluten, corn, sugar, and artificial ingredients are five types of food that autism children should avoid [1]. The reason is that the different consumption of nutrition will make different ASD conditions that are wildly overactive or often due to an inflammatory. Besides that, according to the website “Food for the brain”, with the title about autism, no single cause has been confirmed, although genetic and environ- mental factors are involved. There is developing proof that nourishing treatment can truly have a major effect on children with autism. Many have extremely disturbed digestion, so restoring balance in the gut is a key focus for nutritional treatment. Also important is balancing blood sugar, checking for brain-polluting heavy metals, excluding food additives, identifying food allergies and possible nutrient deficien- cies, and ensuring an optimal intake of essential fats [9]. Autism is already well known in Malaysia, but most parents do not realize that their children are facing autism that causes them to face difficulty in daily activities and children’s growth. Recommended nutrient intake has been listed as the information on good nutri- tion for the process of growing for Malaysian society in RNI 2017 [15]. The body weights for different age/gender groups were important to standardize in developing the recommendations. There are four objectives of this proposed study:

Binary Programming for Primary School Diet … 191

• To determine the nutritional requirement for autism children at the optimum cost. • To establish mathematical modeling as the optimal solution to diet problems for

autism children. • To develop a new mathematical algorithm for the optimal diet solution problem

for autism children. • To develop a decision support systembased on the proposed algorithm in objective

4.

Through this study, linear programming, integer programming, and binary program- ming will be used to solve the diet problem for autism disorder patients. Computer software such as Matlab with LPSolve will be used for computation purposes. This study only involves the Malaysian recipes, which are included in the book Nutrient Composition ofMalaysian Foods [25]. This dietmenu is for autism disorder patients and specifically for primary school children-aged 7 until 12. All of them have different kinds of nutritional requirements regarding their age, activity, allergens, and others. Few studies have been done, which relates to solving diet problem through mathematical approach [21–24] and other research on optimization and analysis [11, 17].

2 Literature Review

Numerous approaches have been implemented in developing mathematical diet models. In this approach, there are two techniques (Linear programming and Integer programming). The diet problem involves the establishment of the mathematical model, application of optimization method to deal with the problem, and formula- tion of strategies and solutions. This is an interactive case study, which is originated from Optimization Technology Center (OTC) [3].

One of the example on diet problem through optimization approach is for the athlete. Twomain objectives are the preparedmenu that meets the nutritional require- ments of athletes and keeps those expenditures allocated for athletes staying with the predetermined budget. The mathematical models were built in this research. The model is aimed to prepare the weekly menu for enhancing the athletes’ performance during the tournament period. The establishment of strong athletes’ physical heavily relies on the well-planned diet menu. The athletes carried out intense training and practices around the corner of the competition period. These diets are especially important to boost the athletes’ potential at the best [12]. An optimization study is done by Darmon, Ferguson, and Briend in 2006, to investigate the food choice of French women to prepare a balanced meal with the cost constraint [5]. The method used is linear programming modeling to find that the food combination is optimal in nutritionwith the lowest cost. The sample for this study consists of 476Frenchwomen from different socioeconomic levels. The experiment was conducted in a district in Paris. Based on the analyses, this model included 64 food items, which collated into 21 food groups and excluded some drinks such as coffee, tea, and alcohol. The diets

192 F. B. Baharom et al.

were developed by linear programming technique, which is the Simplex procedure of the Premium Solver Platform 5.0 for Excel. The researcher proposed that the diet includes some affordable food choices (fish, fruits, and vegetables) instead of animal fats or cheese to minimize the costs and enhance the balance of nutrients in the diet [5]. Fourer, Gay, and Kernighan in 2003 generated a linear programming model to fulfill a week of predetermined nutritional requirements and cheapest packages combination of food such as chicken, macaroni, spaghetti, and so on [7]. The result obtained is a monotonous diet that included only 46.667 packages of macaroni and cheese with the lowest expenditure at $88.20. This was not his desired solution. He then modified and developed an AMPL model for this diet problem. The adjusted diet are differ from previous results but still acceptable. The diet now comprises 19.5 packages of chicken, 16.3 packages of macaroni and cheese, and 4.3 of meatloaf. However, the cost is increased from $88.20 to $89.99. Suchmodification to the linear program will generate a more acceptable solution in solving the diet problem. The constraints for this model:

• Protein (not less than 38%) • Lipid (not less than 6%) • Carbohydrate (not less than 26%) • Calcium (not less than 1%) • Phosphorous (not less than 0.6%) • Amount needed (The sum for the food item as fish feed is 100 kg).

In this case, the linear programming method to generate the feed formulation is more efficient and effective than the trial-and-error method that results in lower productivity of fishes [7]. The different types of programming approaches have been discussed and summarized in Table 1.

3 Methodology

The method used or the research framework (Fig. 1) is discussed thoroughly in this section. This research part begins by observation on the arising problem (autism primary school). The relevant data regarding the problem are collected from the dietician and nutritionist. The diet problem is concerned in the area of operational research. This study would help the autism primary school to develop a balanced diet menu that meets the nutritional requirements for daily life and minimize the cost. The operational research approach is used to find the optimal solution for solving the diet problem.

Binary Programming for Primary School Diet … 193

Table 1 Summary of optimization study

Study Technique Research problems

Sklan and Dariel [19] Mixed integer-linear programming

To determine nutrition at minimum costs for people’s diet. However, this study does not determine an optimum in choosing their diet to make the meals more palatable.

Fourer et al. [7] Linear programming To develop a linear programming model to achieve a week of fixed nutritional requirements and cheapest packages combination of food. The solution for the linear programming model could not fulfill all the constraints that lead to an optimal solution.

Darmon et al. [4] Linear programming To construct a linear programming model to achieve a week for of fixed nutritional requirements and cheapest packages combination of food. The solution for the French women from low economic level may not practical; the meal planning is not familiar and not designed according to their preference.

Sufahani and Ismail [20] Integer programming To develop a mathematical model for diet planning that meets the necessary nutrient intake for the secondary school student as well as minimizing a budget. The planning menus for a secondary school based on the cost of food items and RDA for children aged between 13 and 18 years old are not considered in this study.

Nath and Talukdar [14] Linear programming To come out fish feed compounds and in return to raise the productivity of fishes and the profit earning by the fishes by using linear programming to develop the feed formulation. The upper bounds for the nutrient contents do not consider in the research.

Patil and Kasturi [15] Integer programming Implemented the optimization research about the nutritional ingredient needed by humans aged 40–45 and minimize the total diet cost at the same time. The food items involved in the research are limited.

(continued)

194 F. B. Baharom et al.

Table 1 (continued)

Study Technique Research problems

Sheng and Sufahani [18] Integer programming To undergo various diet problems, and mathematical models were built to decide a diet plan as optimal solution, which satisfy all the requirements and restrictions. The feasible solution generated for eczema patients with the diet problem.

3.1 Data Collection

Primary data and secondary data are used in this study. The primary data are taken from the interviews with the dietician, autism center, and the Malaysian Ministries. The data obtained are nutrient contents, food group requirements, and also the lower bound or upper bound of each nutrient. Next, the secondary data are extracted from books, journals, reports, and others. In this study, the food items that taken into the model only involve the Malaysian recipes in the book Nutrient Composition of Malaysian Foods [13, 25]. The food items are in standardized portion size and with their respective nutrient contents have stated. In developing a diet planning model, some data should take into consideration, for instance, the cost for the standardized portion size of the food items, the nutrient contents of each food item, and Reference Nutrient Intake (RNI) for Malaysians at any age.

Reference Nutrient Intake (RNI) indicates that the recommended amount of nutri- ents such as minerals or vitamins is needed by different ages of individuals. RNI ensures that the sufficient nutrients are provided to the people. RNI satisfies the nutrient requirements of up to 97.5% for healthy individuals. Upper tolerable nutri- ents (ULs) are the maximum nutrient intake from the food. A normal person should meet his nutritional requirements in the range of RNI and UL to prevent deficiency and toxicity. The distribution of requirements to prevent deficiency and toxicity is shown in Fig. 2.

3.2 Data Collection

In this study, three types of programming approaches will be used; linear program- ming, integer programming, and binary programming. Linear programming is the technique taking account of some linear inequalities in solving a certain problem. Then, the optimal solutionwill be obtained,which satisfies these conditions or restric- tions. While integer programming is a mathematical optimization that turns the vari- ables to be integers, as well as linear programming, integer programming searches for the optimal solution under the constraints. Furthermore, in this study, 11 types of nutrients and 10 types of food groups will be considered.

Binary Programming for Primary School Diet … 195

Fig. 1 Research flow: a proposed theoretical model

196 F. B. Baharom et al.

Fig. 2 Conceptual framework for FAO/WHO recommended nutrient intake (2002)

There are two types of the model generated in this study, which is Small Data model, which consists of 100 variables (100 types of food) from 10 food groups and the Big Data model, which consists of 426 variables (426 types of food) from 10 food groups.

General Equation for Menu Planning Model

Minimize cost = N∑

i=1

P∑

j=1

Q∑

k=1

ci xi jk (1)

where;

xi jk decision variables of food items i for 10 food group, j and 6 meals, k

ci cost for each food item i.

P the number of meals per day.

Q the number of food groups.

The Constraint for the General Nutritional Requirements

Lower bound of nutrients ≤ N∑

i=1

10∑

j=1

6∑

k=1

wi xi jk ≤ Upper bound of nutrients (2)

where wi is the weight of nutrients for the food. The constraints in this study are expressed as follows:

Energy (kcal) : L ≤ 426∑

i=1

10∑

j=1

6∑

k=1

Ei xi jk ≤ U (3)

Protein (g) : L ≤ 426∑

i=1

10∑

j=1

6∑

k=1

Pi xi jk ≤ U (4)

Binary Programming for Primary School Diet … 197

Fats (g) : L ≤ 426∑

i=1

10∑

j=1

6∑

k=1

Fi xi jk ≤ U (5)

Carbohydrates (g) : L ≤ 426∑

i=1

10∑

j=1

6∑

k=1

Ci xi jk ≤ U (6)

Calcium (mg) : L ≤ 426∑

i=1

10∑

j=1

6∑

k=1

Cai xi jk ≤ U (7)

Iron (mg) : L ≤ 426∑

i=1

10∑

j=1

6∑

k=1

Fei xi jk ≤ U (8)

Niacin (mg) : L ≤ 426∑

i=1

10∑

j=1

6∑

k=1

Niai xi jk ≤ U (9)

Vitamin A (µg) : L ≤ 426∑

i=1

10∑

j=1

6∑

k=1

Vai xi jk ≤ U (10)

Vitamin B1(mg) : L ≤ 426∑

i=1

10∑

j=1

6∑

k=1

Vb1i xi jk ≤ U (11)

Vitamin B2(mg) : L ≤ 426∑

i=1

10∑

j=1

6∑

k=1

Vb2i xi jk ≤ U (12)

Vitamin C (mg) : L ≤ 426∑

i=1

10∑

j=1

6∑

k=1

Vci xi jk ≤ U (13)

L Lower bound for each nutrient content. U Upper bound for each nutrient content. Ei Energy in Kcal for the food item, i. Pi Amount of protein in gram for the food item, i. Fi Amount of fat in gram for the food item, i. Ci Amount of carbohydrate in gram for the food item, i. Cai Amount of calcium in milligram for the food item, i. Fei Amount of iron in milligram for the food item, i. Niai Amount of niacin in milligram for the food item, i. Vai Amount of Vitamin A in microgram for the food item, i. Vb1i Amount of Vitamin B1 in microgram for the food item, i. Vb2i Amount of Vitamin B2 in microgram for the food item, i. Vci Amount of Vitamin C in microgram for the food item, i.

198 F. B. Baharom et al.

The Constraints of Food Group Requirements

Beverages : 37∑

i=1

xi,1 = r , where plain water = 2 (14)

Cereal Flour Based : 85∑

i=38

xi,2 = r (15)

Rice Flour Based : 113∑

i=86

xi,3 = r (16)

Cereal Meal Based : 126∑

i=114

xi,4 = r (17)

Meat : 158∑

i=127

xi,5 = r (18)

Vegetables : 212∑

i=159

xi,6 = r (19)

Fruits : 261∑

i=213

xi,7 = r (20)

Wheat Flour Based : 286∑

i=262

xi,8 = r (21)

Seafood : 324∑

i=287

xi,9 = r (22)

Miscellaneous 426∑

i=325

xi,10 = r (23)

where r is the daily requirement for each food group.

Definition of Decision Variable

The decision variables involved in the menu planning model are various Malaysian styles of recipes. These combinations of foodwill be shownup inmenu lists according to six categories of dishes. It can be written as below:

Binary Programming for Primary School Diet … 199

The parameters include the nutritional content (such as Energy, Calories, and so on.) and the price for each menu. The lower and upper bound for every nutrient is based on the Malaysian RNI 2017 [16] along with the consultation of the dietician. Therefore, along with the decision-making in the menu planning model, there are assumptions to be made, for example:

The food items in eachmenu are in standardized portions. The nutrients contained in each menu are assumed to be consumed as a whole unit without change during the process of preparing, cooking, and serving the menus.

The effectiveness of the methods in solving this menu planning problem has been proven in past studies [6, 28].

3.3 Solution Approach

The model will search for an optimal solution integer programming. The coding will be programmed using Mathlab with LPSolve. Finallly, an automated system will be established whereby the user key in the data to generate a list of menus for one day as an output.

3.4 Develop the Model

Linear Programming approach, Integer Programming, and Binary Programming approach are applied in this study to construct the model that can yield the best solution. A computer program will be developed usingMathlab with LPSolve where users produce a menu list for 1-day menus that consist of Malaysian recipes for autism primary school.

3.5 Stopping Criteria

Linear Programming, Integer Programming, and Binary Programming will find the most optimal solution as the best solutions.

200 F. B. Baharom et al.

4 Expected Result

The five objectives in this proposal are expected to be achieved throughout the study:

• To prepare a menu to meet certain nutritional requirements and cost constraints at the lowest level for autism children.

• To determine the balanced nutrient required by the autism children. • To establish mathematical modeling as the optimal solution to diet problems for

autism children. • To develop a mathematical modeling and a new algorithm for autism children. • To develop a decision support system based on the proposed mathematical model

and new algorithm.

By seeking the dietician and referring to the nutritional guidelines, the balanced nutrient that required by the autism primary school will be identified. About 426 food items are selected into the daily menu planning for this study. In addition, there are some results to be expected in this research such as the menus can be prepared to meet certain nutritional requirements also can determine the balanced nutrient that is required by the autism primary school. Besides, this research alsowill help to provide a complete menu planning for 1 day including all the essential vitamins and minerals in the meal, and all the range of nutritional requirements is defined according to their food groups. Subsequently, mathematical modeling will be established, which serves as the optimal solution to the diet problem for autism primary school. Not just that, the total cost of daily food intake also can be minimized throughout this study.

5 Conclusion

Planning a balanced and nutritious diet for autism children through decision-making and optimization model study will contribute a better approach to preparing a balanced diet menu that meets nutritional requirements and is suitable for autism children of all ages or other diseases that required diet control. Furthermore, it is a good to explore the knowledge of food intolerance, food, and their respective nutri- tional value and in order to promote a healthy lifestyle and at the same time try to help autism children for a better life.

Acknowledgements Fundamental Research Grant Scheme (FRGS) Number K175 (FRGS/1/2019/STG06/UTHM/02/2) from the Ministry of Higher Education Malaysia (MOHE) and GPPS H419 Universiti Tun Hussein Onn Malaysia (UTHM).

Binary Programming for Primary School Diet … 201

References

1. Foods That Can Make Autism Worse: (2019). Retrieved from https://www.amenclinics.com/ blog/5-foods-can-make-autism-worse/

2. About Autism (2020). Retrieved from https://www.foodforthebrain.org/nutrition-solutions/aut ism/ about-autism.aspx

3. Czyzyk, J., Wisniewski, T., Wright, S.: Optimization case studies in the NEOS Guide. Soc. Ind. Appl. Math. 41(1), 148–163 (1999)

4. Darmon, N., Ferguson, E.L., Briend, A.: Impact of a cost constraint on nutritionally adequate food choices for French women: an analysis by linear programming. J. Nutr. Educ. Behav. 38(2), 82–90 (2006)

5. Dover, C.J., Couteur, A.L.: How to diagnose autism. Arch. Dis. Child. 92(6), 540–545 (2007) 6. Fletcher, L.R., Soden, P.M., Zinober, A.S.: Linear programming techniques for the construction

of palatable human diets. J. Oper. Res. Soc. 45(5), 489–496 (1994) 7. Fourer, R., Gay, D.M., Kernighan, B.W.: AML: a modelling language for mathematical

programming, 2nd edn. Thomson/Brooks/Cole & Duxbury Press, Pacific Groove, California (2003)

8. Grabrucker, A.M.: Environmental factors in Autism. Front. Psychiatry 3 (2013) 9. Gluten Free/Dairy Free Diet for Autism: My Experience. (2017). Retrieved from https://aut

ismawarenesscentre.com/my-experience-with-the-gfcf-diet/ 10. Hertz-Picciotto, I., Croen, L.A., Hansen, R., Jones, C.R., Water, J.V., Pessah, I.N.: The

CHARGE study: an epidemiologic investigation of genetic and environmental factors contributing to Autism. Environ. Health Perspect. 114(7), 1119–1125 (2006)

11. Idris, A.I.M., Fahmy-Abdullah, M., Sieng, L.W.: Technical efficiency of soft drink manufac- turing industry in Malaysia. Int. J. Supply Chain Manage. 8, 908–916 (2019)

12. Magdić, D., Kljusurić, J.G., Matijević, L., Frketić, D.: Analysis of diet optimization models for enabling conditions for hypertrophic muscle enlargement in athletes. Croat. J. Food Sci. Technol. 5(1), 18–28 (2013)

13. Malaysian Dietary Guidelines for Children and Adolescents: Technical working group on Nutritional Guidelines (for National Coordinating on Food and Nutrition) (2013)

14. Nath, T., Talukdar, A.: Linear programming technique in fish feed formulation. International Journal of Engineering Trends and Technology 17(3), 132–135 (2014)

15. Patil, A.N., Kasturi, S.: Optimal diet decision using linear programming. International Research Journal of engineering and technology (IRJET) 3(8), 2197–2199 (2016)

16. Recommended Nutrient Intak, RNI (2017). http://nutrition.moh.gov.my/wp-content/uploads/ 2017/05/FA-Buku-RNI.pdf

17. Soebagyo, D., Fahmy-Abdullah, M.O.H.D., Sieng, L.W., Panjawa, J.L.: Income inequality and convergence in Central Java under regional autonomy. Int. J