Optimizing Menu Planning for Children with Autism  Using Improved Multi-Goal Programming Model

Nur Rasyida Mohd Rashid; Suliadi Firdaus Sufahani; Nur Hana Hamzaid

doi:10.29207/resti.v9i4.6649

Authors

Nur Rasyida Mohd Rashid Universiti Tun Hussein Onn,
Suliadi Firdaus Sufahani Universiti Tun Hussein Onn
Nur Hana Hamzaid Universiti Kebangsaan Malaysia

DOI:

https://doi.org/10.29207/resti.v9i4.6649

Keywords:

autism, goal programming, menu planning, optimization

Abstract

Menu planning for every individual is essential to obtain a balanced and healthy food intake for growth and development. Children with Autism Spectrum Disorders (ASD) face more feeding difficulties than their peers due to neurodevelopmental disorders such as social skills problems and repetitive behaviors. They also tended to refuse or be selective for certain food intakes. Proper menu planning for children with ASD is important to maintain their overall well-being and mitigate autism-related dietary issues. The manual menu planning for children with ASD does not consider proper nutritional intake, food variation, or total cost minimization. Currently, the application of mathematical modelling for menu planning in children with ASD is limited. Thus, this study aims to explore the extent to which the optimization approach can solve the menu planning problem with more than one objective. Finally, this research constructed daily menu planning for children with ASD, which indicates the feasibility of utilizing the Improved GP (IGP) model compared to the Goal Programming model (GP) in terms of the value for the deviational variables for the unachieved goals. The unachieved deviational variables by IGP model for Day-2 had decreased by 17.69% and by 34.43 % on Day-3. The total cost of the IGP model is also less than RM 0.50 of the GP model.

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References

J. M. Ramos-Pérez, G. Miranda, E. Segredo, C. León, and C. Rodríguez-León, “Application of multi-objective evolutionary algorithms for planning healthy and balanced school lunches,” Mathematics, vol. 9, no. 1, pp. 1–24, Jan. 2021, doi: 10.3390/math9010080.

L. Z. Sheng and S. Sufahani, “Optimal Diet Planning for Eczema Patient Using Integer Programming,” Journal of Physics: Conference Series, vol. 995, no. 1. 2018, doi: 10.1088/1742-6596/995/1/012049.

S. F. Sufahani, and Z. Ismail, “A diet planning model for malaysian boarding school using zero-one integer programming,” Prosiding Seminar Kebangsaan Aplikasi Sains Dan Matematik”, Oct. 2013.

B. K. Seljak, “Computer based dietary menu planning,” Journal of Food Composition and Analysis, vol. 22, pp. 414-420, 2009.

K. E. Drummond and L. M. Brefere, Nutrition for Foodservice and Culinary Professionals, 8th ed. John Wiley and Sons Inc, 2014.

M. Esposito, P. Mirizzi, R. Fadda, C. Pirollo, O. Ricciardi, M Mazza, and M. Valenti, “Food Selectivity in Children with Autism: Guidelines for Assessment and Clinical Interventions,” International Journal of Environmental Research and Public Health vol. 20, no. 6, 2023, doi: 10.3390/ijerph20065092.

S. A. Cermak, C. Curtin, and L. G. Bandini, “Food Selectivity and Sensory Sensitivity in Children with Autism Spectrum Disorders,” Journal of the American Dietetic Association, vol. 110, no. 2, pp. 238–246, Feb. 2010, doi: 10.1016/j.jada.2009.10.032.

F. Fulceri, M. Morelli, E. Santocchi, H. Cena, T. Del Bianco, A. Narzisi, S. Calderoni, and F. Muratori, “Gastrointestinal symptoms and behavioral problems in preschoolers with Autism Spectrum Disorder,” Digestive and Liver Disease, vol. 48, no. 3, pp. 248–254, Mar. 2016, doi: 10.1016/j.dld.2015.11.026.

J. Y. Tee, and S. F Sufahani, “Vegetarian Menu Planning Through Optimization Method: An Overview,” ACCESS Online Journal IJACSSEJournal-International Journal of Advanced Computer Systems and Software Engineering, vol. 2, pp. 30–36, 2021.

S. Sufahani, and Z. Ismail, “A new menu planning model for Malaysian secondary schools using optimization approach,” Applied Mathematical Sciences, vol. 8, pp. 149–152, 2014, doi:10.12988/ams.2014.49725.

F. Martos-Barrachina, L. Delgado-Antequera, M. Hernández, and R. Caballero, “An extensive search algorithm to find feasible healthy menus for humans,” Operational Research, vol. 22, no. 5, 2022, doi: 10.1007/s12351-022-00702-4.

D. Basyuk, I. Levytska, L. Ivchenko, I. Semenyshyna, and S. Koliadenko, “Optimization of the menu for institutions of restaurant industry based on mathematical modelling methods,” Intellectual Economics, vol. 14, no. 1, pp. 130–143, 2020, doi: 10.13165/IE-20-14-1-08.

L. Donkor, E. Essien, and N. S. Afrifah, “A Systematic Review of Linear Programming Techniques as Applied to Diet Optimisation and Opportunities for Improvement,” Journal of Optimization, vol. 2023, 2023, doi: 10.1155/2023/1271115.

Z. Taha and K. A. Abdalhai, “A review of the efficacy of the dietary intervention in autism spectrum disorder,” Open Access Macedonian Journal of Medical Sciences, vol. 9, pp. 88–94, 2021, doi: 10.3889/oamjms.2021.5743.

G. Petitpierre, A. C. Luisier, and M. Bensafi, “Eating behavior in autism: senses as a window towards food acceptance,” Current Opinion in Food Science, vol. 41, pp. 210–216, 2021, doi: 10.1016/j.cofs.2021.04.015.

B. I. Osman and S. F. Sufahani, “Nutritious Menu Planning for Sinusitis Patient in Malaysian Through Optimization Approach,” Lecture Notes in Networks and Systems, vol. 348, pp. 31–44, 2022, doi: 10.1007/978-981-16-7597-3_3.

L.M Lancaster, “The history of the application of mathematical programming to menu planning,” European Journal of Operational Research, vol.57, pp.339-347, 1992.

C. Türkmenoğlu, A. Ş. Etaner Uyar, and B. Kiraz, “Recommending healthy meal plans by optimising nature-inspired many-objective diet problem,” Health Informatics Journal, vol. 27, no. 1, 2021, doi: 10.1177/1460458220976719.

R. Alaini, R. Rajikan, and S. M. Elias, “Diet optimization using linear programming to develop low-cost cancer prevention food plan for selected adults in Kuala Lumpur, Malaysia,” BMC Public Health, vol. 19, 2019, doi: 10.1186/s12889-019-6872-4.

H. Okubo, S. Sasaki, K. Murakami, T. Yokoyama, N. Hirota, A. Notsu, M. Fukui, and C. Date, “Designing optimal food intake patterns to achieve nutritional goals for Japanese adults through the use of linear programming optimization models,” Nutrition Journal, vol. 14, no. 1, 2015, doi: 10.1186/s12937-015-0047-7.

L. K. Gautam, M. L. K. Gautam, and V. S. Gulhane, “Optimization Methods and its Application in Nutritional Diet,” [Online]. Available: https://www.researchgate.net/publication/357048291, 2020.

V. D. G. Balcita, A. T. A. Bejar, T. P. P. Goy, R. K. C. Billones, and E. P. Dadios, “Optimizing the Allocation of Renewable Energy Generation and Energy Consumption of Power Plants in the Philippines using Linear Programming,” in 2021 IEEE 13th Int. Conf. on Humanoid, Nanotechnology, Information Technology, Communication and Control, Environment, and Management (HNICEM), 2021, doi: 10.1109/HNICEM54116.2021.9732024.

R. Kunwar and H. P. Sapkota, “Introduction to Linear Programming Problems with Some Real-Life Applications,” European Journal of Mathematics and Statistics, vol. 3, no. 2, pp. 21–27, 2022, doi: 10.24018/ejmath.2022.3.2.108.

S. Sengupta, T. Christensen, G. Ravn-Haren, and R. Andersen, “Vitamin D Food Fortification Strategies on Population-Based Dietary Intake Data Using Mixed-Integer Programming,” Foods, vol. 12, no. 4, 2023, doi: 10.3390/foods12040698.

M. Padovan, F. R. de Senna, J. K. Kimura, S. T. Nascimento, A. C. Moretti, and C. D. Capitani, “Optimized menu formulation to enhance nutritional goals: design of a mixed integer programming model for the workers’ food program in Brazil,” BMC Nutrition, vol. 9, no. 1, 2023, doi: 10.1186/s40795-023-00705-0.

A. Briend, N. Darmon, E. Ferguson, and J. G. Erhardt, “Linear Programming: A Mathematical Tool for Analyzing and Optimizing Children’s Diets During the Complementary Feeding Period,” 2003.

Y. M. R. Aboelmagd, “Linear programming applications in construction sites,” Alexandria Engineering Journal, vol. 57, no. 4, pp. 4177–4187, 2018, doi: 10.1016/j.aej.2018.11.006.

M. Ali, S. Sufahani, and Z. Ismail, “A new diet scheduling model for Malaysian school children using zero-one optimization approach,” Global Journal of Pure and Applied Mathematics, vol. 12, no. 1, 2016.

M. A. Jamaludin and S. F. Sufahani, “Nutritious Menu and Nutrient Planning for Avoiding Stroke Disease by Using Optimization Technique,” Lecture Notes in Networks and Systems, vol. 348, pp. 45–56, 2022, doi: 10.1007/978-981-16-7597-3_4.

A. J. L. Pe, J. K. Coaching, S. G. D. Yeung, W. Akeboshi, and R. K. C. Billones, “Cost Optimization for Weekly Meal Planning of College Students Based on Calorie Constraints using Linear Programming (LP) Method,” in 2022 IEEE 14th Int. Conf. on Humanoid, Nanotechnology, Information Technology, Communication and Control, Environment, and Management (HNICEM), 2022, doi: 10.1109/HNICEM57413.2022.10109597.

M. D. S. Spak and J. C. Colmenero, “University restaurants menu planning using mathematical modelling,” Journal of Food and Nutrition Research, vol. 60, no. 1, 2021.

A. Coleen, S. De Leon, C. T. Ninobla, N. Joyce, S. Sibal, K. Mile, J. B. Yu, E. Gabriel, and C. Bucu, “Low-cost Dietary Plan for COVID-19 Immunity Response Using Mixed-Integer Linear Programming,” 2022.

R. Abejón, L. Batlle-Bayer, J. Laso, A. Bala, I. Vazquez-Rowe, G. Larrea-Gallegos, M. Margallo, J. Cristobal, R. Puig, P. Fullana-I-palmer, and R. Aldaco, “Multi-objective optimization of nutritional, environmental and economic aspects of diets applied to the Spanish context,” Foods, vol. 9, no. 11, 2020, doi: 10.3390/foods9111677.

F. De Oliveira, N. M. P. Volpi, and C. R. Sanquetta, “Goal programming in a planning problem,” Applied Mathematics and Computation, vol. 140, no. 1, pp. 165–178, 2003, doi: 10.1016/S0096-3003(02)00220-5.

K. Wise and D. E. Perushek, “Goal Programming as a Solution Technique”, 2000. [Online]. Available: https://trace.tennessee.edu/utk_libpub/5.

N. Hassan, D. F. Azmi, T. S. Guan, and L. W. Hoe, “A goal programming approach for library acquisition allocation,” Applied Mathematical Sciences, vol. 7, no. 137–140, pp. 6977–6981, 2013, doi: 10.12988/ams.2013.310574.

I. Hasbiyati, R. Desri, and M. D. H. Gamal, “Pre-Emptive Goal Programming Method for Optimizing Production Planning,” BAREKENG: Jurnal Ilmu Matematika Dan Terapan, vol. 17, no. 1, pp. 0065–0074, 2023, doi: 10.30598/barekengvol17iss1pp0065-0074.

N. Rasyida, M. Rashid, B. A. Halim, N. Hassan, I. Shah, M. Zawawi, and H. Aris, “Supplier Selection using Zero-One Goal Programming Method,” Journal of Advanced Research in Dynamical and Control Systems, vol. 11, 2019, [Online]. Available: https://www.researchgate.net/publication/338987352.

W. S. Lam, P. F. Lee, and W. H. Lam, “Optimization on the Financial Management of Construction Companies with Goal Programming Model,” IOCMA 2023, p. 29, 2023, doi: 10.3390/iocma2023-14420.

N. Rasyida, M. Rashid, N. M. Lip, F. Farhayu, M. Salim, N. F. Kamazan, S. Nor, and A. M. Latib, “Feeding Blend Optimization for Livestock by Using Goal Programming Approach,” Malaysian Journal of Computing, vol. 5, no. 2, pp. 495–503, 2020.

I. Jridi, B. Jerbi, and H. Kamoun, “Menu planning with a dynamic goal programming approach,” Multiple Criteria Decision Making, vol. 13, pp. 74–87, 2018, doi: 10.22367/mcdm.2018.13.04.

D. Lestari, A. M. Abadi, A. Dhorurri, A. I. Tarigan, and E. Herlinawati, “Optimization of Nutritional-Menu Planning for Toddlers by Goal Programming Model,” 2021.

Z. Alwadood, N. Fadhlin, H. Ayob, and N. M. Noor, “A diet plan for Malaysian adolescent athletes using integer goal programming model,” Transactions on Science and Technology, vol. 10, no. 1, 2023. [Online]. Available: http://tost.unise.org/

C. Sen, “Improved Multi Goal Programming Model,” Journal of Operational Research, vol. 10, pp. 45–48, 2021.

Ministry of Health Malaysia, Recommended nutrient intakes for Malaysia 2017. Putrajaya, Malaysia: Ministry of Health Malaysia, 2017.