Pareto Frontier Approach to Determining the Optimal Path on Multi-Objectives


  • Annisa Pratiwi Graduate Student of Mathematics Department, Universitas Sumatera Utara, Indonesia
  • M.K.M. Nasution Mathematics Department Universitas Sumatera Utara
  • E. Herawati Mathematics Department Universitas Sumatera Utara




Ant Colony Optimization, Multiobjective, Pareto Frontier, Time Windows, Vehicle Routing Problem


Every issue we face in daily life can be resolved through mathematical modeling. The use of mathematical modeling to generate solutions frequently produces value that serves a single purpose. Sometimes a single-purpose function's solution does not offer the best solution value. In this study, the author models the multiobjective time-dependent vehicle routing problem using the Ant Colony Optimization (ACO) metaheuristic algorithm. The author then applies the pareto optimization principle to the determination of the optimal starting point for the route. An optimal Pareto frontier principle solution on a multi-objective model under control of the Ant Colony Optimization algorithm is the outcome of this study.


GS Cited Analysis


Download data is not yet available.

Author Biographies

M.K.M. Nasution, Mathematics Department Universitas Sumatera Utara



E. Herawati, Mathematics Department Universitas Sumatera Utara




Bentley, P. J., & Wakefield, J. P. (1997). Finding Acceptable Pareto-Optimal Solutions using Multiobjective Genetic Algorithms. Soft Computing in Engineering Design and Manufacturing, 1–16.

Camisa, A., Farina, F., Notarnicola, I., & Notarstefano, G. (2021). Distributed constraint-coupled optimization via primal decomposition over random time-varying graphs. Automatica, 131, 109739.

Djunaidy, A., Angresti, N. D., & Mukhlason, A. (2019). Hyper-heuristik untuk Penyelesaian Masalah Optimasi Lintas Domain dengan Seleksi Heuristik berdasarkan Variable Neighborhood Search. Khazanah Informatika: Jurnal Ilmu Komputer Dan Informatika, 5(1), 51–60.

Ferliani, M., Schmidt, S., Schulz, V., Binois, M., Picheny, V., Vodopija, A., Tušar, T., Filipič, B., Roostapour, V., Neumann, A., Neumann, F., Friedrich, T., Personal, M., Archive, R., ESTECO, Roberts, M. C., Dizier, A. S. T., Vaughan, J., Ŝcap, D., … Lu, X. (2022). Determination of the pareto frontier for multiobjective optimization problem. مجلة اسيوط للدراسات البيئة, 10(2), 103597.

Frazzoli, E. (2010). Copyright © by SIAM . Unauthorized reproduction of this article is prohibited . Society, 48(5), 3224–3245.

Fu, Y., & Diwekar, U. M. (2004). An efficient sampling approach to multiobjective optimization. Annals of Operations Research, 132(1–4), 109–134.

Kachroudi, S., & Bhouri, N. (2009). A multimodal traffic responsive strategy using particle swarm optimization. In IFAC Proceedings Volumes (IFAC-PapersOnline) (Vol. 42, Issue 15). IFAC.

Kumar, S. (2022). Modeling usage intention for sustainable transport: Direct, mediation, and moderation effect. Sustainable Production and Consumption, 32, 781–801.

L’Hostis, A. (2017). Detour and break optimising distance, a new perspective on transport and urbanism. Environment and Planning B: Urban Analytics and City Science, 44(3), 441–463.

Lin, X., Chen, H., Pei, C., Sun, F., Xiao, X., Sun, H., Zhang, Y., Ou, W., & Jiang, P. (2019). A pareto-eficient algorithm for multiple objective optimization in e-commerce recommendation. RecSys 2019 - 13th ACM Conference on Recommender Systems, 20–28.

Liu, Y., Ishibuchi, H., Nojima, Y., Masuyama, N., & Han, Y. (2019). Searching for Local Pareto Optimal Solutions: A Case Study on Polygon-Based Problems. 2019 IEEE Congress on Evolutionary Computation, CEC 2019 - Proceedings, 61876075, 896–903.

Nordström, P. (2014). Multi-objective optimization and Pareto navigation for voyage planning. Uppsala Universitet.

Shan, S., & Wang, G. G. (2005). An efficient Pareto set identification approach for multiobjective optimization on black-box functions. Journal of Mechanical Design, Transactions of the ASME, 127(5), 866–874.

Zhu, S., Sun, H., & Guo, X. (2022). Cooperative scheduling optimization for ground-handling vehicles by considering flights’ uncertainty. Computers and Industrial Engineering, 169(March), 108092.


Crossmark Updates

How to Cite

Pratiwi, A., Nasution, M., & Herawati, E. (2023). Pareto Frontier Approach to Determining the Optimal Path on Multi-Objectives . Sinkron : Jurnal Dan Penelitian Teknik Informatika, 7(3), 1379-1388.