# Application of a Modified ACO Algorithm for Optimizing Routes and Externality Effect of Solid Waste Management

## Authors

• Stephen Kwaku Okrah Department of Mathematics and Statistics, Ghana Communication Technology University, PMB 100, Tesano - Accra, Ghana,Mathematical Sciences Department, University of Mines and Technology, P. O. Box 237, Tarkwa, Ghana.
• Eric Neebo Wiah Mathematical Sciences Department, University of Mines and Technology, P. O. Box 237, Tarkwa, Ghana.
• Henry Otoo Department of Mathematics, Shama Senior High School, P. O. Box 30, Shama, Western Region, Ghana.
• Justice Kangah Department of Mathematics, Shama Senior High School, P. O. Box 30, Shama, Western Region, Ghana.

## Keywords:

Ant colony optimization, ant colony system algorithm, metaheuristic, bi-objective problem, externality effects, waste management

## Abstract

To improve solid waste management and maintain its sustainability, it is important to reduce both the solid waste operational cost which includes the monetary value of distances covered and the externality effects of solid waste management. Therefore, this paper presents an application of a modified Ant Colony System algorithm to a bi-objective model for solid waste management in the Shama District in the Western Region of Ghana. The objective is to optimize route lengths and externality effects of solid waste management. Data on route lengths and population of communities along the routes were collected from 20 communities in the Shama Distric. Externality effect was measured by considering the population of the communities along the routes, the cost of treating a common cold subject to the assumption of two percent of the population being affected by the externality effect. The implemented algorithm has demonstrated the bi-objective optimal solution of route length (km) and externality effect (GHS) of (11, 2100) achievable on the path , which respectively represents a path linking the following communities: Aboadze, Abuesi Assorko Essaman, Beposo, Bosomdo and Fawomanye. There is therefore the need to ensure that the communities involved are linked with good roads.

## References

M. A. Akaateba, I. Yakubu. Householders’ satisfaction towards solid waste

collection services of zoomlion ghana ltd in Wa, ghana. European scientific journal,

(32), 2013.

J. A. Addor, E. N. Wiah, F. I. Alao. Mathematical Model for the Cyclical Dynamics of Plastic Waste Management: A Two-state Closed Model. Journal of Materials Sciences Research and Reviews, 9(2): 15-36, 2022a.

M. Vaccari, T. Tudor, G. Vinti. Characteristics of leachate from landfills and damp sites in Asia, Africa and Latin America: An overeview. Waste Management 95, 416-431, 2019.

N. Ferronato, V. Torretta. Waste management in developing countries: International Journal of Environmental Research and Public Health 16(6), 1060, 2019.

M. Akhtar, M. A. Hannan, H. Basri, E. Scavino. Solid waste generation, and collection efficiencies: Issues and challenges, Jurnal Teknologi, 75(11), 41-49, 2015.

A. Sulemana, E. A. Donkor, E. K. Forkuo, S. Oduro-Kwarteng. Optimal routing of solid waste collection trucks: A review of methods. Journal of Engineering 2018, 1-12, 2018.

J. A. Addor, E. N. Wiah, F. I. Alao. An Improved Two-states Cyclical Dynamics for Plastic Waste Management. Asian Research Journal of Mathematics, 18(5): 52-68, 2022b.

L. Godfrey et al. Solid waste management in Africa: Governance failure or development opportunity? regional development in Africa. Intech Open, 2020

A. Tweneboah-Koduah. Domestic solid waste management practices in the Bekwai Municipality in the Ashanti Region of Ghana. Master Thesis, KNUST, Ghana, 2016.

Geyer, R., Jambeck, J. R., & Law, K. L. (2017). Production, use, and fate of all plastics ever made. Sci. Adv, 3(7), e1700782. https://doi.org/10.1126/sciadv.1700782

E. N. Wiah, J. A. Addor, F. I. Alao. Transitional Probabilities for Plastic Waste Management and Implication on Sustainability. Sustainable Environment, 8(1): 2118654, 2022.

A. Padi, J. A. Addor, V. F. Nunfam. An econometric model of factors influencing household’s willingness to pay for improved solid waste management service within the Sekondi-Takoradi Metropolis in the Western Region of Ghana. Journal of Economics and Sustainable Development, 6(16): 15-29, 2015.

Belfiore, P., Tsugunobu, H., and Yoshizaki, Y. Scatter search for vehicle routing

problem with time windows and split deliveries. In Vehicle Routing Problem. InTech, 2013.

J. A. Addor, S. K. Amponsah, J. Annan, C. Sebil. School Bus Routing: A Case Study of Wood Bridge School Complex, Sekondi-Takoradi, Ghana. International Journal of Business and Social Research, 3 (12): 26-36, 2013, 2013.

J. Wang, S. Kumar, S.-F. Chang. Sequential projection learning for hashing with compact codes. In International Conference on Machine Learning, Haifa, Israel, 2010.

D. Y. Kparib, S. B. Twum, D. K. Boah. A Min Max Strategy to Aid Decision Making in a Bi-Objective Discrete Optimization Problem using an Improved Ant Colony Algorithm. American Journal of Operations Research, 9(4), 141-174, 2019.

J. K. Kangah, J. K. Appati, J. F Darkwa, M. A. T. Soli. Implementation of an H-PSOGA optimization model for vehicle routing problem. International Journal of Applied Metaheuristic Computing (IJAMC) 12(3) 148-162, 2021.

J. Kangah, H. Otoo, J. Acquah. A Hybrid Optimization Model for Vehicle Routing Problem, a Case Study at Zoomlion Ghana Limited, Shama District. Asian Research Journal of Mathematics 18(11): 148-161, 2022.

G. Malewicz, M. Austern, A. Bik, J. Dehnert, I. Horn, N. Leiser, G. Czakowski. Pregel: A System for Large Scale Gragh Processing. Proceedings of the International Conference on Management of Data. ISBN: 978-1- 4503- 0032- 2, 2010.

E. C. Ukwosah, J. A. Oladunjoge, E. Siman. A study of intelligent route guidance system Djikstra’s heuristic shortest path algorithm. International Journal of Information, Technology and Innovations in Africa, ISSN: 2360 – 9772, 1 – 23, 2018.

A. Layeb, Z. Benayad. A Novel Firefly Algorithm Based Ant Colony Optimization for Solving Combinatorial Optimization Problems. IJCSA, 11(2), 19 – 37, 2014.

L. M. Gambardella, E. D. Tailllard, M. Dorigo. Ant colonies for the quadratic assignment problem. Journal of the Operational Research Society, 50(2), 167 -702, 1999.

M. Dorigo, T. Stützle, Ant Colony Optimization. MIT Press, Cambridge, 2004.

R. Ashena, J. Moghadasi. Bottom hole pressure estimation using evolved neural networks by real coded ant colony optimization and genetic algorithm. Journal of Petroleum Science and Engineering, 77 (3–4), 375-385, 2011.

D. Otoo, S. K. Amponsah, C. Sebil. Capacitated Clustering and collection of solid waste in Kwadaso estate, Kumasi. Journal of Asian Scientific Research, 4(8), 460-472, 2014.

D. Otoo. Multi objective node routing problem with time windows: an alternate approach to solid waste collection and disposal in developing countries. PhD Thesis, Department of Mathematics, KNUST, Kumasi, Ghana, 2015.

A. Hatampour, R. Razmi, M. H. Sedaghat. Improving performance of a neural network model by artificial ant colony optimization for predicting permeability of petroleum reservoir rocks. Middle East Journal of Scientific Research, 13 (9), 1217-1223, 2013.

S. Das, B. K. Bhattacharyya. Estimation of municipal solid waste generation and future trends in greater metropolitan regions of Kolkata, India. Journal of

Industrial Engineering and Management Innovation, 1(1):31–38, 2014.

C. K. M. Lee, C. L. Yeung, Z. R. Ziong, S. H. Chung. A mathematical model for municipal solid waste management – A case study in Hong Kong. Elsivier, 58, 430-441, 2016.

A. Bagirov, A. Rubinov. On Minimization of Max-Min Functions. In: L. Qi, K. Teo, X. Yang, (eds) Optimization and Control with Applications. Applied Optimization, 96. Springer, Boston, MA, 2005.

J. S. Angelo, E. Krempser, H. J. C. Barbosa. Differential evolution assisted by a surrogate model for bilevel programming problems, in ‘Evolutionary Computation (CEC), 2014 IEEE Congress on’, IEEE, 1784–1791, 2014.

B. Oghenefejiri, L. I. Nwaogazie, J. C. Agunwamba. Development of Ant Colony Optimization Software as a Solid Waste Management System. British Journal of Applied Science & Technology, 15(5): 1-19, 2016.

R. Xu, H. Chen, X. Li. Makespan minimization on single batch-processing machine via ant colony optimization. Computers & Operations Research, 3(39), 582-593, 2012.

J. Solís-Guzmán, M. Marrero, M. V. Montes-Delgado, A. Ramírez-de-Arellano, A Spanish model for quantification and management of construction waste. Waste management, 29(9), 2542-2548, 2009.

M. López-Ibáñez, T. Stützle, Automatic configuration of multiobjective ACO algorithms. In International Conference on Swarm Intelligence, 95-106. Springer, Berlin, Heidelberg, 2010, September.

C. H. Chen, C. J. Ting. Applying two-stage ant colony optimization to solve the large-scale vehicle routing problem. Journal of the Eastern Asia Society for Transportation Studies, 8(4), 761-776, 2009.

B. Yu, Y. Zhang, B. Yao, An improved ant colony optimization for vehicle routing problem. European journal of operational research, (196) 1, 171-185, 2009.

2023-06-10

## How to Cite

Okrah, S. K., Wiah, E. N. ., Otoo, H., & Justice Kangah. (2023). Application of a Modified ACO Algorithm for Optimizing Routes and Externality Effect of Solid Waste Management. American Scientific Research Journal for Engineering, Technology, and Sciences, 93(1), 140–155. Retrieved from https://asrjetsjournal.org/index.php/American_Scientific_Journal/article/view/8961

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