Optimisation of Multi-Source Minimal Spanning Trees For Solid Waste Collection

Abstract

This study develops a robust optimisation framework grounded in Multi-Source Minimum Spanning Trees (MS-MST), in which Kruskal’s Algorithm is systematically integrated with the Teaching–Learning-Based Optimisation (TLBO) technique to enhance the operational efficiency of solid waste collection systems. The proposed model is designed for semi-automatic collection and incorporates data from smart waste bins, enabling dynamic prioritisation of collection points based on real-time conditions. In doing so, it addresses well-documented limitations of conventional routing approaches, particularly their reliance on static routes and single-depot structures. The model's performance was evaluated on a simulated network that reflects realistic urban waste-collection conditions. The results indicate that the traditional collection system recorded a total traversal cost of 93 khrs. In contrast, the MS-MST framework achieved progressively lower costs across different configurations: 71 khrs for a single-source system, 65 khrs for a two-source system, and 60 khrs for a three-source system. These outcomes correspond to a maximum cost reduction of 35.48%, demonstrating the efficiency gains attainable through multi-source routing and metaheuristic optimisation. Further validation using real-world operational data reveals consistent improvements across key performance indicators, including reduced travel distance, lower fuel consumption, and shorter collection times. The findings demonstrate that the integration of MS-MST with TLBO offers a computationally efficient, scalable, and practically viable solution for modern urban waste management, particularly in environments characterised by decentralised collection infrastructure and variable waste-generation patterns.