Adaptable optimisation that preserves efficiency under time-varying system dynamics necessitates modern task management in innovative city development and in distributed edge-cloud computing systems. Conservative optimisation techniques such as genetic algorithms, particle swarm optimisation, and classical monarch butterfly optimisation (MBO) suffer from premature convergence, poor multi-objective performance, and limited adaptability to changing environments. Further, virtualised infrastructures contextualise operational constraints that impair their ability to homogenously support heterogeneity in task types and quality-of-service demands. We present a hybrid scheduling framework called multi-strategy fuzzy-enhanced monarch butterfly optimisation (MF-MBO) that combines fuzzy dominance for strong multi-objective ranking, self-adaptive quantum-inspired tunnelling (classical acceptance strategy) to escape stagnation, and bounded greedy migration for stable local refinement and load balancing. To accelerate convergence while maintaining task fairness across distributed virtual machines, MF-MBO dynamically balances exploration and exploitation. In the experimental evaluation under different workload conditions, MF-MBO clearly outperforms baseline algorithms, providing improvements of 17.4% in task execution time, 22.8% in load-balancing efficiency, and 15.6% in energy consumption. The results are reported with respect to the standard MBO, while we also compare them with both GA and PSO under the same evaluation budget and workload conditions. The results show increased operational efficiency and scalability, along with greater robustness across varying environments. The idea behind the introduced MF-MBO framework enables practical adaptation for smart city infrastructure services, distributed edge computing, and IoT-based applications, through a reproducible, explainable optimisation pipeline. The last part of this study reports empirical results and sets a few benchmarks to support future extensions, such as broader-angle benchmarking and hardware-aware validation.
Reddy et al. (Sat,) studied this question.