Heterogeneous cluster-based multi/many-core platforms are promising solutions to deliverhigh computing performances and energy efficiency in modern embedded systems. Theseplatforms support per-cluster Dynamic Voltage/Frequency Scaling (DVFS), allowing to changethe voltage/frequency levels for each cluster independently. To better cope with the increasingcomplexity and dynamism of running applications on multi-core platforms, this article presentsa 0-1 ILP based run-time management approach that aims to improve the overall system energy.The proposed approach adopts a hierarchical management organisation where a global managementstrategy determines application-to-cluster assignments and cluster frequency configurations, whilea local management strategy determines task-to-core mapping to optimize resource usage withineach cluster. Our approach can achieve near-optimal solutions with reduced strategy complexity,and delivers good scalability with respect to different platform sizes. The experimental results showthat the proposed global management strategy results in an exploration process speed 1614 timesfaster than an exhaustive search and only 6.4% higher energy consumption than the optimal solution.Our proposed approach demonstrates how significantly the local management of resource usage canimpact the global management leading to an improvement of energy efficiency up to 60.72% in ourexperiments when multiple active applications are competing for platform resources.