<p>Modern data centres are increasingly adopting containers to enhance power and performance efficiency. These data centres comprise heterogeneous machines, each offering varying capacities of CPU, memory, I/O, and network bandwidth. Resources are leased to applications, which may run for extended periods, provided their demands are met. Some applications perform better on specific machines, a concept referred to as affinity, while others are incompatible with specific machines known as anti-affinity. These two factors are based on performance, legal reasons, security and reliability history. In this work, we consider the problem of placing multiple applications on machines in a manner that maximizes affinity satisfaction and minimizes energy costs. The electricity cost, primarily driven by CPU usage, grows cubically with the total CPU consumption, presenting a complex optimization challenge. To address this, we formulate the application placement problem to minimize the total system cost by minimizing electricity consumption and maximizing the number of affinity-compliant placements. We propose a four-phase solution framework: (a) data preprocessing to prepare necessary input parameters, (b) generation of initial placements using power-aware and affinity-aware heuristics, (c) an integrated optimization phase that combines these placements to balance power and affinity, and (d) further improving the solution using a genetic algorithm. Experimental results on real-world datasets demonstrate that our approach improves the affinity satisfaction ratio by up to 4%, reduces total system cost by up to 26%, and enhances the affinity payoff ratio by up to 37% compared to state-of-the-art techniques.</p>