Hardware-aware Neural Architecture Search approaches (HW-NAS) automate the design of deep learning architectures, tailored specifically to a given target hardware platform. Yet, these techniques demand substantial computational resources, primarily due to the expensive process of assessing the performance of identified architectures. To alleviate this problem, a recent direction in the literature has employed representation similarity metric for efficiently evaluating architecture performance. Nonetheless, since it is inherently a single objective method, it requires multiple runs to identify the optimal architecture set satisfying the diverse hardware cost constraints, thereby increasing the search cost. Furthermore, simply converting the single objective into a multi-objective approach results in an under-explored architectural search space. In this study, we propose a Multi-Objective method to address the HW-NAS problem, called MO-HDNAS, to identify the trade-off set of architectures in a single run with low computational cost. This is achieved by optimizing three objectives: maximizing the representation similarity metric, minimizing hardware cost, and maximizing the hardware cost diversity. The third objective, i.e. hardware cost diversity, is used to facilitate a better exploration of the architecture search space. Experimental results demonstrate the effectiveness of our proposed method in efficiently addressing the HW-NAS problem across six edge devices for the image classification task.