Automated Essay Scoring (AES) is a task that utilizes Natural Language Processing (NLP) techniques to assign scores to essays written by students. AES has been developed since the early days of computers, to where it is currently, where the use of deep learning is very common. Recent research mostly uses the Automated Student Assessment Prize (ASAP) dataset to develop models and methods for AES task. Current approaches mostly rely on essay-score pairs to train deep learning models, and they demonstrated good performance on the ASAP dataset. However, a limitation of these models is their lack of interpretability and alignment with the rubric guidelines provided. To address this, this paper proposes a rubric-aligned AES model that is trained using the triplet loss function. Furthermore, we introduce a dual-anchor triplet loss to enhance performance and training efficiency. Our experiments demonstrate that the proposed rubric-aligned AES model outperforms few-shot GPT-4 approaches that incorporate the rubric, and achieves comparable results with the current state-of-the-art AES approaches while improving interpretability.