The adoption of machine learning techniques within the domain of drug design provides an opportunity of systematic and efficient exploration of the vast chemical search space. In recent years, advancements in this domain have been achieved through the application of deep reinforcement learning (DRL) frameworks. However, the scalability and performance of existing methodologies are constrained by prolonged training periods and inefficient sample data utilization. Furthermore, generalization capabilities of these models have not been fully investigated. To overcome these limitations, we take a multi-objective optimization perspective and introduce SMORE-DRL, a fragment and transformer-based multi-objective DRL architecture for the optimization of molecules across multiple pharmacological properties, including binding affinity to a cancer protein target. Our approach involves pretraining a transformer-encoder model on molecules encoded by a novel hybrid fragment-SMILES representation method. Fine-tuning is performed through a novel gradient-alignment-based DRL, where lead molecules are optimized by selecting and replacing their fragments with alternatives from a fragment dictionary, ultimately resulting in more desirable drug candidates. Our findings indicate that SMORE-DRL is superior to current DRL models for lead optimization in terms of quality, efficiency, scalability, and robustness. Furthermore SMORE-DRL demonstrates the capability of generalizing its optimization process to lead molecules that are not present during the pretraining or fine-tuning phases.