Discovering optimal material designs in the design space can be significantly accelerated by leveraging machine learning (ML) models for screening candidates. However, the quality of these designs depends on the prediction accuracy of the ML models and the efficiency of the optimization algorithms used. This study comprehensively compares different ML modeling strategies, optimization algorithms and evaluation strategies. Thereby, automated ML, tree-based ML models and neural networks were compared. Various optimization algorithms were analyzed, including random search, evolutionary and swarm-based methods. In addition, different strategies for evaluating the predictive performance of the ML models were investigated, which is particularly important as these models are expected to predict design parameters that deviate significantly from the known designs in the training data throughout the optimization. Our results highlight the capability of the proposed workflow to discover material designs that significantly outperform those within the training database and approach theoretical optima. Overall, this research contributes to advancing the field of material design optimization by providing a versatile and practical workflow that introduces automated ML into material design optimization and new model error assessment strategies tailored explicitly to optimization tasks.