Test case generation techniques based on adversarial examples are commonly used to enhance the reliability and robustness of image-based and text-based machine learning applications. However, efficient techniques for speech recognition systems are still absent. This paper proposes a family of methods that generate targeted adversarial examples for speech recognition systems. All are based on the firefly algorithm (F), and are enhanced with gauss mutations and / or gradient estimation (F-GM, F-GE, F-GMGE) to fit the specific problem of targeted adversarial test case generation. We conduct an experimental evaluation on three different types of speech datasets, including Google Command, Common Voice and LibriSpeech. In addition, we recruit volunteers to evaluate the performance of the adversarial examples. The experimental results show that, compared with existing approaches, these approaches can effectively improve the success rate of the targeted adversarial example generation. The code is publicly available at https://github.com/HanboCai/FGMGE.