Audio recordings used as evidence have become increasingly important to litigation. Before their admissibility as evidence, an audio forensic expert is often required to help determine whether the submitted audio recordings are altered or authentic. Within this field, the copy-move forgery detection (CMFD), which focuses on finding possible forgeries that are derived from the same audio recording, has been an urgent problem in blind audio forensics. However, most of the existing methods require idealistic pre-segmentation and artificial threshold selection to calculate the similarity between segments, which may result in serious misleading and misjudgment especially on high frequency words. In this work, we present a robust method for detecting and locating an audio copy-move forgery on the basis of constant Q spectral sketches (CQSS) and the integration of a customised genetic algorithm (GA) and support vector machine (SVM). Specifically, the CQSS features are first extracted by averaging the logarithm of the squared-magnitude constant Q transform. Then, the CQSS feature set is automatically optimised by a customised GA combined with SVM to obtain the best feature subset and classification model at the same time. Finally, the integrated method, named CQSS-GA-SVM, is evaluated against the state-of-the-art approaches to blind detection of copy-move forgeries on real-world copy-move datasets with read English and Chinese corpus, respectively. The experimental results demonstrate that the proposed CQSS-GA-SVM exhibits significantly high robustness against post-processing based anti-forensics attacks and adaptability to the changes of the duplicated segment duration, the training set size, the recording length, and the forgery type, which may be beneficial to improving the work efficiency of audio forensic experts.