The automatic identification of emotions from speech holds significance in facilitating interactions between humans and machines. To improve the recognition accuracy of speech emotion, we extract mel-frequency cepstral coefficients (MFCCs) and pitch features from raw signals, and an improved differential evolution (DE) algorithm is utilized for feature selection based on K-nearest neighbor (KNN) and random forest (RF) classifiers. The proposed multivariate DE (MDE) adopts three mutation strategies to solve the slow convergence of the classical DE and maintain population diversity, and employs a jumping method to avoid falling into local traps. The simulations are conducted on four public English speech emotion datasets: eNTERFACE05, Ryerson Audio-Visual Database of Emotional Speech and Song (RAVDESS), Surrey Audio-Visual Expressed Emotion (SAEE), and Toronto Emotional Speech Set (TESS), and they cover a diverse range of emotions. The MDE algorithm is compared with PSO-assisted biogeography-based optimization (BBO_PSO), DE, and the sine cosine algorithm (SCA) on emotion recognition error, number of selected features, and running time. From the results obtained, MDE obtains the errors of 0.5270, 0.5044, 0.4490, and 0.0420 in eNTERFACE05, RAVDESS, SAVEE, and TESS based on the KNN classifier, and the errors of 0.4721, 0.4264, 0.3283 and 0.0114 based on the RF classifier. The proposed algorithm demonstrates excellent performance in emotion recognition accuracy, and it finds meaningful acoustic features from MFCCs and pitch.