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Skin cancer is a significant healthcare problem with a high mortality rate worldwide. Skin lesions occur due to the abnormal growth of skin cells in humans. Failure of early prediction and proper lesion diagnosis may lead to a malignant stage. In recent times, different skin lesion images have appeared with high similarity. Hence, classification is a more challenging task with imbalances in the dataset. The proposed work is implemented as a hybrid model with a dynamic salp swarm algorithm (DSSA) with a weighted extreme learning machine (DSSA-WELM) that addresses the imbalances in the dataset and performs the classification with higher accuracy. GoogleNet is a pre-trained network model used with the hybrid model, which helps converge faster with the optimization process. The extreme learning machine (ELM) is a multiclass classifier for accurate dermoscopic image classification. The DSSA, the best feature selection algorithm enhances the classification accuracy of the WELM. Image classification is accomplished with the International Skin Imaging Collaboration 2019 benchmark dataset. The proposed solution classifies images into eight classes: melanoma, melanocytic nevus, basal cell carcinoma, actinic keratosis, dermatofibroma, vascular lesion, squamous cell carcinoma and unknown lesion. The efficiency of the proposed solution is proved by comparing it with various state-of-the-art approaches such as support vector machine (SVM), ELM, and particle swarm optimization (PSO) methods. Results are evaluated using standard metrics of sensitivity, specificity and precision. The proposed solution outperforms all these older approaches.