This paper proposes a Sine Cosine hybrid optimization algorithm with Modified Whale Optimization Algorithm (SCMWOA). The goal is to leverage the strengths of WOA and SCA to solve problems with continuous and binary decision variables. The SCMWOA algorithm is first tested on nineteen datasets from the UCI Machine Learning Repository with different numbers of attributes, instances, and classes for feature selection. It is then employed to solve several benchmark functions and classical engineering case studies. The SCMWOA algorithm is applied for solving constrained optimization problems. The two tested examples are the welded beam design and the tension/compression spring design. The results emphasize that the SCMWOA algorithm outperforms several comparative optimization algorithms and provides better accuracy compared to other algorithms. The statistical analysis tests, including one-way analysis of variance (ANOVA) and Wilcoxon’s rank-sum, confirm that the SCMWOA algorithm performs better.