This study proposes a new evolutionary algorithm, namely NL-SHADE, that combines the linear population size reduction-based SHADE (L-SHADE) with the Nutcracker Optimization Algorithm (NOA) to better solve global optimization and real-world constrained optimization problems. Several optimization algorithms have been developed in the literature to address these issues. However, they still stall in local optima and exhibit slow convergence speed, which are the main limitations that motivate us to propose the NL-SHADE algorithm. In this algorithm, the SHADE algorithm is responsible for the exploration operator in the early stages of the optimization process to avoid stagnation in local optima, while NOA is responsible for improving convergence speed. Furthermore, at the end of each generation, the linear population size reduction method is used to exclude some inferior solutions that might lead to local optima and reduce convergence speed. To solve the constrained optimization problems, NL-SHADE is combined with a gradient-based repair method to propose a new variant, rNL-SHADE, which uses gradient information from the constraint set to direct infeasible solutions into feasible regions. In this study, two experiments are conducted. In the first experiment, the proposed NL-SHADE is evaluated using two unconstrained CEC benchmarks, CEC2017 and CEC2020, and compared with numerous cutting-edge algorithms using several performance metrics. In the second experiment, the performance of the proposed algorithms is also tested by solving 29 RWC optimization problems from four different domains. The experimental findings demonstrate that, for the majority of the solved RWC problems, rNL-SHADE can perform better than all compared algorithms.