<p>Differential evolution (DE) has demonstrated its significant contribution to the optimization of different real-world applications as well as standard benchmarks. This paper presents a novel variant of the DE algorithm, known as the LSHADESPA algorithm. The LSHADESPA algorithm incorporates three significant modifications to enhance its performance. Firstly, a proportional shrinking population mechanism is employed to reduce the computational burden. Secondly, a simulated annealing (SA)-based scaling factor is introduced to improve the exploration properties of the algorithm. Finally, an oscillating inertia weight-based crossover rate is utilized to strike a balance between exploitation and exploration. These modifications aim to enhance the overall efficiency and effectiveness of the DE algorithm. The proposed LSHADESPA algorithm has been empirically evaluated on a set of benchmark problems, namely the CEC 2014, CEC 2017, CEC 2021, as well as CEC 2022. The experimental outcomes show that the LSHADESPA algorithm performs superior to other MH algorithms. Additionally, the Wilcoxon rank-sum as well as the Friedman rank test proves the statistical significance of the proposed LSHADESPA in comparison to other algorithms under comparison. The outcomes indicate that the LSHADESPA algorithm has statistical significance, with Friedman statistics for the CEC 2014, CEC 2017, and CEC 2022 benchmark functions achieving the lowest f-rank value compared to the other MH algorithms which are found to be 41, 77, and 26, respectively, and obtained 1st rank. Note that this paper is an invited extended version of the paper published in ISCMI 2022 conference.</p>