GDESA: Gradient Differential Evolution-Simulated Annealing Hybrid

This paper presents an innovative approach to enhance the hybrid Differential Evolution (DE) algorithm by focusing on improved convergence speed, exploration capabilities, and solution precision. This is achieved through the integration of elitism in evolutionary algorithms, gradient methods, and the Metropolis acceptance criterion in Simulated Annealing (SA). We introduce the Gradient Differential Evolution-Simulated Annealing Hybrid (GDESA) framework, refined through parameter sensitivity analysis, which led to the development of two variants: Multi-Phase GDESA (M-GDESA) and Adaptive Elitist GDESA (A-GDESA). M-GDESA improves convergence by adding user-controlled phases but struggles with parameter fine-tuning and semi-static selection. In contrast, A-GDESA allows each individual to dynamically choose between elitist and SA offspring selection schemes at each iteration, enhancing adaptability to diverse problems. Our hybrid frameworks are highly flexible, accommodating any DE variant as the main program. Even with standard DE, our approach is highly competitive on the CEC2017 benchmark for 30-dimensional problems, statistically outperforming existing DE-SA hybrids like iSADE and HDESA, as well as state-of-the-art heuristics such as DE, PSO, ABC, and WOA. Not only does A-GDESA outperform each of the six baselines in at least 24 out of the 29 test functions, but it also achieves the fastest convergence. When using the advanced L-SHADE variant as the main program, our framework outperforms even well-known optimizers and top performers from CEC competitions like L-SHADE and LSHADE-cnEpSin on 100-dimensional problems. The obtained results highlight the effectiveness of the GDESA framework in enhancing DE-SA hybrid optimization and demonstrate the exceptional potential of the self-adaptive scheme with gradient methods.