A Hybrid Metaheuristic Algorithm for Large-Scale Nonlinear Optimization Problems: Combining Adaptive Lévy Flight and Opposition-Based Learning

Although decades of research have been conducted on solving large-scale nonlinear optimization problems with hundreds or thousands of variables, nonconvex objective functions, and many interacting constraints, the problem remains extremely challenging to solve in practice. Specifically, when the objective is nonsmooth or its gradients are unavailable, the gradient-based methods are inefficient or inapplicable, and on the other hand, the standard population-based metaheuristics are often slow to converge in high dimensions and may get stuck or wander in the flat areas of the search space. There is thus a practical performance gap for problems with a dimensionality between about 100 and 1,000 variables, which is exactly the range encountered in many areas of applications, such as structural design, hyperparameter tuning in machine learning, and systems biology models. To fill this gap, this article proposes a novel algorithm called HMALO (Hybrid Metaheuristic with Adaptive Lévy-flight and Opposition-based Learning), which combines four complementary