This study presented an upgraded version of the Harris Hawk optimization algorithm (UHHO) designed to overcome the inherent limitations of the original algorithm, especially in solving nonlinear constrained optimization problems that tend to converge prematurely and fall into local optima. First, the initial population generated in a random way was replaced by a good point set strategy. Second, we replaced the linear strategy with a nonlinear strategy in the intermediate stage in order to optimize the global search process. Furthermore, the sine-cosine strategy and L-C cascade chaos strategy were introduced in the development stage to perturb the population's position. This aimed to better explore the neighborhood of Harris Hawk optimal individuals in depth, enhance the local search ability of the algorithm, and avoid the algorithm falling into local optima. Some numerical experiments for solving nonlinear inequality constrained optimization problems are presented at the end of this paper. The simulation results show that the multi-strategy upgraded Harris Hawk algorithm can effectively avoid the problem of the standard Harris Hawk optimization algorithm falling into local optima.

Symbolic functions, as an important class of nonsmooth functions, play a key role in many fields such as system control and optimization theory. In this study, the special case of nonlinear optimization problems with sign function constraints is discussed in depth. Based on the smooth approximation theory, the study first adopts an approximate substitution method to smooth the nonsmooth constraints and then transforms them into differentiable optimization problems, thus effectively avoiding the numerical computational difficulties caused by the sign function. Second, the constrained optimization problem is transformed into an unconstrained optimization problem by constructing an exact penalty function. Third, two forms of second-order dynamical systems are established to solve the problem, and a rigorous theoretical analysis of the stability of these systems is conducted. Finally, the convergence and computational efficiency of the proposed method are verified by numerical simulation experiments of the system, and the simulation results fully prove the effectiveness and practicality of the algorithm.