Nature Inspired Global Optimization

The concept of Meta-heuristic algorithms are discussed. Detailed algorithms for the Particle Swarm and Black Hole methods are given and demonstrated by 1D and 2D examples for solving nonlinear systems and polynomial programming. Different global optimization techniques, such as simulated annealing, differential evolution, random search and black hole, are compared. Summary Meta-heuristic algorithms widely used to solve real-life global optimization problems have a number of attractive properties that have ensured their success among engineers and practitioners. First, they have limpid nature-inspired interpretations explaining how these algorithms simulate behaviors of populations of individuals. Other reasons that have led to a wide spread of meta-heuristics are the following; they do not require high level of mathematical preparation to understand them, their implementations are usually simple and many codes are freely available. Finally, they do not need a lot of memory as they work at each moment with only a limited population of points in the search domain. On the flip side, meta-heuristics have some drawbacks, which include usually a high number of parameters to tune, and the absence of rigorously proven global convergence conditions ensuring that sequences of trial points generated by these methods always converge to the global solution x*. In fact, populations used by these methods can degenerate prematurely, returning only a locally optimal solution instead of a global one or even non-locally optimal point if it has been obtained at one of the last evaluations of f(x) and the budget of M evaluations has not allowed it to proceed with an improvement of the obtained solution. Nature Inspired Global Optimization Meta-heuristic algorithms are based on natural phenomenon such as Particle Swarm Optimization simulating fish schools or bird groups, Firefly Algorithm simulating the flashing behavior of the fireflies, Artificial Bee or Ant Colony representing a colony of bees or ants in search of the food sources, Differential Evolution and Genetic algorithms simulating the evolution on a phenotype and genotype levels, respectively, Harmony Search method is inspired by the underlying principles of the musicians’ improvisation of the harmony, Black Hole Algorithm is motivated by the black hole phenomenon, namely if a star gets too close to the black hole, it will be swallowed by the black hole and is gone forever, Immunized Evolutionary Programming where adaptive mutation and selection operations based on adjustment of artificial immune system, Cuckoo Search based on the brood parasitism of some cuckoo species, along with Levy flights random walks, just to mention some of them, see (Haneen et al. 2019). In this section, extending on the works of (Awange et al. in Encyclopedia of mathematical geosciences. Encyclopedia of earth sciences series. Springer, Cham, (2021)), a detailed exposition of the topic is presented.