Page 17 - Mathematical Models and Algorithms for Power System Optimization

Introduction 7

The stochastic optimization algorithms could avoid optimization around the local points,
by which further improvement of the objective function of the optimization model could
randomly restart from many directions. The genetic algorithm and simulated annealing
method are the typical stochastic optimization algorithms that attempt to consider
optimization from a biological or physical point of view rather than from an engineering
point of view. The process of biological evolution is a process of survival of the fittest,
whereas the process of metal sintering annealing is a process of changing the lattice
structure and raising the metal strength. Both algorithms can avoid optimizing around the
local points but with multipoint searching in the solution space, so as to obtain the global
optimal point. Furthermore, these algorithms do not require such conditions: the objective
function and constraint function should be continuous.

(4) Considerations for the future expectations
The complex relationship between the variables and models for the actual problems is
expected to be expressed by some new technologies in the near future. With the invention
and development of artificial intelligent and computer vision technology, it is possible to
understand the relationship that is not intuitive and convert the original nonvisual problem
into a visual image, which provides us with vivid and intuitive perceptual materials, allows
us to understand the complex process, and inspires researchers to form scientific
conjectures and viewpoints, to make theoretical creations. Therefore, the use of simple
computer simulations to obtain the complex relationship between theoretical models and
actual problems is expected.

1.5 Ideas about the Applications of Artificial Intelligence Technology

Although most optimization algorithms involve complicated mathematics and logic, nearly
every optimization method involves a smart imaginative step to find the best solution by
comprehensively analyzing the solvability, such as search scope, initial point, the type of the
variables, and the range of the equations.
Generally speaking, optimization mathematics is complicated, but the application of the
concept is very simple. There are many modeling methods to obtain optimal solutions in nature,
such as human evolution, insect behavior, and steel cooling processes, which can be
mathematically used to form new algorithms.

AI (Artificial Intelligence) and big data technologies have become very important tools in
recent years. In terms of applications in the field of optimization, they are actually composed of
several different non-numerical methods that can be used to build a set of rules and not just rely
on smart imagination and experience. This book has many examples of initiatives in the field of
AI based on human experience and manual approaches or natural methods that help to solve the
problems in a reasonable way by computers (heuristics method).