Static Optimization problems solved by CI

Static Optimization problems solved by CI

 

The general nonlinear programming problem (NLP) is to find  x so as to  

There is no known method of determining the global maximum (or minimum) to the general nonlinear programming problem. Only if the objective function f(x) and the constraints c(x) satisfy certain properties, the global optimum can sometimes be found. Several algorithms were developed for unconstrained problems (e.g., direct search method, gradient method) and constrained problems (these algorithms usually are classified as indirect and direct methods. An indirect method attacks the problem by extracting one or more linear problems from the original one, whereas a direct method tries to determine successive search points. This is usually done by converting the original problem into unconstrained one for which gradient methods are applied with some modifications. Despite the active research and progress in global optimization in recent years, it is probably fair to say that no efficient solution procedure is in sight for the general nonlinear problems NLP.

 There are many other problems connected with traditional optimization techniques. For example, most proposed methods are local in scope, they depend on the existence of derivative, and they are insufficient by robust in discontinuous, vast multimodal , or noisy search spaces, It is important then to investigate other (heuristic) methods, which, for many real world problems, many prove very useful. 

(Ref: Ch. 7 Handling Constraints, pp.121-122, by Z. Michalewicz, Genetic Algorithms + Data Structures= Evolution Programs, Springer) 

Recently, A Springer 2013 book, entitled “Innovative Computational Intelligence: A Rough Guide to 134 Clever Algorithms” by Bo Xing and Wen-Jing Gao, introduces a number of new computational intelligence (CI) algorithms during the past decade. The mission of this book is really important since those algorithms are going to be a new revolution in computer science. They hope it will stimulate the readers to make novel contributions or to even start a new paradigm based on nature phenomena. This book introduces 134 innovative CI algorithms (Biology-based Algorithms, Physics-based Algorithms, Chemistry-based Algorithms, and Mathematics-based Algorithms). Our algorithm contribute it in their chapter 11. However, only a simple idea is introduced in this chapter. I hope that we can share more details in the future in this blog.

In the past, some readers asked me to share the whole source codes of FOA to help them to accomplish their works. But I indeed takes a lot of time and efforts to write our FOA manual, so readers have to wait. We also really hope that our source codes will not be sold in business behavior (not for academic purpose) without our permission.   

Many applications will be sent step by step later.