2019 IEEE Congress on Evolutionary Computation (CEC 2019)
Special Session and Competition on “Evolutionary Algorithms for Nonlinear Equation Systems”
School of Information Science and Engineering, Central South University, Changsha 410083, China
School of Computer Science, China University of Geosciences, Wuhan 430074, China.
Department of Computer Science, Brunel University London, Uxbridge, UB8 3PH, U.K.
In 1998, Fields medalist Steven Smale listed 18 challenging problems for the twenty-first century including "Does P=NP?" in "Mathematical problems for the next century. Mathematical Intelligencer, vol. 20, no. 2, pp. 7-15, 1998". Among them, the following three challenging problems are related to nonlinear equation systems (NESs):
Problem 4: Integer zeros of a polynomial
Problem 8: Introduction of dynamics into economic theory
Problem 17: Solving polynomial equations
Therefore, finding the roots of NESs is not only of great significance for solving practical problems, but also one of the core problems of mathematics.
NESs frequently arise in many physical, electronic, and mechanical processes. Very often, a NES may contain multiple roots. Since all these roots are important for a given NES in the real-world applications, it is desirable to simultaneously locate them in a single run, such that the decision maker can select one final root which matches at most his/her preference.
For solving NESs, several classical methods, such as Newton-type methods, have been proposed. However, these methods have some disadvantages in the sense that they are heavily dependent on the starting point of the iterative process, can easily get trapped in a local optimal solution, and require derivative information. Moreover, these methods tend to locate just one root rather than multiple roots when solving NESs. During the past decade, evolutionary algorithms (EAs) have been applied to solve NESs due to the fact that EAs are insensitive to the shapes of the objective function and easy to implement.
Solving NESs by EAs is a very important area in the community of evolutionary computation, which is challenging and of practical interest. However, systematic work in this area is still very limited. The aim of special session is to facilitate the development of EAs for locating multiple roots of NESs.
The topics of this special session include, but are not limited to:
Theoretical and experimental analyses of the roots in NESs
Novel search engines in evolutionary computation for NESs
Novel techniques for transforming a NES into a kind of optimization problems
Locating multiple roots of NESs by multiobjective optimization-based methods
Locating multiple roots of NESs by repulsion-based techniques
Please download the CFP and source codes: