Recent Advances in Real-Parameter Evolutionary Algorithms
Prenters: P. N. Suganthan & Qin Kai School of Electrical and Electronic Engineering Nanyang Technological University, Singapore Some Software Resources Available from: u.edu.sg/home/epnsugan SEAL’06 October 2006
RP-EAs & Related Issues Covered
Benchmark Test Functions Methods Modeled After conventional GAs CMA-ES / Covariance Matrix Adapted Evolution Strategy PSO / Particle Swarm Optimization DE / Differential Evolution EDA / Estimation of Distribution Algorithms CEC’05, CEC’06 benchmarking Coverage is biad in favor of our rearch and results of the CEC-05/06 competitions while overlap with other SEAL tutorial prentations is reduced.
-2-
Benchmark Test Functions
Resources available from u.edu.sg/home/epnsugan (limited to our own work)
From Prof Xin Yao’s group www.cs.bham.ac.uk/rearch/projects/ecb/ Includes diver problems.
-3-
Why do we require benchmark problems?
Why we need test functions?
To evaluate a novel optimization algorithm’s property on different types of landscapes Compare different optimization algorithms
Types of benchmarks
Bound constrained problems
Constrained problems Single / Multi-objective problems Static / Dynamic optimization problems Multimodal problems (niching, crowding, etc.)
电力文章-4-
Shortcomings in Bound constrained Benchmarks
手抄报文字大全
Some properties of benchmark functions may make them unrealistic or may be exploited by some algorithms: Global optimum having the same parameter values for different variables\dimensions Global optimum at the origin Global optimum lying in the center of the arch range Global optimum on the bound Local optima lying along the coordinate axes no linkage among the variables / dimensions or the same linkages over the whole arch range Repetitive landscape structure over the entire space
Do real-world problems posss the properties? Liang et. al 2006c (Natural Computation) has more details.
-5-
How to Solve?
Shift the global optimum to a random position to make the global optimum to have different parameter values for different dimensions Rotate the functions as below:
F ( x) = f ( R * x)
郴读什么
where R is an orthogonal rotation matrix U different kinds of benchmark functions, different rotation matrices to compo a single test problem. Mix different properties of different basic test functions together to destroy repetitive structures and to construct novel Composition Functions
-6-
Novel Composition Test Functions
Compo the standard benchmark functions to construct a more challenging function with a randomly located global optimum and veral randomly located deep local optima with different linkage properties over the arch space. Gaussian functions are ud to combine the benchmark functions and to blur individual functions’ structures mainly around the transition regions. More details in Liang, et al 2005.
-7-斯皮尔伯格
Novel Composition Test Functions
is.
-8-
皮的组词Novel Composition Test Functions
-9-
Novel Composition Test Functions
-10-
A couple of Examples
Many composition functions are available from our homepage
red音标Composition Function 1 (F1): Made of Sphere Functions
Composition Function 2 (F2): Made of Griewank’s Functions
Similar analysis is needed for other benchmarks too
-11-
咖啡的故事Methods Modeled After Conventional GAs
Some resources available from www.iitk.ac.in/kangal/
-12-
>防暴演练
