Many real-world problems may be formulated as optimization problems of parameters with variables in continuous domains (continuous optimization problems). Over the past few years, an increasing interest has arisen in solving this kind of problems using different Evolutionary Algorithms (EAs) models and metaheuristics (MH). They include: Real-coded Genetic Algorithms, Evolution Strategies, Evolutionary Programming, Memetic Algorithms, Particle Swarm Optimization, and Differential Evolution. Other Metaheuristic (MHs) approaches have been considered as well to deal with these problems, such as: Ant Colony Optimization Algorithms, Simulated Annealing, Iterated Local Search, Variable Neighbourhood Search, Tabu Search, Scatter Search, and GRASP. Nowadays, large scale optimization problems arise as a very interesting field of research, because they appear in many important new real-world problems (bio-computing, data mining, etc.). Unfortunately, the performance of most available optimization algorithms deteriorates rapidly as the dimensionality of the search space increases. Thus, the ability of being scalable for high-dimensional problems becomes an essential requirement for modern optimization algorithm approaches. The aim of the special issue is to provide a forum to disseminate and discuss the way different EA and MH models respond to increase the dimensionality of continuous optimization problems. In concrete, this special issue has been conceived to serve as a double perspective: Comparison with some state-of-the-art algorithms in the topic, with the objective of identifying key mechanisms that make EAs and MHs to be scalable on these problems. In order do to do this, a set of scalable function optimization problems are provided and particular requirements on the simulation procedure are specified. To propose new mechanism/studies for the scalability of EAs and MHs for high dimensional problems for parameter optimization.

 

Experimental Framework

      

• For the experiments, we have considered 19 scalable function optimization problems:
1. 6 Funcionts: F1-F6 of the CEC'2008 test suite. A detailled description may be found in: K. Tang, X. Yao, P. N. Suganthan, C. MacNish, Y. P. Chen, C. M. Chen, and Z. Yang. Benchmark Functions for the CEC'2008 Special Session and Competition on Large Scale Global Optimization. Technical Report, Nature Inspired Computation and Applications Laboratory, USTC, China, 2007. (Source code).
2. 5 Shifted Functions: Schwefel’s Problem 2.22 (F7), Schwefel’s Problem 1.2 (F8), Extended f10 (F9), Bohachevsky (F10), and Schaffer (F11). (Updated description) (Updated source code *May 20, 2010*).
3. 8 Hybrid Composition Functions (F12-F19*): They are non-separable functions built by combining two functions belonging to the set of functions F1-F11 (F15 and F19* have been shifted). (Updated description) (Updated source code *May 20, 2010*).


Document with a complete description of the 19 test functions: Updated description F1-F19*.



• The requirements on the simulation procedure are the following:
1. Each algorithm is run 25 times for each test function.
2. The performance measures that should be provided are:
• Average of error of the best individuals found in the 25 runs. For a solution x, the error measure is defined as: f(x)-f(op), where op is the optimum of the function.

• Maximum error achieved in the 25 runs.

• Minimum error achieved in the 25 runs.

• Median of the error achieved in the 25 runs.

3. The study should be made with dimensions D = 50, D = 100, D=200, D=500, and D = 1,000. The maximum number of fitness evaluations is 5,000·D. Each run stops when the maximal number of evaluations is achieved.

 

Contributions

      

• The contributions should include:
1. An experimental study following the experimental setup described above. In particular, authors should compare their algorithms with the following evolutionary algorithms:
   • Real-coded CHC (Eshelman, L.J., Schaffer, J.D. (1993). Real-coded genetic algorithms and interval-schemata. In: Foundations of Genetic Algorithms 2, L. D. Whitley, Ed. San Mateo, CA: Morgan Kaufmann, p. 187–202).

   • G-CMA-ES (Auger, A., Hansen, N. (2005). A restart CMA evolution strategy with increasing population size. In: Proc. of the 2005 IEEE Congress on Evolutionary Computation, p. 1769-1776).

   • Differential Evolution (Storn, R., Price, K. (1997). Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11 (4), 341–359).

   
   Document with the information for the basic algorithms: Components and Parameters of DE, Real-coded CHC, and G-CMA-ES.
   
   The results of DE, Real-coded CHC, and G-CMA-ES (considering the updated functions) are now available . All the results below 1e-14 have been approximated to 0.0. (Excel file *June 18, 2010*).
   
   
2. Statistical analysis on the average error. A comparision should be carried out by applying non-parametric tests, such as Wilcoxon's test and Holm's test. General information and software on these tests may be found in the following link: http://sci2s.ugr.es/sicidm/. See as well:
   
   S. Garcia, D. Molina, M. Lozano, F. Herrera, A study on the use of non-parametric tests for analyzing the evolutionary algorithms' behaviour: a case study on the CEC'2005 Special Session on Real Parameter Optimization. Journal of Heuristics 15 (2009) 617-644. doi: 10.1007/s10732-008-9080-4. (Pdf file).

3. An analysis of the scalability behaviour of the proposed algorithms.
4. An investigation of the computational running time of the algorithms. Authors should provide, for each function, the average running time on the 25 runs. In addition, the computational conditions (machine, programming language, compiler, etc.) should be specified in the paper.

• In addition, authors should provide the following material:
1. The source code of the algorithms. The source codes of the algorithms will be published as complementary material to the special issue (they will be available from an associated website).
2. An Excel file having the performance measures achieved by the algorithms on every test problem.

 

Important Dates

Papers Submission: March 26, 2010.

First revision: May 1, 2010.

Updated version: May 31, 2010.

Second revision: June 20, 2010.

Final revision: July 5, 2010.

 

Organizers and Contact

Manuel Lozano. Contact information:

• Email address: lozano[at]decsai.ugr.es
• Postal address: Department of Computer Science and Artificial Intelligence, University of Granada, E-18071 Granada, Spain
• Telephone number: +34-958-244258
• Fax Number: +34-958-243317

Francisco Herrera. Contact information:

• Email address: herrera[at]decsai.ugr.es
• Postal address: Department of Computer Science and Artificial Intelligence, University of Granada, E-18071 Granada, Spain
• Telephone number: +34-958-240598
• Fax Number: +34-958-243317