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Time complexity of evolutionary algorithms for combinatorial optimization: A decade of results

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Abstract

Computational time complexity analyzes of evolutionary algorithms (EAs) have been performed since the mid-nineties. The first results were related to very simple algorithms, such as the (1+1)-EA, on toy problems. These efforts produced a deeper understanding of how EAs perform on different kinds of fitness landscapes and general mathematical tools that may be extended to the analysis of more complicated EAs on more realistic problems. In fact, in recent years, it has been possible to analyze the (1+1)-EA on combinatorial optimization problems with practical applications and more realistic population-based EAs on structured toy problems. This paper presents a survey of the results obtained in the last decade along these two research lines. The most common mathematical techniques are introduced, the basic ideas behind them are discussed and their elective applications are highlighted. Solred problems that were still open are enumerated as are those still awaiting for a solution. New questions and problems arisen in the meantime are also considered.

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Authors and Affiliations

  1. The Center of Excellence for Research in Computational Intelligence and Applications (CERCIA), School of Computer Science, University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK

    Pietro S. Oliveto, Jun He & Xin Yao

Authors
  1. Pietro S. Oliveto
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  2. Jun He
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  3. Xin Yao
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Corresponding author

Correspondence to Jun He.

Additional information

This work was supported by an EPSRC grant (No. EP/C520696/1).

Pietro S. Oliveto received the Laurea degree in computer science from the University of Catania, Italy, in 2005. Since 2006 he has been a Ph.D. candidate at the School of Computer Science, University of Birmingham, UK.

His Ph.D. topic is the computational complexity analysis of evolutionary algorithms which is part of an EPSRC funded project. His main research interest is the time complexity analysis of randomized algorithms for combinatorial optimization problems. He is currently considering local search, evolutionary, and artificial immune system algorithms.

Jun He received his Ph.D. degree in computer science from Wuhan University, China in 1995. Currently he is a research fellow at the School of Computer Science, University of Birmingham, England.

His research interests include evolutionary computation, data mining and network security.

Xin Yao obtained his B.Sc. from the University of Science and Technology of China (USTC) in Hefei. China, in 1982, M.Sc. from the North China Institute of Computing Technology in Beijing, China, in 1985, and Ph.D. from USTC in Hefei, China, in 1990.

He was an associate lecturer and lecturer between 1985 and 1990 at USTC while working on his Ph.D.. His Ph.D. work on simulated annealing and evolutionary algorithms was awarded the President’s Award for Outstanding Thesis by the Chinese Academy of Sciences. He took up a postdoctoral fellowship in the Computer Sciences Laboratory at the Australian National University (ANU) in Canberra in 1990, and continued his work on simulated annealing and evolutionary algorithms. He joined the Knowledge-Based Systems Group at CSIRO Division of Building, Construction and Engineering in Melbourne in 1991, working primarily on an industrial project on automatic inspection of sewage pipes. He returned to Canberra in 1992 to take up a lectureship in the School of Computer Science, University College, the University of New South Wales (UNSW), the Australian Defence Force Academy (ADFA), where he was later promoted to a senior lecturer and associate professor. Attracted by the English weather, he moved to the University of Birmingham, England, as a professor (chair) of computer science on 1 April 1999. Currently he is the director of CERCIA (the Center of Excellence for Research in Computational Intelligence and Applications) at Birmingham, UK, a distinguished visiting professor of the University of Science and Technology of China in Hefei, China, and a visiting professor of three other universities.

He has more than 200 refereed research publications. In his spare time, he does the voluntary work as the editor-in-chief of IEEE Transactions on Evolutionary Computation, an associate editor or editorial board member of several other journals, and the editor of the World Scientific book series on “Advances in Natural Computation”. He has been invited to give more than 45 invited keynote and plenary speeches at conferences and workshops world-wide. His major research interests include evolutionary computation, neural network ensembles, and their applications.

Prof. Yao is an IEEE Fellow and a distinguished lecturer of IEEE Computational Intelligence Society. He won the 2001 IEEE Donald G. Fink Prize Paper Award for his work on evolutionary artificial neural networks.

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Oliveto, P.S., He, J. & Yao, X. Time complexity of evolutionary algorithms for combinatorial optimization: A decade of results. Int J Automat Comput 4, 281–293 (2007). https://doi.org/10.1007/s11633-007-0281-3

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