The Cooperative Coevolutionary (11) EA

Coevolutionary algorithms are variants of traditional evolutionary algorithms and are often considered more suitable for certain kinds of complex tasks than noncoevolutionary methods. One example is a general cooperative coevolutionary framework for function optimization. This paper presents a thorough and rigorous introductory analysis of the optimization potential of cooperative coevolution. Using the cooperative coevolutionary framework as a starting point, the CC (11) EA is defined and investigated from the perspective of the expected optimization time. The research concentrates on separability, a key property of objective functions. We show that separability alone is not sufficient to yield any advantage of the CC (11) EA over its traditional, non-coevolutionary counterpart. Such an advantage is demonstrated to have its basis in the increased explorative possibilities of the cooperative coevolutionary algorithm. For inseparable functions, the cooperative coevolutionary set-up can be harmful. We prove that for some objective functions the CC (11) EA fails to locate a global optimum with overwhelming probability, even in infinite time; however, inseparability alone is not sufficient for an objective function to cause difficulties. It is demonstrated that the CC (11) EA may perform equal to its traditional counterpart, and may even outperform it on certain inseparable functions.

[1]  Larry Bull.  On coevolutionary genetic algorithms , 2001, Soft Comput..

[2]  Marc Schoenauer,et al.  Rigorous Hitting Times for Binary Mutations , 1999, Evolutionary Computation.

[3]  Kenneth O. Stanley and Joseph Reisinger and Risto Miikkulainen,et al.  The Dominance Tournament Method of Monitoring Progress in Coevolution , 2002 .

[4]  Xiaodong Li,et al.  Parameter Control within a Co-operative Co-evolutionary Genetic Algorithm , 2002, PPSN.

[5]  Kenneth A. De Jong,et al.  Cooperative Coevolution: An Architecture for Evolving Coadapted Subcomponents , 2000, Evolutionary Computation.

[6]  Kenneth A. De Jong,et al.  Modeling Variation in Cooperative Coevolution Using Evolutionary Game Theory , 2002, FOGA.

[7]  Ingo Wegener,et al.  Methods for the Analysis of Evolutionary Algorithms on Pseudo-Boolean Functions , 2003 .

[8]  J. Crutchfield,et al.  Optimizing Epochal Evolutionary Search: Population-Size Dependent Theory , 1998, Machine Learning.

[9]  G. Hancock,et al.  The Quest for α: Developments in Multiple Comparison Procedures in the Quarter Century Since Games (1971) , 1996 .

[10]  Carsten Witt,et al.  Runtime Analysis of the ( μ +1) EA on Simple Pseudo-Boolean Functions , 2006 .

[11]  R. Eriksson,et al.  Cooperative Coevolution in Inventory Control Optimisation , 1997, ICANNGA.

[12]  Dave Cliff,et al.  Tracking the Red Queen: Measurements of Adaptive Progress in Co-Evolutionary Simulations , 1995, ECAL.

[13]  Alan C. Schultz,et al.  Heterogeneity in the Coevolved Behaviors of Mobile Robots: The Emergence of Specialists , 2001, IJCAI.

[14]  Ingo Wegener,et al.  Fitness Landscapes Based on Sorting and Shortest Paths Problems , 2002, PPSN.

[15]  Kwong-Sak Leung,et al.  Probabilistic cooperative-competitive hierarchical modeling as a genetic operator in global optimization , 1998, SMC'98 Conference Proceedings. 1998 IEEE International Conference on Systems, Man, and Cybernetics (Cat. No.98CH36218).

[16]  Larry Bull,et al.  Evolutionary computing in multi-agent environments: Partners , 1997 .

[17]  C. Witt.  Population Size vs . Runtime of a Simple Evolutionary Algorithm , 2003 .

[18]  R. Paul Wiegand,et al.  Biasing Coevolutionary Search for Optimal Multiagent Behaviors , 2006, IEEE Transactions on Evolutionary Computation.

[19]  R. Paul Wiegand,et al.  An empirical analysis of collaboration methods in cooperative coevolutionary algorithms , 2001 .

[20]  Gregory R. Hancock,et al.  The Quest for α: Developments in Multiple Comparison Procedures in the Quarter Century Since Games (1971) , 1996 .

[21]  Kenneth A. De Jong,et al.  A Cooperative Coevolutionary Approach to Function Optimization , 1994, PPSN.

[22]  Heinz Mühlenbein,et al.  How Genetic Algorithms Really Work: Mutation and Hillclimbing , 1992, PPSN.

[23]  Thomas Jansen,et al.  On the Optimization of Unimodal Functions with the (1 + 1) Evolutionary Algorithm , 1998, PPSN.

[24]  Kenneth A. De Jong,et al.  The Coevolution of Antibodies for Concept Learning , 1998, PPSN.

[25]  J. Pollack,et al.  Challenges in coevolutionary learning: arms-race dynamics, open-endedness, and medicocre stable states , 1998 .

[26]  J. Crutchfield,et al.  Optimizing Epochal Evolutionary Search: Population-Size Dependent Theory , 1998, Machine-mediated learning.

[27]  C. Witt.  Population size vs. runtime of a simple EA , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[28]  Thomas Jansen,et al.  Exploring the Explorative Advantage of the Cooperative Coevolutionary (1+1) EA , 2003, GECCO.

[29]  Kenneth A. De Jong,et al.  The Effects of Representational Bias on Collaboration Methods in Cooperative Coevolution , 2002, PPSN.

[30]  Risto Miikkulainen,et al.  Forming Neural Networks Through Efficient and Adaptive Coevolution , 1997, Evolutionary Computation.

[31]  Kalyanmoy Deb,et al.  Long Path Problems , 1994, PPSN.

[32]  Thomas Jansen,et al.  Design and Management of Complex Technical Processes and Systems by means of Computational Intelligence Methods On the Choice of the Mutation Probability for the ( 1 + 1 ) EA , 2006 .

[33]  Thomas Jansen,et al.  Sequential versus parallel cooperative coevolutionary (1+1) EAs , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[34]  Jordan B. Pollack,et al.  A Game-Theoretic Approach to the Simple Coevolutionary Algorithm , 2000, PPSN.

[35]  Thomas Jansen,et al.  On the analysis of the (1+1) evolutionary algorithm , 2002, Theor. Comput. Sci..

[36]  Rajeev Motwani,et al.  Randomized Algorithms , 1995, SIGA.