A new evolutionary search strategy for global optimization of high-dimensional problems

Global optimization of high-dimensional problems in practical applications remains a major challenge to the research community of evolutionary computation. The weakness of randomization-based evolutionary algorithms in searching high-dimensional spaces is demonstrated in this paper. A new strategy, SP-UCI is developed to treat complexity caused by high dimensionalities. This strategy features a slope-based searching kernel and a scheme of maintaining the particle population's capability of searching over the full search space. Examinations of this strategy on a suite of sophisticated composition benchmark functions demonstrate that SP-UCI surpasses two popular algorithms, particle swarm optimizer (PSO) and differential evolution (DE), on high-dimensional problems. Experimental results also corroborate the argument that, in high-dimensional optimization, only problems with well-formative fitness landscapes are solvable, and slope-based schemes are preferable to randomization-based ones.

[1]  Riccardo Poli,et al.  Evolving Problems to Learn About Particle Swarm Optimizers and Other Search Algorithms , 2006, IEEE Transactions on Evolutionary Computation.

[2]  Shiu Yin Yuen,et al.  A Genetic Algorithm That Adaptively Mutates and Never Revisits , 2009, IEEE Trans. Evol. Comput..

[3]  R. Bellman Dynamic programming. , 1957, Science.

[4]  Bruce A. Robinson,et al.  Self-Adaptive Multimethod Search for Global Optimization in Real-Parameter Spaces , 2009, IEEE Transactions on Evolutionary Computation.

[5]  Wei Chu,et al.  A Solution to the Crucial Problem of Population Degeneration in High-Dimensional Evolutionary Optimization , 2011, IEEE Systems Journal.

[6]  Bin Li,et al.  Multi-strategy ensemble particle swarm optimization for dynamic optimization , 2008, Inf. Sci..

[7]  Toshio Odanaka,et al.  ADAPTIVE CONTROL PROCESSES , 1990 .

[8]  Nikolaus Hansen,et al.  On the Adaptation of Arbitrary Normal Mutation Distributions in Evolution Strategies: The Generating Set Adaptation , 1995, ICGA.

[9]  S. Sorooshian,et al.  Effective and efficient global optimization for conceptual rainfall‐runoff models , 1992 .

[10]  Jeffrey C. Lagarias,et al.  Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions , 1998, SIAM J. Optim..

[11]  Jing J. Liang,et al.  Dynamic multi-swarm particle swarm optimizer with local search for Large Scale Global Optimization , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).

[12]  David H. Wolpert,et al.  No free lunch theorems for optimization , 1997, IEEE Trans. Evol. Comput..

[13]  Amit Konar,et al.  Differential Evolution Using a Neighborhood-Based Mutation Operator , 2009, IEEE Transactions on Evolutionary Computation.

[14]  George Kuczera,et al.  Probabilistic optimization for conceptual rainfall-runoff models: A comparison of the shuffled complex evolution and simulated annealing algorithms , 1999 .

[15]  C. T. Kelley,et al.  Detection and Remediation of Stagnation in the Nelder--Mead Algorithm Using a Sufficient Decrease Condition , 1999, SIAM J. Optim..

[16]  Andries Petrus Engelbrecht,et al.  A Cooperative approach to particle swarm optimization , 2004, IEEE Transactions on Evolutionary Computation.

[17]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[18]  Josien P. W. Pluim,et al.  Evaluation of Optimization Methods for Nonrigid Medical Image Registration Using Mutual Information and B-Splines , 2007, IEEE Transactions on Image Processing.

[19]  Nikolaus Hansen,et al.  Adapting arbitrary normal mutation distributions in evolution strategies: the covariance matrix adaptation , 1996, Proceedings of IEEE International Conference on Evolutionary Computation.

[20]  Sanghamitra Bandyopadhyay,et al.  Multi-Objective Particle Swarm Optimization with time variant inertia and acceleration coefficients , 2007, Inf. Sci..

[21]  Jing J. Liang,et al.  Problem Definitions and Evaluation Criteria for the CEC 2005 Special Session on Real-Parameter Optimization , 2005 .

[22]  Janez Brest,et al.  Self-Adapting Control Parameters in Differential Evolution: A Comparative Study on Numerical Benchmark Problems , 2006, IEEE Transactions on Evolutionary Computation.

[23]  Wei Chu,et al.  Handling boundary constraints for particle swarm optimization in high-dimensional search space , 2011, Inf. Sci..

[24]  Peng Shi,et al.  Using investment satisfaction capability index based particle swarm optimization to construct a stock portfolio , 2011, Inf. Sci..

[25]  Hitoshi Iba,et al.  Accelerating Differential Evolution Using an Adaptive Local Search , 2008, IEEE Transactions on Evolutionary Computation.

[26]  Jing J. Liang,et al.  Novel composition test functions for numerical global optimization , 2005, Proceedings 2005 IEEE Swarm Intelligence Symposium, 2005. SIS 2005..

[27]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[28]  José Neves,et al.  The fully informed particle swarm: simpler, maybe better , 2004, IEEE Transactions on Evolutionary Computation.

[29]  M.M.A. Salama,et al.  Opposition-Based Differential Evolution , 2008, IEEE Transactions on Evolutionary Computation.

[30]  S. Sorooshian,et al.  Shuffled complex evolution approach for effective and efficient global minimization , 1993 .

[31]  K. I. M. McKinnon,et al.  Convergence of the Nelder-Mead Simplex Method to a Nonstationary Point , 1998, SIAM J. Optim..

[32]  Soroosh Sorooshian,et al.  Calibration of rainfall‐runoff models: Application of global optimization to the Sacramento Soil Moisture Accounting Model , 1993 .

[33]  R. Bellman,et al.  V. Adaptive Control Processes , 1964 .

[34]  Wenjian Luo,et al.  Differential evolution with dynamic stochastic selection for constrained optimization , 2008, Inf. Sci..

[35]  Adam Liwo,et al.  Recent improvements in prediction of protein structure by global optimization of a potential energy function , 2001, Proceedings of the National Academy of Sciences of the United States of America.