Extending Minimum Population Search towards large scale global optimization

Minimum Population Search is a new metaheuristic specifically designed for optimizing multi-modal problems. Its core idea is to guarantee exploration in all dimensions of the search space with the smallest possible population. A small population increases the chances of convergence and the efficient use of function evaluations - an important consideration when scaling a search technique up towards large scale global optimization. As the cost to converge to any local optimum increases in high dimensional search spaces, metaheuristics must focus more and more on gradient exploitation. To successfully maintain its balance between exploration and exploitation, Minimum Population Search uses thresheld convergence. Thresheld convergence can ensure that a search technique will perform a broad, unbiased exploration at the beginning and also have enough function evaluations allocated for proper convergence at the end. Experimental results show that Minimum Population Search outperforms Differential Evolution and Particle Swarm Optimization on complex multi-modal fitness functions across a broad range of problem sizes.

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

[2]  Xiaodong Li,et al.  Cooperative Co-evolution with delta grouping for large scale non-separable function optimization , 2010, IEEE Congress on Evolutionary Computation.

[3]  Anne Auger,et al.  Real-Parameter Black-Box Optimization Benchmarking 2009: Noiseless Functions Definitions , 2009 .

[4]  Antonio Bolufé Röhler,et al.  Differential evolution with thresheld convergence , 2013, 2013 IEEE Congress on Evolutionary Computation.

[5]  Wei Chu,et al.  A new evolutionary search strategy for global optimization of high-dimensional problems , 2011, Inf. Sci..

[6]  James Montgomery,et al.  A simple strategy for maintaining diversity and reducing crowding in differential evolution , 2012, 2012 IEEE Congress on Evolutionary Computation.

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

[8]  Andries Petrus Engelbrecht,et al.  Particle swarm optimization: Velocity initialization , 2012, 2012 IEEE Congress on Evolutionary Computation.

[9]  James Kennedy,et al.  Defining a Standard for Particle Swarm Optimization , 2007, 2007 IEEE Swarm Intelligence Symposium.

[10]  Xiaodong Li,et al.  Cooperatively Coevolving Particle Swarms for Large Scale Optimization , 2012, IEEE Transactions on Evolutionary Computation.

[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]  James Montgomery,et al.  A Simple Strategy to Maintain Diversity and Reduce Crowding in Particle Swarm Optimization , 2011, Australasian Conference on Artificial Intelligence.

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

[14]  Marcus Gallagher,et al.  A general-purpose tunable landscape generator , 2006, IEEE Transactions on Evolutionary Computation.

[15]  Janez Brest,et al.  High-dimensional real-parameter optimization using Self-Adaptive Differential Evolution algorithm with population size reduction , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).

[16]  Bin Li,et al.  Two-stage based ensemble optimization for large-scale global optimization , 2010, IEEE Congress on Evolutionary Computation.

[17]  Antonio Bolufé Röhler,et al.  Minimum population search - Lessons from building a heuristic technique with two population members , 2013, 2013 IEEE Congress on Evolutionary Computation.

[18]  Francisco Luna,et al.  Solving large-scale real-world telecommunication problems using a grid-based genetic algorithm , 2008 .

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

[20]  R. Storn,et al.  On the usage of differential evolution for function optimization , 1996, Proceedings of North American Fuzzy Information Processing.

[21]  Ponnuthurai Nagaratnam Suganthan,et al.  Benchmark Functions for the CEC'2013 Special Session and Competition on Large-Scale Global Optimization , 2008 .

[22]  Jürgen Branke,et al.  Experimental Analysis of Bound Handling Techniques in Particle Swarm Optimization , 2013, IEEE Transactions on Evolutionary Computation.

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

[24]  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.

[25]  Fred W. Glover,et al.  EM323: a line search based algorithm for solving high-dimensional continuous non-linear optimization problems , 2011, Soft Comput..