Leapfrogging and synoptic Leapfrogging: A new optimization approach

Abstract A novel optimization technique is introduced and demonstrated. Leapfrogging starts with a randomly located set of trial solutions (termed players) within the feasible decision variable (DV) space. At each iteration, the player with the worst objective function (OF) value is relocated to a random position within its DV-space reflection on the other side of the player with the best OF value. Test cases reveal that this simple algorithm has benefits over classic direct and gradient-based methods and particle swarm in speed of finding the optimum and in handling surface aberrations, including ridges, multi-optima, and stochastic objective functions. Potential limitations and analysis opportunities are discussed.

[1]  Günter Wozny,et al.  A new algorithm for global optimization: Molecular-Inspired Parallel Tempering , 2009, Comput. Chem. Eng..

[2]  R. Russell Rhinehart,et al.  Grouped neural network model-predictive control , 2003 .

[3]  Zuomin Dong,et al.  Trends, features, and tests of common and recently introduced global optimization methods , 2010 .

[4]  Patrick Siarry,et al.  Tabu Search applied to global optimization , 2000, Eur. J. Oper. Res..

[5]  B R Young,et al.  A tuning algorithm for model predictive controllers based on genetic algorithms and fuzzy decision making. , 2008, ISA transactions.

[6]  Zbigniew Michalewicz,et al.  Genetic Algorithms + Data Structures = Evolution Programs , 2000, Springer Berlin Heidelberg.

[7]  Michel Gendreau,et al.  A guide to vehicle routing heuristics , 2002, J. Oper. Res. Soc..

[8]  Grzegorz Ziomek,et al.  Random search optimization approach for highly multi-modal nonlinear problems , 2005, Adv. Eng. Softw..

[9]  Mahmoud Reza Pishvaie,et al.  Stochastic and global real time optimization of Tennessee Eastman challenge problem , 2008, Eng. Appl. Artif. Intell..

[10]  Chen-Chien Hsu,et al.  Digital redesign of uncertain interval systems based on time-response resemblance via particle swarm optimization , 2008, 2008 IEEE Conference on Soft Computing in Industrial Applications.

[11]  Gilbert Syswerda,et al.  A Study of Reproduction in Generational and Steady State Genetic Algorithms , 1990, FOGA.

[12]  Uğur Yüzgeç,et al.  Performance comparison of differential evolution techniques on optimization of feeding profile for an industrial scale baker's yeast fermentation process. , 2010, ISA transactions.

[13]  Sundararajan V Madihally,et al.  Assessing viscoelastic properties of chitosan scaffolds and validation with cyclical tests. , 2012, Acta biomaterialia.

[14]  R. R. Rhinehart,et al.  Heuristic random optimization , 1998 .

[15]  Julio R. Banga,et al.  Scatter search for chemical and bio-process optimization , 2007, J. Glob. Optim..

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

[17]  R. R. Rhinehart,et al.  A method to determine the required number of neural-network training repetitions , 1999, IEEE Trans. Neural Networks.

[18]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[19]  Nasser Sadati,et al.  Hierarchical optimal control of large-scale nonlinear chemical processes. , 2009, ISA transactions.

[20]  Ignacio E. Grossmann,et al.  Retrospective on optimization , 2004, Comput. Chem. Eng..

[21]  Graham Kendall,et al.  Diversity in genetic programming: an analysis of measures and correlation with fitness , 2004, IEEE Transactions on Evolutionary Computation.

[22]  Masao Fukushima,et al.  Tabu Search directed by direct search methods for nonlinear global optimization , 2006, Eur. J. Oper. Res..

[23]  Ulrich Derigs,et al.  Applying the attribute based hill climber heuristic to the vehicle routing problem , 2007, Eur. J. Oper. Res..

[24]  Riccardo Poli,et al.  Particle swarm optimization , 1995, Swarm Intelligence.

[25]  G. R. Hext,et al.  Sequential Application of Simplex Designs in Optimisation and Evolutionary Operation , 1962 .

[26]  Ian David Lockhart Bogle,et al.  Computers and Chemical Engineering , 2008 .

[27]  Fred W. Glover,et al.  ' s personal copy Continuous Optimization Finding local optima of high-dimensional functions using direct search methods , 2008 .

[28]  Yee Leung,et al.  Degree of population diversity - a perspective on premature convergence in genetic algorithms and its Markov chain analysis , 1997, IEEE Trans. Neural Networks.

[29]  Gang Chen,et al.  Preserving and Exploiting Genetic Diversity in Evolutionary Programming Algorithms , 2009, IEEE Transactions on Evolutionary Computation.

[30]  R. R. Rhinehart,et al.  A novel method to stop neural network training , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[31]  F. Franze,et al.  A tabu‐search‐based algorithm for continuous multiminima problems , 2001 .

[32]  Ian F. C. Smith,et al.  A direct stochastic algorithm for global search , 2003, Appl. Math. Comput..

[33]  Hari Om Gupta,et al.  ANN based estimator for distillation—inferential control , 2005 .

[34]  B. V. Babu,et al.  Modified differential evolution (MDE) for optimization of non-linear chemical processes , 2006, Comput. Chem. Eng..