A simple self-adaptive Differential Evolution algorithm with application on the ALSTOM gasifier

Differential Evolution (DE) has gathered a reputation for being a powerful yet simple global optimiser with continually outperforming many of the already existing stochastic and direct search global optimisation techniques. It is however well established that DE is particularly sensitive to its control parameters, most notably the mutation weighting factor F. This sensitivity is further studied here and a simple randomised self-adaptive scheme is proposed for the DE mutation weighting factor F. The performance of this algorithm is studied with the use of several benchmark problems and applied to a difficult control systems design case study.

[1]  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.

[2]  J. A. Rossiter,et al.  An advanced predictive control approach to the ALSTOM gasifier problem , 2000 .

[3]  Neil Munro,et al.  A sequential loop closing approach to the ALSTOM gasifier problem , 2000 .

[4]  L. G. van Willigenburg,et al.  Efficient Differential Evolution algorithms for multimodal optimal control problems , 2003, Appl. Soft Comput..

[5]  Riccardo Poli,et al.  New ideas in optimization , 1999 .

[6]  Peter C. Young,et al.  Proportional-integral-plus (PIP) control of the ALSTOM gasifier problem , 2000 .

[7]  Ian Griffin,et al.  Multi-objective optimization approach to the ALSTOM gasifier problem , 2000 .

[8]  Hans-Paul Schwefel,et al.  Numerical optimization of computer models , 1981 .

[9]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[10]  Chun Zhang,et al.  Mixed-discrete nonlinear optimization with simulated annealing , 1993 .

[11]  Thomas Bäck,et al.  Evolutionary computation: comments on the history and current state , 1997, IEEE Trans. Evol. Comput..

[12]  H. Rosenbrock,et al.  Mathematics of dynamical systems , 1970 .

[13]  E. Sandgren,et al.  Nonlinear Integer and Discrete Programming in Mechanical Design Optimization , 1990 .

[14]  A. E. Eiben,et al.  Introduction to Evolutionary Computing , 2003, Natural Computing Series.

[15]  Guo-Ping Liu,et al.  Multi-objective optimal-tuning proportional-integral controller design for the ALSTOM gasifier problem , 2000 .

[16]  R. Salomon Re-evaluating genetic algorithm performance under coordinate rotation of benchmark functions. A survey of some theoretical and practical aspects of genetic algorithms. , 1996, Bio Systems.

[17]  David B. Fogel,et al.  A Note on the Empirical Evaluation of Intermediate Recombination , 1995, Evolutionary Computation.

[18]  A. Farag,et al.  MULTIVARIABLE PID-CONTROLLER DESIGN FOR A GASIFIER PLANT USING PENALTY-BASED-MULTI-OBJECTIVE GA , 2004 .

[19]  E. Bristol On a new measure of interaction for multivariable process control , 1966 .

[20]  Kao-Shing Hwang,et al.  CO-EVOLUTIONARY HYBRID DIFFERENTIAL EVOLUTION FOR MIXED-INTEGER OPTIMIZATION PROBLEMS , 2001 .

[21]  Anne Auger,et al.  Convergence results for the (1, lambda)-SA-ES using the theory of phi-irreducible Markov chains , 2005, Theor. Comput. Sci..

[22]  Zbigniew Michalewicz,et al.  Parameter control in evolutionary algorithms , 1999, IEEE Trans. Evol. Comput..

[23]  Colin R. Reeves,et al.  Genetic Algorithms and the Design of Experiments , 1999 .

[24]  Kalyanmoy Deb,et al.  Self-Adaptive Genetic Algorithms with Simulated Binary Crossover , 2001, Evolutionary Computation.

[25]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[26]  Ralf Salomon,et al.  Some Comments on Evolutionary Algorithm Theory , 1996, Evolutionary Computation.

[27]  Riccardo Poli,et al.  Evolving problems to learn about particle swarm and other optimisers , 2005, 2005 IEEE Congress on Evolutionary Computation.

[28]  David W. Corne,et al.  No Free Lunch and Free Leftovers Theorems for Multiobjective Optimisation Problems , 2003, EMO.

[29]  J. M. Edmunds Input and output scaling and reordering for diagonal dominance and block diagonal dominance , 1998 .

[30]  William A. Barrett,et al.  Spiders: a new user interface for rotation and visualization of n-dimensional point sets , 1994, Proceedings Visualization '94.

[31]  David E. Goldberg,et al.  Genetic Algorithms and Walsh Functions: Part II, Deception and Its Analysis , 1989, Complex Syst..

[32]  H. P. Schwefel,et al.  Numerische Optimierung von Computermodellen mittels der Evo-lutionsstrategie , 1977 .

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

[34]  Ioannis K. Kookos On the feasibility of constrained linear control problems with application to the ALSTOM gasifier , 2005 .

[35]  Thomas Bäck,et al.  Empirical Investigation of Multiparent Recombination Operators in Evolution Strategies , 1997, Evolutionary Computation.

[36]  Amin Nobakhti,et al.  Minimal Structure Control: A Proposition , 2003 .

[37]  Jim Smith,et al.  Self adaptation of mutation rates in a steady state genetic algorithm , 1996, Proceedings of IEEE International Conference on Evolutionary Computation.

[38]  Thomas Jansen,et al.  Design and Management of Complex Technical Processes and Systems by Means of Computational Intelligence Methods Perhaps Not a Free Lunch but at Least a Free Appetizer Perhaps Not a Free Lunch but at Least a Free Appetizer , 2022 .

[39]  Zbigniew Michalewicz,et al.  Genetic algorithms + data structures = evolution programs (2nd, extended ed.) , 1994 .

[40]  Omprakash K. Gupta Branch and bound experiments in nonlinear integer programming , 1980 .

[41]  Thomas Bäck,et al.  Evolutionary Algorithms in Theory and Practice , 1996 .

[42]  Terence C. Fogarty,et al.  Varying the Probability of Mutation in the Genetic Algorithm , 1989, ICGA.

[43]  Thomas Bäck,et al.  Evolutionary algorithms in theory and practice - evolution strategies, evolutionary programming, genetic algorithms , 1996 .

[44]  H. Abbass The self-adaptive Pareto differential evolution algorithm , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[45]  Zbigniew Michalewicz,et al.  Adaptation in evolutionary computation: a survey , 1997, Proceedings of 1997 IEEE International Conference on Evolutionary Computation (ICEC '97).

[46]  Ivan Zelinka,et al.  MIXED INTEGER-DISCRETE-CONTINUOUS OPTIMIZATION BY DIFFERENTIAL EVOLUTION Part 1: the optimization method , 2004 .

[47]  I. Burdon Winning combination [integrated gasification combined-cycle process] , 2006 .

[48]  David B. Fogel,et al.  Meta-evolutionary programming , 1991, [1991] Conference Record of the Twenty-Fifth Asilomar Conference on Signals, Systems & Computers.

[49]  Ian Postlethwaite,et al.  Robust control of the gasifier using a mixed-sensitivity H∞ approach , 2000 .

[50]  K. Deb An Efficient Constraint Handling Method for Genetic Algorithms , 2000 .

[51]  William H. Press,et al.  Numerical recipes in C , 2002 .

[52]  Hans-Georg Beyer,et al.  Toward a Theory of Evolution Strategies: Self-Adaptation , 1995, Evolutionary Computation.

[53]  Ian Postlethwaite,et al.  Multivariable Feedback Control: Analysis and Design , 1996 .

[54]  Nikolaus Hansen,et al.  Step-Size Adaption Based on Non-Local Use of Selection Information , 1994, PPSN.

[55]  Xin Yao,et al.  Fast Evolutionary Programming , 1996, Evolutionary Programming.

[56]  Lester Ingber,et al.  Simulated annealing: Practice versus theory , 1993 .

[57]  Reinhard Männer,et al.  Towards an Optimal Mutation Probability for Genetic Algorithms , 1990, PPSN.

[58]  William L. Luyben,et al.  Simple Regulatory Control of the Eastman Process , 1996 .

[59]  Lino A. Costa,et al.  Evolutionary algorithms approach to the solution of mixed integer non-linear programming problems , 2001 .

[60]  E. E. Osborne On Pre-Conditioning of Matrices , 1960, JACM.

[61]  Roger Dixon,et al.  The ALSTOM benchmark challenge on gasifier control , 2000 .

[62]  Zbigniew Michalewicz,et al.  Evolutionary algorithms , 1997, Emerging Evolutionary Algorithms for Antennas and Wireless Communications.

[63]  Zbigniew Michalewicz,et al.  Genetic Algorithms + Data Structures = Evolution Programs , 1996, Springer Berlin Heidelberg.

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

[65]  Zbigniew Michalewicz,et al.  Evolutionary Algorithms for Constrained Parameter Optimization Problems , 1996, Evolutionary Computation.

[66]  Zbigniew Michalewicz,et al.  Handbook of Evolutionary Computation , 1997 .

[67]  Rajnikant V. Patel,et al.  Multivariable System Theory and Design , 1981 .

[68]  M. F. Cardoso,et al.  A simulated annealing approach to the solution of minlp problems , 1997 .

[69]  W. Vent,et al.  Rechenberg, Ingo, Evolutionsstrategie — Optimierung technischer Systeme nach Prinzipien der biologischen Evolution. 170 S. mit 36 Abb. Frommann‐Holzboog‐Verlag. Stuttgart 1973. Broschiert , 1975 .

[70]  Sandro Ridella,et al.  Minimizing multimodal functions of continuous variables with the “simulated annealing” algorithmCorrigenda for this article is available here , 1987, TOMS.

[71]  Yun Shang,et al.  A Note on the Extended Rosenbrock Function , 2006 .

[72]  E. F. Vogel,et al.  A plant-wide industrial process control problem , 1993 .

[73]  Rainer Storn,et al.  System design by constraint adaptation and differential evolution , 1999, IEEE Trans. Evol. Comput..