A hybrid sequential niche algorithm for optimal engineering design with solution multiplicity

Abstract This paper introduces a new hybrid algorithm for locating all solutions in multimodal optimization problems. This algorithm combines an adaptive sequential niche technique with deterministic local optimization to detect all extrema efficiently and reliably. A genetic element of the hybrid algorithm performs a global search while the deterministic local optimizer computes the precise coordinates of the extremum. Once an extremum is precisely located, a niche demarcating the area of attraction around the local minimum is recorded. The sequential process proceeds to search for additional extrema. Our novel method overcomes challenges to distinguish multiple extrema in problem-specific terrain by an automatic niche radius adjustment. Several comparative simulation experiments with previous niche algorithms demonstrate the novel algorithm's performance and reliability. We also present a difficult case study for solution multiplicity in catalytic pellets. We determine multiple solutions for distributed inversion problems.

[1]  Ofer M. Shir,et al.  Niche Radius Adaptation in the CMA-ES Niching Algorithm , 2006, PPSN.

[2]  Ralph R. Martin,et al.  A Sequential Niche Technique for Multimodal Function Optimization , 1993, Evolutionary Computation.

[3]  Kalyanmoy Deb,et al.  An Investigation of Niche and Species Formation in Genetic Function Optimization , 1989, ICGA.

[4]  J. David Schaffer,et al.  Proceedings of the third international conference on Genetic algorithms , 1989 .

[5]  David E. Goldberg,et al.  Sizing Populations for Serial and Parallel Genetic Algorithms , 1989, ICGA.

[6]  Márk Jelasity,et al.  UEGO, an Abstract Niching Technique for Global Optimization , 1998, PPSN.

[7]  K. Warwick,et al.  Dynamic Niche Clustering: a fuzzy variable radius niching technique for multimodal optimisation in GAs , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

[8]  R. K. Aggarwal,et al.  Fast and accurate power dispatch using a relaxed genetic algorithm and a local gradient technique , 2000 .

[9]  Andreas A. Linninger,et al.  Multiscale Modeling and Solution Multiplicity in Catalytic Pellet Reactors , 2008 .

[10]  David E. Goldberg,et al.  Genetic Algorithms with Sharing for Multimodalfunction Optimization , 1987, ICGA.

[11]  W. Seider,et al.  Homotopy-continuation method for stability analysis in the global minimization of the Gibbs free energy , 1995 .

[12]  A. Lucia,et al.  Global terrain methods , 2002 .

[13]  Edmund K. Burke,et al.  Parallel Problem Solving from Nature - PPSN IX: 9th International Conference, Reykjavik, Iceland, September 9-13, 2006, Proceedings , 2006, PPSN.

[14]  A. V. Levy,et al.  The Tunneling Algorithm for the Global Minimization of Functions , 1985 .

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

[16]  Patrick Siarry,et al.  Genetic and Nelder-Mead algorithms hybridized for a more accurate global optimization of continuous multiminima functions , 2003, Eur. J. Oper. Res..

[17]  Kenneth Alan De Jong,et al.  An analysis of the behavior of a class of genetic adaptive systems. , 1975 .

[18]  Angelo M. Sabatini,et al.  A hybrid genetic algorithm for estimating the optimal time scale of linear systems approximations using Laguerre models , 2000, IEEE Trans. Autom. Control..

[19]  Michael J. Shaw,et al.  Genetic algorithms with dynamic niche sharing for multimodal function optimization , 1996, Proceedings of IEEE International Conference on Evolutionary Computation.

[20]  Andreas A. Linninger,et al.  A barrier-terrain methodology for global optimization , 2008 .

[21]  Samir W. Mahfoud.  Crowding and Preselection Revisited , 1992, PPSN.

[22]  Michalis Xenos,et al.  Discovery of transport and reaction properties in distributed systems , 2007 .

[23]  Mark A. Stadtherr,et al.  ROBUST PHASE STABILITY ANALYSIS USING INTERVAL METHODS , 1998 .

[24]  Christodoulos A. Floudas,et al.  Global optimization for the phase stability problem , 1995 .

[25]  Andreas A. Linninger,et al.  Solving kinetic inversion problems via a physically bounded Gauss - Newton (PGN) method , 2005 .