The application of evolutionary multi-criteria optimization to dynamic molecular alignment

This study introduces the multi-criteria approach to the optimization of dynamic molecular alignment by shaped femtosecond laser pulses, which has been considered so far only as a single-criterion problem. The paper applies advanced Pareto front approximation algorithms to this challenging real-world, high-dimensional, and computationally expensive problem, working with low-dimensional parameterizations of the electric field. Standard approaches (NSGA-II) and their metamodel-assisted extensions based on Kriging, are applied to this optimization task and compared among each other. The study confirms the conflicting nature of the objectives. Interesting features of the problem domain, such as the geometry of the Pareto front are revealed. Furthermore, metamodel-assistance, in particular pre-screening with the Kriging-based expected improvement criterion, proves to be a valuable ingredient for improving the numerical results.

[1]  Nicola Beume,et al.  An EMO Algorithm Using the Hypervolume Measure as Selection Criterion , 2005, EMO.

[2]  Eckart Zitzler,et al.  Evolutionary algorithms for multiobjective optimization: methods and applications , 1999 .

[3]  H. Rabitz,et al.  Molecular alignment by trains of short laser pulses. , 2003, Physical review letters.

[4]  M. Vrakking,et al.  Revival structures in picosecond laser-induced alignment of I2 molecules. I. Experimental results , 2002 .

[5]  R. K. Ursem.  Multi-objective Optimization using Evolutionary Algorithms , 2009 .

[6]  Henrik Stapelfeldt,et al.  Colloquium: Aligning molecules with strong laser pulses , 2003 .

[7]  Thomas Bäck,et al.  Metamodel-Assisted Evolution Strategies , 2002, PPSN.

[8]  Andy J. Keane,et al.  Metamodeling Techniques For Evolutionary Optimization of Computationally Expensive Problems: Promises and Limitations , 1999, GECCO.

[9]  Ofer M. Shir,et al.  Evolutionary Algorithms in the Optimization of Dynamic Molecular Alignment , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[10]  N. Hansen,et al.  The Multi-objective Variable Metric Evolution Strategy Part I , 2005 .

[11]  Dudley R. Herschbach,et al.  Steric proficiency of polar 2Σ molecules in congruent electric and magnetic fields , 2000 .

[12]  Ofer M. Shir,et al.  Evolutionary algorithms in the optimization of dynamic molecular alignment , 2006 .

[13]  Michael T. M. Emmerich,et al.  Single- and multiobjective evolutionary optimization assisted by Gaussian random field metamodels , 2006, IEEE Transactions on Evolutionary Computation.

[14]  M. Vrakking,et al.  Revival structures in picosecond laser-induced alignment of I2 molecules. II. Numerical modeling , 2002 .

[15]  Ofer M. Shir,et al.  Niching in Evolution Strategies and Its Application to Laser Pulse Shaping , 2005, Artificial Evolution.

[16]  Alain Ratle,et al.  Accelerating the Convergence of Evolutionary Algorithms by Fitness Landscape Approximation , 1998, PPSN.

[17]  Ofer M. Shir,et al.  The complete-basis-functions parameterization in ES and its application to laser pulse shaping , 2006, GECCO.