Quantum control experiments as a testbed for evolutionary multi-objective algorithms

Experimental multi-objective Quantum Control is an emerging topic within the broad physics and chemistry applications domain of controlling quantum phenomena. This realm offers cutting edge ultrafast laser laboratory applications, which pose multiple objectives, noise, and possibly constraints on the high-dimensional search. In this study we introduce the topic of multi-observable quantum control (MOQC), and consider specific systems to be Pareto optimized subject to uncertainty, either experimentally or by means of simulated systems. The latter include a family of mathematical test-functions with a practical link to MOQC experiments, which are introduced here for the first time. We investigate the behavior of the multi-objective version of the covariance aatrix adaptation evolution strategy (MO-CMA-ES) and assess its performance on computer simulations as well as on laboratory closed-loop experiments. Overall, we propose a comprehensive study on experimental evolutionary Pareto optimization in high-dimensional continuous domains, draw some practical conclusions concerning the impact of fitness disturbance on algorithmic behavior, and raise several theoretical issues in the broad evolutionary multi-objective context.

[1]  Ofer M. Shir,et al.  The application of evolutionary multi-criteria optimization to dynamic molecular alignment , 2007, 2007 IEEE Congress on Evolutionary Computation.

[2]  Lothar Thiele,et al.  Multiobjective Optimization Using Evolutionary Algorithms - A Comparative Case Study , 1998, PPSN.

[3]  Bernhard Sendhoff,et al.  Trade-Off between Performance and Robustness: An Evolutionary Multiobjective Approach , 2003, EMO.

[4]  Robert J. Vanderbei,et al.  Robust Optimization of Large-Scale Systems , 1995, Oper. Res..

[5]  Bernhard Sendhoff,et al.  On the Impact of Systematic Noise on the Evolutionary Optimization Performance—A Sphere Model Analysis , 2004, Genetic Programming and Evolvable Machines.

[6]  Herschel Rabitz,et al.  Coherent Control of Quantum Dynamics: The Dream Is Alive , 1993, Science.

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

[8]  Kalyanmoy Deb,et al.  Multiobjective Problem Solving from Nature: From Concepts to Applications (Natural Computing Series) , 2008 .

[9]  Joshua D. Knowles.  Closed-loop evolutionary multiobjective optimization , 2009, IEEE Computational Intelligence Magazine.

[10]  Ofer M. Shir,et al.  Algorithms for Finding Maximum Diversity of Design Variables in Multi-Objective Optimization , 2012, CSER.

[11]  Lothar Thiele,et al.  Defining and Optimizing Indicator-Based Diversity Measures in Multiobjective Search , 2010, PPSN.

[12]  Christian Igel,et al.  A computational efficient covariance matrix update and a (1+1)-CMA for evolution strategies , 2006, GECCO.

[13]  H. Rabitz,et al.  Optimal control of quantum-mechanical systems: Existence, numerical approximation, and applications. , 1988, Physical review. A, General physics.

[14]  Marco Laumanns,et al.  Mutation Control and Convergence in Evolutionary Multi-Object Optimization , 2001 .

[15]  Gustav Gerber,et al.  Femtosecond quantum control of molecular dynamics in the condensed phase. , 2007, Physical chemistry chemical physics : PCCP.

[16]  Joshua D. Knowles,et al.  Closed-loop, multiobjective optimization of two-dimensional gas chromatography/mass spectrometry for serum metabolomics. , 2007, Analytical chemistry.

[17]  Nikolaus Hansen,et al.  Evaluating the CMA Evolution Strategy on Multimodal Test Functions , 2004, PPSN.

[18]  I. N. Egorov,et al.  HOW TO EXECUTE ROBUST DESIGN OPTIMIZATION , 2002 .

[19]  Gary B. Lamont,et al.  Evolutionary algorithms for solving multi-objective problems, Second Edition , 2007, Genetic and evolutionary computation series.

[20]  Luigi Bonacina,et al.  Multiobjective genetic approach for optimal control of photoinduced processes , 2007 .

[21]  H. Schwefel,et al.  Approximating the Pareto Set: Concepts, Diversity Issues, and Performance Assessment , 1999 .

[22]  Marco Laumanns,et al.  Performance assessment of multiobjective optimizers: an analysis and review , 2003, IEEE Trans. Evol. Comput..

[23]  Qingfu Zhang,et al.  Multiobjective Optimization Problems With Complicated Pareto Sets, MOEA/D and NSGA-II , 2009, IEEE Transactions on Evolutionary Computation.

[24]  S. Azarm,et al.  Multi-objective robust optimization using a sensitivity region concept , 2005 .

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

[26]  A. Bartelt,et al.  Assuring robustness to noise in optimal quantum control experiments (9 pages) , 2005 .

[27]  Patrick M. Reed,et al.  Diagnostic Assessment of Search Controls and Failure Modes in Many-Objective Evolutionary Optimization , 2012, Evolutionary Computation.

[28]  Lothar Thiele,et al.  The Hypervolume Indicator Revisited: On the Design of Pareto-compliant Indicators Via Weighted Integration , 2007, EMO.

[29]  Mike Preuss.  Reporting on experiments in evolutionary computation , 2007 .

[30]  Stefan M. Weber,et al.  Multi-objective optimization on alkali dimers , 2007 .

[31]  Yew-Soon Ong,et al.  Curse and Blessing of Uncertainty in Evolutionary Algorithm Using Approximation , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[32]  Evan J. Hughes,et al.  Evolutionary Multi-objective Ranking with Uncertainty and Noise , 2001, EMO.

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

[34]  Bernhard Sendhoff,et al.  Evolution Strategies for Robust Optimization , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[35]  Hans-Georg Beyer,et al.  Local Performance of the (μ/μ, μ)-ES in a Noisy Environment , 2000, FOGA.

[36]  Kay Chen Tan,et al.  An Investigation on Noisy Environments in Evolutionary Multiobjective Optimization , 2007, IEEE Transactions on Evolutionary Computation.

[37]  Ofer M. Shir,et al.  Enhancing Decision Space Diversity in Evolutionary Multiobjective Algorithms , 2009, EMO.

[38]  Bernhard Sendhoff,et al.  Robust Optimization - A Comprehensive Survey , 2007 .

[39]  Kalyanmoy Deb,et al.  Multiobjective Problem Solving from Nature: From Concepts to Applications , 2008, Natural Computing Series.

[40]  Ofer M. Shir,et al.  Performance analysis of derandomized evolution strategies in quantum control experiments , 2008, GECCO '08.

[41]  Joshua D. Knowles,et al.  ParEGO: a hybrid algorithm with on-line landscape approximation for expensive multiobjective optimization problems , 2006, IEEE Transactions on Evolutionary Computation.

[42]  Ofer M. Shir,et al.  A Reduced-Cost SMS-EMOA Using Kriging, Self-Adaptation, and Parallelization , 2008, MCDM.

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

[44]  Monte Lunacek,et al.  Calibration of liquid crystal ultrafast pulse shaper with common-path spectral interferometry and application to coherent control with a covariance matrix adaptation evolutionary strategy. , 2008, The Review of scientific instruments.

[45]  Eckart Zitzler,et al.  Integrating decision space diversity into hypervolume-based multiobjective search , 2010, GECCO '10.

[46]  Hans-Georg Beyer,et al.  Toward a Theory of Evolution Strategies: Some Asymptotical Results from the (1,+ )-Theory , 1993, Evolutionary Computation.

[47]  Hans-Paul Schwefel,et al.  TWO-PHASE NOZZLE AND HOLLOW CORE JET EXPERIMENTS. , 1970 .

[48]  Raymond Ros,et al.  A Simple Modification in CMA-ES Achieving Linear Time and Space Complexity , 2008, PPSN.

[49]  A. Weiner.  Femtosecond pulse shaping using spatial light modulators , 2000 .

[50]  P. Koumoutsakos,et al.  Multiobjective evolutionary algorithm for the optimization of noisy combustion processes , 2002 .

[51]  Jürgen Teich,et al.  Pareto-Front Exploration with Uncertain Objectives , 2001, EMO.

[52]  Dirk V. Arnold,et al.  Noisy Optimization With Evolution Strategies , 2002, Genetic Algorithms and Evolutionary Computation.

[53]  David H. Wolpert,et al.  No free lunch theorems for optimization , 1997, IEEE Trans. Evol. Comput..

[54]  Eckart Zitzler,et al.  Robustness in Hypervolume-based Multiobjective Search TIK Report , 2010 .

[55]  Gary B. Lamont,et al.  Multiobjective Evolutionary Algorithms: Analyzing the State-of-the-Art , 2000, Evolutionary Computation.

[56]  Hans-Georg Beyer,et al.  Local performance of the (1 + 1)-ES in a noisy environment , 2002, IEEE Trans. Evol. Comput..

[57]  Kalyanmoy Deb,et al.  Introducing Robustness in Multi-Objective Optimization , 2006, Evolutionary Computation.

[58]  Qingfu Zhang,et al.  Multiobjective evolutionary algorithms: A survey of the state of the art , 2011, Swarm Evol. Comput..

[59]  Jürgen Branke,et al.  Evolutionary Optimization in Dynamic Environments , 2001, Genetic Algorithms and Evolutionary Computation.

[60]  Herschel Rabitz,et al.  Quantum control of tightly competitive product channels. , 2009, Physical review letters.

[61]  D. Fogel.  Evolutionary algorithms in theory and practice , 1997, Complex..

[62]  H. Rabitz,et al.  Teaching lasers to control molecules. , 1992, Physical review letters.

[63]  Lily Rachmawati,et al.  Multiobjective Evolutionary Algorithm With Controllable Focus on the Knees of the Pareto Front , 2009, IEEE Transactions on Evolutionary Computation.

[64]  Gary B. Lamont,et al.  Evolutionary Algorithms for Solving Multi-Objective Problems (Genetic and Evolutionary Computation) , 2006 .

[65]  Ofer M. Shir,et al.  On the evolution of laser pulses under a dynamic Quantum Control environment , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).

[66]  Kalyanmoy Deb,et al.  Evolutionary multiobjective optimization , 2007, GECCO '07.

[67]  Ofer M. Shir,et al.  On the diversity of multiple optimal controls for quantum systems , 2008 .

[68]  Keith E. Mathias,et al.  In Parallel Problem Solving from Nature-PPSN III , 1994 .

[69]  Stefan Roth,et al.  Covariance Matrix Adaptation for Multi-objective Optimization , 2007, Evolutionary Computation.

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

[71]  Marco Laumanns,et al.  A Tutorial on Evolutionary Multiobjective Optimization , 2004, Metaheuristics for Multiobjective Optimisation.

[72]  Michael T. M. Emmerich,et al.  Test Problems Based on Lamé Superspheres , 2007, EMO.

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

[74]  Nicola Beume,et al.  SMS-EMOA: Multiobjective selection based on dominated hypervolume , 2007, Eur. J. Oper. Res..

[75]  Herschel Rabitz,et al.  Quantum Pareto optimal control , 2008 .

[76]  H. Beyer,et al.  Noisy Local Optimization with Evolution Strategies , 2002 .

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