On the robustness of population-based versus point-based optimization in the presence of noise

Practical optimization problems often require the evaluation of solutions through experimentation, stochastic simulation, sampling, or even interaction with the user. Thus, most practical problems involve noise. We address the robustness of population-based versus point-based optimization on a range of parameter optimization problems when noise is added to the deterministic objective function values. Population-based optimization is realized by a genetic algorithm and an evolution strategy. Point-based optimization is implemented as the classical Hooke-Jeeves pattern search strategy and threshold accepting as a modern local search technique. We investigate the performance of these optimization methods for varying levels of additive normally distributed fitness-independent noise and different sample sizes for evaluating individual solutions. Our results strongly favour population-based optimization, and the evolution strategy in particular.

[1]  John J. Grefenstette,et al.  Genetic algorithms in noisy environments , 1988, Machine Learning.

[2]  L. Darrell Whitley,et al.  Searching in the Presence of Noise , 1996, PPSN.

[3]  Kalyanmoy Deb,et al.  Genetic Algorithms, Noise, and the Sizing of Populations , 1992, Complex Syst..

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

[5]  Günter Rudolph,et al.  Reflections on Bandit Problems and Selection Methods in Uncertain Environments , 1998, ICGA.

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

[7]  Jörg Biethahn,et al.  Determining a Good Inventory Policy with a Genetic Algorithm , 1995 .

[8]  Thomas Bäck,et al.  Evolution Strategies on Noisy Functions: How to Improve Convergence Properties , 1994, PPSN.

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

[10]  James E. Baker,et al.  Reducing Bias and Inefficienry in the Selection Algorithm , 1987, ICGA.

[11]  Gerhard W. Dueck,et al.  Threshold accepting: a general purpose optimization algorithm appearing superior to simulated anneal , 1990 .

[12]  Volker Nissen,et al.  Solving the quadratic assignment problem with clues from nature , 1994, IEEE Trans. Neural Networks.

[13]  David H. Wolpert,et al.  Bandit problems and the exploration/exploitation tradeoff , 1998, IEEE Trans. Evol. Comput..

[14]  John J. Grefenstette,et al.  Deception Considered Harmful , 1992, FOGA.

[15]  David B. Fogel,et al.  Schema processing under proportional selection in the presence of random effects , 1997, IEEE Trans. Evol. Comput..

[16]  Hans-Paul Schwefel,et al.  Evolution and optimum seeking , 1995, Sixth-generation computer technology series.

[17]  John H. Holland,et al.  Genetic Algorithms and the Optimal Allocation of Trials , 1973, SIAM J. Comput..

[18]  Volker Nissen,et al.  Optimization with Noisy Function Evaluations , 1998, PPSN.

[19]  Volker Nissen,et al.  A modification of threshold accepting and its application to the quadratic assignment problem , 1995 .

[20]  David B. Fogel,et al.  Using fitness distributions to design more efficient evolutionary computations , 1996, Proceedings of IEEE International Conference on Evolutionary Computation.

[21]  Günter Rudolph,et al.  Massively Parallel Simulated Annealing and Its Relation to Evolutionary Algorithms , 1993, Evolutionary Computation.