Convergence of a discretized selfadaptive evolutionary algorithm on multidimensional problems.
Abstract
We consider the convergence properties of a nonelitist selfadaptive evolutionary strategy (ES) on multidimensional problems. In particular, we apply our recent convergence theory for a discretized (1,{lambda})ES to design a related (1,{lambda})ES that converges on a class of seperable, unimodal multidimensional problems. The distinguishing feature of selfadaptive evolutionary algorithms (EAs) is that the control parameters (like mutation step lengths) are evolved by the evolutionary algorithm. Thus the control parameters are adapted in an implicit manner that relies on the evolutionary dynamics to ensure that more effective control parameters are propagated during the search. Selfadaptation is a central feature of EAs like evolutionary stategies (ES) and evolutionary programming (EP), which are applied to continuous design spaces. Rudolph summarizes theoretical results concerning selfadaptive EAs and notes that the theoretical underpinnings for these methods are essentially unexplored. In particular, convergence theories that ensure convergence to a limit point on continuous spaces have only been developed by Rudolph, Hart, DeLaurentis and Ferguson, and Auger et al. In this paper, we illustrate how our analysis of a (1,{lambda})ES for onedimensional unimodal functions can be used to ensure convergence of a related ES on multidimensional functions. This (1,{lambda})ES randomly selects a search dimension in each iteration,more »
 Authors:
 Publication Date:
 Research Org.:
 Sandia National Laboratories
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1005077
 Report Number(s):
 SAND20033240J
TRN: US201105%%184
 DOE Contract Number:
 AC0494AL85000
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Proposed for publication in IEEE Transactions on Evolutionary Computation.
 Country of Publication:
 United States
 Language:
 English
 Subject:
 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; ALGORITHMS; CONVERGENCE; DESIGN; DIMENSIONS; MUTATIONS; PROGRAMMING
Citation Formats
Hart, William Eugene, and DeLaurentis, John Morse. Convergence of a discretized selfadaptive evolutionary algorithm on multidimensional problems.. United States: N. p., 2003.
Web.
Hart, William Eugene, & DeLaurentis, John Morse. Convergence of a discretized selfadaptive evolutionary algorithm on multidimensional problems.. United States.
Hart, William Eugene, and DeLaurentis, John Morse. 2003.
"Convergence of a discretized selfadaptive evolutionary algorithm on multidimensional problems.". United States.
doi:.
@article{osti_1005077,
title = {Convergence of a discretized selfadaptive evolutionary algorithm on multidimensional problems.},
author = {Hart, William Eugene and DeLaurentis, John Morse},
abstractNote = {We consider the convergence properties of a nonelitist selfadaptive evolutionary strategy (ES) on multidimensional problems. In particular, we apply our recent convergence theory for a discretized (1,{lambda})ES to design a related (1,{lambda})ES that converges on a class of seperable, unimodal multidimensional problems. The distinguishing feature of selfadaptive evolutionary algorithms (EAs) is that the control parameters (like mutation step lengths) are evolved by the evolutionary algorithm. Thus the control parameters are adapted in an implicit manner that relies on the evolutionary dynamics to ensure that more effective control parameters are propagated during the search. Selfadaptation is a central feature of EAs like evolutionary stategies (ES) and evolutionary programming (EP), which are applied to continuous design spaces. Rudolph summarizes theoretical results concerning selfadaptive EAs and notes that the theoretical underpinnings for these methods are essentially unexplored. In particular, convergence theories that ensure convergence to a limit point on continuous spaces have only been developed by Rudolph, Hart, DeLaurentis and Ferguson, and Auger et al. In this paper, we illustrate how our analysis of a (1,{lambda})ES for onedimensional unimodal functions can be used to ensure convergence of a related ES on multidimensional functions. This (1,{lambda})ES randomly selects a search dimension in each iteration, along which points generated. For a general class of separable functions, our analysis shows that the ES searches along each dimension independently, and thus this ES converges to the (global) minimum.},
doi = {},
journal = {Proposed for publication in IEEE Transactions on Evolutionary Computation.},
number = ,
volume = ,
place = {United States},
year = 2003,
month = 8
}

The discretized lightcone quantization method is applied to study twobody relativistic boundstate problems in a selfinteracting complex scalar field model in 1+1 dimensions. The interaction Hamiltonian is constructed in the discretized version in the lightcone formulation of quantum field theory and the problem is numerically solved by diagonalizing the invariantmass operator in a truncated Fockspace basis in the positivecharge sector of the field. Results for binding energies, valence wave functions, structure functions, and the valence and nonvalence contributions to the momentum distribution functions are presented. Solutions of the problems in threebody and multibody states are also discussed.

On the use of multialgorithm, genetically adaptive multiobjective method for multisite calibration of the SWAT model
With the availability of spatially distributed data, distributed hydrologic models are increasingly used for simulation of spatially varied hydrologic processes to understand and manage natural and human activities that affect watershed systems. Multiobjective optimization methods have been applied to calibrate distributed hydrologic models using observed data from multiple sites. As the time consumed by running these complex models is increasing substantially, selecting efficient and effective multiobjective optimization algorithms is becoming a nontrivial issue. In this study, we evaluated a multialgorithm, genetically adaptive multiobjective method (AMALGAM) for multisite calibration of a distributed hydrologic model—Soil and Water Assessment Tool (SWAT), and comparedmore » 
A SmoothingType Algorithm for Solving Linear Complementarity Problems with Strong Convergence Properties
In this paper, we construct an augmented system of the standard monotone linear complementarity problem (LCP), and establish the relations between the augmented system and the LCP. We present a smoothingtype algorithm for solving the augmented system. The algorithm is shown to be globally convergent without assuming any prior knowledge of feasibility/infeasibility of the problem. In particular, if the LCP has a solution, then the algorithm either generates a maximal complementary solution of the LCP or detects correctly solvability of the LCP, and in the latter case, an existing smoothingtype algorithm can be directly applied to solve the LCP withoutmore » 
An adaptive multilevel simulation algorithm for stochastic biological systems
Discretestate, continuoustime Markov models are widely used in the modeling of biochemical reaction networks. Their complexity often precludes analytic solution, and we rely on stochastic simulation algorithms (SSA) to estimate system statistics. The Gillespie algorithm is exact, but computationally costly as it simulates every single reaction. As such, approximate stochastic simulation algorithms such as the tauleap algorithm are often used. Potentially computationally more efficient, the system statistics generated suffer from significant bias unless tau is relatively small, in which case the computational time can be comparable to that of the Gillespie algorithm. The multilevel method [Anderson and Higham, “Multilevel Montemore » 
SUCBRA01: Interactive AutoSegmentation for Bowel in Online Adaptive MRIGuided Radiation Therapy by Using a MultiRegion Labeling Algorithm
Purpose: In MRIguided online adaptive radiation therapy, recontouring of bowel is timeconsuming and can impact the overall time of patients on table. The study aims to autosegment bowel on volumetric MR images by using an interactive multiregion labeling algorithm. Methods: 5 Patients with locally advanced pancreatic cancer underwent fractionated radiotherapy (18–25 fractions each, total 118 fractions) on an MRIguided radiation therapy system with a 0.35 Tesla magnet and three Co60 sources. At each fraction, a volumetric MR image of the patient was acquired when the patient was in the treatment position. An interactive twodimensional multiregion labeling technique based on graphmore »