Evolutionary algorithms (EAs) have received increasing interests both in the academy and industry. One main difficulty in applying EAs to real-world applications is that EAs usually need a large number of fitness evaluations before a satisfying result can be obtained. However, fitness evaluations are not always straightforward in many real-world applications. Either an explicit fitness function does not exist, or the evaluation of the fitness is computationally very expensive. In both cases, it is necessary to estimate the fitness function by constructing an approximate model. In this paper, a comprehensive survey of the research on fitness approximation in evolutionary computation is presented. Main issues like approximation levels, approximate model management schemes, model construction techniques are reviewed. To conclude, open questions and interesting issues in the field are discussed.

This is a survey designed for mathematical programming people who do not know molecular biology and want to learn the kinds of combinatorial optimization problems that arise. After a brief introduction to the biology, we present optimization models pertaining to sequencing, evolutionary explanations, structure prediction and recognition. Additional biology is given in the context of the problems, including some motivation for disease diagnosis and drug discovery. Open problems are cited with an extensive bibliography, and we o er a guide to getting started in this exciting frontier.

We instance our experience with six public-domain global optimization software products and report comparative computational results obtained on a set of eleven test problems. The techniques used by the software under study include integral global optimization, genetic algorithms, simulated annealing, clustering, random search, continuation, Bayesian, tunneling, and multi-level methods. The test set contains practical problems: least median of squares regression, protein folding, and multidimensional scaling. These include non-dierentiable, and also discontinuous objective functions, some with an exponential number of local minima. The dimension of the search space ranges from 1 to 20. We evaluate the software in view of engineers addressing black box global optimization problems, i.e. problems with an objective function whose explicit form is unknown and whose evaluation is costly. Such an objective function is common in industry. It is for instance given under the form of computer programmes involving a simulation. Key words: Global optimization, software, test problems, black box, direct methods, genetic algorithms, simulated annealing, clustering, non-convex optimization.

. The aim of this paper is to show how evolutionary algorithms can be applied to protein folding prediction. We start reviewing previous similar approaches, that we criticize emphasizing the key issue of representation. A new evolutionary algorithm is described, based on the notion of distance matrix representation, together with a software package that implements it. Finally, experimental results are discussed. 1 Protein folding prediction Proteins are molecules of extraordinary relevance for live beings. They are chains of aminoacids (called also residues) that assume very rich and involved shapes in vivo. The prediction of protein tertiary structure (3D shape) from primary structure (sequence of aminoacids) is a daunting as well as a fundamental task in molecular biology. A large amount of experimental data is available as far as it concerns sequence, and large projects are creating huge amounts of sequence data. But to infer the biological function (the ultimate goal for molecula...

. The recent advances in genetic engineering, high powered computing and global optimization continue to stimulate interest in the area of molecular modeling and protein structure prediction. The goal of these efforts is the ability to correctly predict native protein conformations and the binding interactions of macromolecules. These two problems currently dominate the field of computational chemistry and, through the use of detailed molecular models, they have also greatly influenced research in the area of global optimization. This article examines some aspects related to conformational energy modeling and reviews a variety of global optimization approaches developed for the protein folding and peptide docking problems. 1. Introduction Proteins are undoubtedly the most complex and vital molecules in nature. This complexity arises from an intricate balance of intra- and inter-molecular interactions which define the native three-dimensional structure of the system, and subsequently i...

A global optimization method is described for identifying the global minimum energy conformation, as well as lower and upper bounds on the global minimum conformer of solvated peptides. Potential energy contributions are calculated using the ECEPP/3 force field model. In considering the effects of hydration, two implicit free energy models are compared. One method is based on the calculation of solvent--accessible surface areas, while the other uses information on the solvent--accessible volume of hydration shells. Detailed information on the potential and solvation energy contributions is presented for the terminally blocked single residue peptides. In addition, based on a procedure that allows the exclusion of domains of the (OE, /) space, a number of oligopeptide structure prediction problems are considered, and the role of the solvation model in defining global minimum conformations is addressed. Keywords : Protein folding, Solvation, Global optimization. Current Address: Corpo...

this paper we propose a new methodology of coupled local minimizers (CLM) for solving continuous nonlinear optimization problems. We pose a somewhat similar challenge as for committee networks but within a di#erent and broader context of solving di#erentiable optimization problems. The aim is to (online) combine the results from local optimizers in order to let the ensemble generate a local minimum that is better than the best result obtained from all individual local minimizers. We show how improved local minima can be obtained by having interaction and information exchange between the local search processes. This is realized through state synchronization constraints that are imposed between the local minimizers by incorporating principles of master--slave dynamics. Synchronization theory has been intensively studied within the area of chaotic systems and secure communications [Chen & Dong, 1998; Pecora & Carroll, 1990; Suykens et al., 1996, 1997, 1998; Wu & Chua, 1994]. The CLM method is related to Lagrange programming network approaches for chaos synchronization [Suykens & Vandewalle, 2000], where identical or generalized synchronization constraints are imposed on dynamical systems. CLMs also fit within the framework of Cellular Neural Networks (CNN) [Chua & Roska, 1993; Chua et al., 1995; Chua, 1998]. By considering the objective of minimizing the average cost of an ensemble of local minimizers subject to pairwise synchronization constraints, a continuous-time optimization algorithm is studied according to Lagrange programming networks [Cichocki & Unbehauen, 1994; Zhang & Constantinides, 1992]. The resulting continuoustime optimization algorithm is described by an array of coupled nonlinear cells or a one-dimensional CNN with bidirectional coupling

A philosophically consistent axiomatic approach to classical and quantum mechanics is given. The approach realizes a strong formal implementation of Bohr's correspondence principle. In all instances, classical and quantum concepts are fully parallel: the same general theory has a classical realization and a quantum realization.

In this paper we propose a VNS-based algorithm for the solution of the Molecular Distance Geometry Problem. First, we use VNS to solve a smoothed version of the problem to identify the most promising zone in the solution space. We then use VNS again to solve the original problem restricted to the promising zone. This algorithm often manages to find a solutions having higher accuracy than other methods. This is important as small differences in the objective function value may mean completely different 3D molecular structures.

We discuss the geometrical interpretation of a well-known smoothing operator applied to the Molecular Distance Geometry Problem, and we then describe a heuristic approach based on Variable Neighbourhood Search on the smoothed and original problem. This algorithm often manages to find solutions having higher accuracy than other methods. This is important as small differences in the objective function value may point to completely different 3D molecular structures.