MATSuMoTo: The MATLAB Surrogate Model Toolbox For Computationally Expensive Black-Box Global Optimization Problems

MATSuMoTo is the MATLAB Surrogate Model Toolbox for computationally expensive, black-box, global optimization problems that may have continuous, mixed-integer, or pure integer variables. Due to the black-box nature of the objective function, derivatives are not available. Hence, surrogate models are used as computationally cheap approximations of the expensive objective function in order to guide the search for improved solutions. Due to the computational expense of doing a single function evaluation, the goal is to find optimal solutions within very few expensive evaluations. The multimodality of the expensive black-box function requires an algorithm that is able to search locally as well as globally. MATSuMoTo is able to address these challenges. MATSuMoTo offers various choices for surrogate models and surrogate model mixtures, initial experimental design strategies, and sampling strategies. MATSuMoTo is able to do several function evaluations in parallel by exploiting MATLAB's Parallel Computing Toolbox.Comment: 13 pages, 7 figure

PhysicsGP: A Genetic Programming Approach to Event Selection

We present a novel multivariate classification technique based on Genetic Programming. The technique is distinct from Genetic Algorithms and offers several advantages compared to Neural Networks and Support Vector Machines. The technique optimizes a set of human-readable classifiers with respect to some user-defined performance measure. We calculate the Vapnik-Chervonenkis dimension of this class of learning machines and consider a practical example: the search for the Standard Model Higgs Boson at the LHC. The resulting classifier is very fast to evaluate, human-readable, and easily portable. The software may be downloaded at: http://cern.ch/~cranmer/PhysicsGP.htmlComment: 16 pages 9 figures, 1 table. Submitted to Comput. Phys. Commu

Metamodelling of multivariable engine models for real-time flight simulation.

Sophisticated real-time distributed flight simulation environments may be constructed from a wide range of modelling and simulation tools. In this way accuracy, detail and model flexibility may be incorporated into the simulator. Distributed components may be constructed by a wide range of methods, from high level environments such as Matlab, through coded environments such as C or Fortran to hardware-in-the- loop. In this paper the Response Surface Methodology is combined with a hyper-heuristic (evolutionary algorithm) and applied to the representation of computationally intensive non-linear multivariable engine modelling. The paper investigates the potential for metamodelling (models of models) dynamic models which were previously too slow to be included in multi-component, high resolution real-time simulation environments. A multi-dimensional gas turbine model with five primary control inputs, six environmental inputs and eleven outputs is considered. An investigation has been conducted to ascertain to what extent these systems can be approximated by response surfaces with experiments which have been designed by hyper-heuristics as a first step towards automatic modelling methodology

Aerodynamic Optimization of High-Speed Trains Nose using a Genetic Algorithm and Artificial Neural Network

An aerodynamic optimization of the train aerodynamic characteristics in term of front wind action sensitivity is carried out in this paper. In particular, a genetic algorithm (GA) is used to perform a shape optimization study of a high-speed train nose. The nose is parametrically defined via Bézier Curves, including a wider range of geometries in the design space as possible optimal solutions. Using a GA, the main disadvantage to deal with is the large number of evaluations need before finding such optimal. Here it is proposed the use of metamodels to replace Navier-Stokes solver. Among all the posibilities, Rsponse Surface Models and Artificial Neural Networks (ANN) are considered. Best results of prediction and generalization are obtained with ANN and those are applied in GA code. The paper shows the feasibility of using GA in combination with ANN for this problem, and solutions achieved are included

Polynomial-Chaos-based Kriging

Computer simulation has become the standard tool in many engineering fields for designing and optimizing systems, as well as for assessing their reliability. To cope with demanding analysis such as optimization and reliability, surrogate models (a.k.a meta-models) have been increasingly investigated in the last decade. Polynomial Chaos Expansions (PCE) and Kriging are two popular non-intrusive meta-modelling techniques. PCE surrogates the computational model with a series of orthonormal polynomials in the input variables where polynomials are chosen in coherency with the probability distributions of those input variables. On the other hand, Kriging assumes that the computer model behaves as a realization of a Gaussian random process whose parameters are estimated from the available computer runs, i.e. input vectors and response values. These two techniques have been developed more or less in parallel so far with little interaction between the researchers in the two fields. In this paper, PC-Kriging is derived as a new non-intrusive meta-modeling approach combining PCE and Kriging. A sparse set of orthonormal polynomials (PCE) approximates the global behavior of the computational model whereas Kriging manages the local variability of the model output. An adaptive algorithm similar to the least angle regression algorithm determines the optimal sparse set of polynomials. PC-Kriging is validated on various benchmark analytical functions which are easy to sample for reference results. From the numerical investigations it is concluded that PC-Kriging performs better than or at least as good as the two distinct meta-modeling techniques. A larger gain in accuracy is obtained when the experimental design has a limited size, which is an asset when dealing with demanding computational models

Genetic optimization of training sets for improved machine learning models of molecular properties

The training of molecular models of quantum mechanical properties based on statistical machine learning requires large datasets which exemplify the map from chemical structure to molecular property. Intelligent a priori selection of training examples is often difficult or impossible to achieve as prior knowledge may be sparse or unavailable. Ordinarily representative selection of training molecules from such datasets is achieved through random sampling. We use genetic algorithms for the optimization of training set composition consisting of tens of thousands of small organic molecules. The resulting machine learning models are considerably more accurate with respect to small randomly selected training sets: mean absolute errors for out-of-sample predictions are reduced to ~25% for enthalpies, free energies, and zero-point vibrational energy, to ~50% for heat-capacity, electron-spread, and polarizability, and by more than ~20% for electronic properties such as frontier orbital eigenvalues or dipole-moments. We discuss and present optimized training sets consisting of 10 molecular classes for all molecular properties studied. We show that these classes can be used to design improved training sets for the generation of machine learning models of the same properties in similar but unrelated molecular sets.Comment: 9 pages, 6 figure