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

A hybrid swarm-based algorithm for single-objective optimization problems involving high-cost analyses

In many technical fields, single-objective optimization procedures in continuous domains involve expensive numerical simulations. In this context, an improvement of the Artificial Bee Colony (ABC) algorithm, called the Artificial super-Bee enhanced Colony (AsBeC), is presented. AsBeC is designed to provide fast convergence speed, high solution accuracy and robust performance over a wide range of problems. It implements enhancements of the ABC structure and hybridizations with interpolation strategies. The latter are inspired by the quadratic trust region approach for local investigation and by an efficient global optimizer for separable problems. Each modification and their combined effects are studied with appropriate metrics on a numerical benchmark, which is also used for comparing AsBeC with some effective ABC variants and other derivative-free algorithms. In addition, the presented algorithm is validated on two recent benchmarks adopted for competitions in international conferences. Results show remarkable competitiveness and robustness for AsBeC.Comment: 19 pages, 4 figures, Springer Swarm Intelligenc

A multifidelity multiobjective optimization framework for high-lift airfoils

High-lift devices design is a challenging task as it involves highly complex flow features while being critical for the overall performance of the aircraft. When part of an optimization loop, the computational cost of the Computational Fluid Dynamics becomes increasingly problematic. Methods to reduce the optimization time has been of major interest over the last 50 years. This paper presents a multiobjective multifidelity optimization framework that takes advantage of two approximation levels of the flow equations: a rapid method that provides quick estimates but of relatively low accuracy and a reference method that provides accurate estimations at the cost of a longer run-time. The method uses a sub-optimization, under a trust-region scheme, performed on the low-fidelity model corrected by a surrogate model that is fed by the high-fidelity tool. The size of the trust region is changed according to the accuracy of the corrected model. The multiobjective optimizer is used to set the positions of the ap and slat of a two-dimensional geometry with lift and drag as objectives with an empirical-based method and a Reynolds Averaged Navier-Stokes equations solver. The multifidelity method shows potential for discovering the complete Pareto front, yet it remains less optimal than the Pareto front from the high-fidelity-only optimization

Optimizing radial basis functions by D.C. programming and its use in direct search for global derivative-free optimization

In this paper we address the global optimization of functions subject to bound and linear constraints without using derivatives of the objective function. We investigate the use of derivative-free models based on radial basis functions (RBFs) in the search step of direct-search methods of directional type. We also study the application of algorithms based on difference of convex (d.c.) functions programming to solve the resulting subproblems which consist of the minimization of the RBF models subject to simple bounds on the variables. Extensive numerical results are reported with a test set of bound and linearly constrained problems