Sébastien Le Digabel

Problem Formulations for Simulation-based Design Optimization using Statistical Surrogates and Direct Search

Categories Applications - Science and Engineering, Constrained Nonlinear Optimization, Nonsmooth Optimization

Typical challenges of simulation-based design optimization include unavailable gradients and unreliable approximations thereof, expensive function evaluations, numerical noise, multiple local optima and the failure of the analysis to return a value to the optimizer. One possible remedy to alleviate these issues is to use surrogate models in lieu of the computational models or simulations and … Read more

Reducing the Number of Function Evaluations in Mesh Adaptive Direct Search Algorithms

Categories Constrained Nonlinear Optimization, Nonsmooth Optimization Tags , , ,

The mesh adaptive direct search (MADS) class of algorithms is designed for nonsmooth optimization, where the objective function and constraints are typically computed by launching a time-consuming computer simulation. Each iteration of a MADS algorithm attempts to improve the current best-known solution by launching the simulation at a finite number of trial points. Common implementations … Read more

The mesh adaptive direct search algorithm with treed Gaussian process surrogates

Categories Constrained Nonlinear Optimization, Nonsmooth Optimization Tags , , ,

This work introduces the use of the treed Gaussian process (TGP) as a surrogate model within the mesh adaptive direct search (MADS) framework for constrained blackbox optimization. It extends the surrogate management framework (SMF) to nonsmooth optimization under general constraints. MADS uses TGP in two ways: one, as a surrogate for blackbox evaluations; and two, … Read more

Snow water equivalent estimation using blackbox optimization

Categories Applications - Science and Engineering, Constrained Nonlinear Optimization, Nonsmooth Optimization Tags , , , ,

Accurate measurements of snow water equivalent (SWE) is an important factor in managing water resources for hydroelectric power generation. SWE over a catchment area may be estimated via kriging on measures obtained by snow monitoring devices positioned at strategic locations. The question studied in this paper is to find the device locations that minimize the … Read more

Use of quadratic models with mesh adaptive direct search for constrained black box optimization

Categories Constrained Nonlinear Optimization, Nonsmooth Optimization Tags , , ,

We consider a derivative-free optimization, and in particular black box optimization, where the functions to be minimized and the functions representing the constraints are given by black boxes without derivatives. Two fundamental families of methods are available: model-based methods and directional direct search algorithms. This work exploits the flexibility of the second type of methods … Read more

Calculating optimal conditions for alloy and process design using thermodynamic and property databases, the FactSage software and the Mesh Adaptive Direct Search algorithm

Categories Applications - Science and Engineering

During alloy and process design, it is often desired to identify regions of design or process variables for which certain calculated functions have optimal values under various constraints, for example: compositions of minimum liquidus temperature in an N-component alloy; compositions where the amount of precipitate in a given phase is maximized or minimized during annealing … Read more

Calculating all local minima on liquidus surfaces using the FactSage software and databases and the Mesh Adaptive Direct Search algorithm

Categories Applications - Science and Engineering

It is often of interest, for a multicomponent system, to identify the low melting compositions at which local minima of the liquidus surface occur. The experimental determination of these minima can be very time-consuming. An alternative is to employ the CALPHAD approach using evaluated thermodynamic databases containing optimized model parameters giving the thermodynamic properties of … Read more

Trade-off studies in blackbox optimization

Categories Applications - OR and Management Sciences, Constrained Nonlinear Optimization

This paper proposes a framework for trade-off analyses of blackbox constrained optimization problems. Two strategies are developed to show the trade-off of the optimal objective function value with tightening or loosening general constraints. These are a simple method which may be performed immediately after a single optimization and a detailed method performing biobjective optimization on … Read more

The mesh adaptive direct search algorithm for periodic variables

Categories Applications - OR and Management Sciences, Convex and Nonsmooth Optimization Tags , , , ,

This work analyzes constrained black box optimization in which the functions defining the problem are periodic with respect to some or all the variables. We show that the natural strategy of mapping trial points into the interval defined by the period in the Mesh Adaptive Direct Search (MADS) framework can be easily done in practice, … Read more

Algorithm 909: NOMAD: Nonlinear Optimization with the MADS algorithm

Categories Applications - OR and Management Sciences, Optimization Software and Modeling Systems Tags , , , ,

NOMAD is software that implements the MADS algorithm (Mesh Adaptive Direct Search) for black-box optimization under general nonlinear constraints. Blackbox optimization is about optimizing functions that are usually given as costly programs with no derivative information and no function values returned for a significant number of calls attempted. NOMAD is designed for such problems and … Read more