Sébastien Le Digabel This work reviews blackbox optimization applications over the last twenty years, addressed using direct search optimization methods. Emphasis is placed on the Mesh Adaptive Direct Search (MADS) derivative-free optimization algorithm. The core of the document describes applications in three specific fields: Energy, materials science, and computational engineering design. Other applications in science and engineering as … Read more
The context of this research is multiobjective optimization where conflicting objectives are present. In this work, these objectives are only available as the outputs of a blackbox for which no derivative information is available. This work proposes a new extension of the mesh adaptive direct search (MADS) algorithm to constrained multiobjective derivative-free optimization. This method … Read more
This work considers the graph partitioning problem known as maximum k-cut. It focuses on investigating features of a branch-and-bound method to efficiently obtain global solutions. An exhaustive experimental study is carried out for two main components of a branch-and-bound algorithm: computing bounds and branching strategies. In particular, we propose the use of a variable neighborhood … Read more
In derivative-free and blackbox optimization, the objective function is often evaluated through the execution of a computer program seen as a blackbox. It can be noisy, in the sense that its outputs are contaminated by random errors. Sometimes, the source of these errors is identified and controllable, in the sense that it is possible to … Read more
We present a stochastic extension of the mesh adaptive direct search (MADS) algorithm originally developed for deterministic blackbox optimization. The algorithm, called StoMADS, considers the unconstrained optimization of an objective function f whose values can be computed only through a blackbox corrupted by some random noise following an unknown distribution. The proposed method is based … Read more
The performance of deep neural networks is highly sensitive to the choice of the hyperparameters that define the structure of the network and the learning process. When facing a new application, tuning a deep neural network is a tedious and time consuming process that is often described as a “dark art”. This explains the necessity … Read more
Computational speed and global optimality are key needs for practical algorithms for the optimal power flow problem. Two convex relaxations offer a favorable trade-off between the standard second-order cone and the standard semidefinite relaxations for large-scale meshed networks in terms of optimality gap and computation time: the tight-and-cheap relaxation (TCR) and the quadratic convex relaxation … Read more
In demand–response programs, aggregators balance the needs of generation companies and end-users. This work proposes a two-phase framework that shaves the aggregated peak loads while maintaining the desired comfort level for users. In the first phase, the users determine their planned consumption. For the second phase, we develop a bilevel model with mixed-integer variables and … Read more
Smart homes have the potential to achieve efficient energy consumption: households can profit from appropriately scheduled consumption. By 2020, 35% of all households in North America and 20% in Europe are expected to become smart homes. Developing a smart home requires considerable investment, and the householders expect a positive return. In this context, we address … Read more
In recent years, the development of new algorithms for multiobjective optimization has considerably grown. A large number of performance indicators has been introduced to measure the quality of Pareto front approximations produced by these algorithms. In this work, we propose a review of a total of 63 performance indicators partitioned into four groups according to … Read more