2022 Optimization Days
HEC Montréal, Québec, Canada, 16 — 18 May 2022
WA8 - Derivative-free and Blackbox Optimization IV
May 18, 2022 10:30 AM – 12:10 PM
Location: METRO INC. (yellow)
Chaired by Charles Audet
10:30 AM - 10:55 AM
Stiffness optimization of orthopedic insoles for flat feet
We will present an optimization of the mechanical properties of a 3D printed orthopedic insole. The main objective is to provide comfortable walking for a patient with flat feet condition. Finite element simulation and derivative-free optimization algorithm were employed to design such an orthopedic insole.
10:55 AM - 11:20 AM
Optimization of Stochastic Epidemiological Models for Disease Control and Prediction
Infectious disease modeling relies on describing the complex human social interactions that govern its spread. Epidemiological models must make assumptions about social interactions that occur between individuals resulting in uncertainty in the predicted pandemic trajectories. Policy makers must rely on the forecasts of these models to guide their decision-making and interfere as necessary to keep the disease in the endemic phase. Decision-making involving such models can be challenging due to the uncertainty involved. We present an epidemiological agent-based model that describes the uncertainty in human social networks by means of agents whose behavior is governed by probabilistic models. We show a first application of the stochastic mesh adaptive direct search (StoMADS) algorithm for derivative-free optimization of noisy black-boxes such as agent-based models and use it to guide decision-making for optimal public health policies that balance socio-economic impact with infection incidence.
11:20 AM - 11:45 AM
Monotonic grey box direct search optimization
We are interested in blackbox optimization for which the user is aware of monotonic behaviour of some constraints defining the problem. That is, when increasing a variable, the user is able to predict if a function increases or decreases, but is unable to quantify the amount by which it varies. We refer to this type of problems as ``monotonic grey box'' optimization problems. Our objective is to develop an algorithmic mechanism that exploits this monotonic information to find a feasible solution as quickly as possible. With this goal in mind, we have built a theoretical foundation through a thorough study of monotonicity on cones of multivariate functions. We introduce a trend matrix and a trend direction to guide the Mesh Adaptive Direct Search (Mads) algorithm when optimizing a monotonic grey box optimization problem. Different strategies are tested on a some analytical test problems, and on a real hydroelectric dam optimization problem.