### 1 — 14:00 — Optimization under hidden constraints and its application to the robust design of wind turbines

The robust design optimization of offshore wind turbines generally requires numerous computationally expensive code simulations associated to the input values of both design variables and environmental wind load variables. However, the simulators encounter simulation crashes due to convergence issues for some values of the environmental and design inputs. These failures correspond to a hidden constraint (not known in advance by the user) and might be as costly to evaluate as a feasible simulation. The latter failures must be used in a wise way to target feasible input areas and thus to avoid unnecessary costly simulation failure during the robust optimization iterations. Therefore, we propose a methodology for derivative-free optimization in the presence of hidden constraints learned with a Gaussian Process Classifier. We also propose an enhanced strategy based on an enrichment criterion focused on improving the classifier when it is useful for optimization convergence. We will present our methodology and different algorithms benchmarks in the presence of simulation crashes on toy problems and a wind turbine design application.

### 2 — 14:30 — Black-box optimization for the design of a jet plate for impingement cooling

In this talk, we present an industrial application that exploits black-box optimization in the design of a cooling system for a nozzle in a gas turbine. We describe a black-box function that simulates an impingement cooling system starting from a well-known model that correlates the design features of the cooling system with efficiency parameters. Then we provide a definition of the constrained optimization problem and a solver based on the Brute Force Optimizer. Finally, we show the effectiveness of the proposed strategy on test cases of practical interest.

### 3 — 15:00 — Blackbox optimization for origami-inspired multistable structures

Multistable mechanical systems exhibit more than one stable configuration where the elastic energy is locally minimized. To realize such systems, the art of origami has been proposed as a versatile platform to design deployable structures with both compact and functional stable states. Conceptually, a multistable origami motif is constructed of two-dimensional surfaces connected by one-dimensional fold lines. This leads to stable configurations exhibiting zero-energy local minima. Physically, origami-inspired structures are three-dimensional, comprising facets and hinges fabricated in a distinct stable state where residual stresses are minimized. This leads to the dominance of one stable state over others. To improve mechanical performance, one can solve the constrained optimization problem of maximizing the multistability of origami structures, defined as the amount of elastic energy required to switch between stable states, while ensuring materials used for the facets and hinges remain within their elastic regime. In this study, the Mesh Adaptive Direct Search (MADS) algorithm, a blackbox optimization technique, is used to solve the optimization problem. Initially, the bistable waterbomb-base origami motif is selected as a case-study to present the methodology. The elastic energy of this origami pattern under deployment is calculated via Finite Element (FE) simulations which serve as the blackbox in the MADS optimization loop. To validate the results, optimized waterbomb-base geometries are built via Fused Filament Fabrication and their response under loading is characterized experimentally on a Uniaxial Test Machine. The methodology is then extended to more complex origami patterns, such as the Kresling cylinder, as well as functional origami-inspired structures, including deployable shelters and multi-modal robotic arms. Ultimately, our method offers a general framework for optimizing multistability in mechanical systems, presenting opportunities for advancement across various engineering applications.

### 4 — 15:30 — Convex optimization of vertical alignment of roads

The road design problem is split between corridor selection, horizontal alignment (computing a satellite view of the road), vertical alignment (where to cut and where to fill to obtain a vertical profile of the road), and earthwork (what material to move from which section to what section). The vertical alignment problem consists in minimizing the road construction costs under regulatory and safety constraints. The variables include the amount of material to cut or fill at each section, and where to move materials from sections to sections. The problem may be solved as part of a 3D alignment optimization problem as a nonlinear discontinuous optimization problem usually tackled with heuristics (genetic algorithms, particle swarm...). When the horizontal alignment is fixed, for example when an existing road needs to be renovated, only the vertical alignment is optimized. In that case, the problem becomes a mixed-integer linear program.

We will present two approaches that result in a convex optimization problem. The first one computes side-slope angles to estimate volumes using trapezoids. The volumes are the limit of volumes computed using a mixed-integer linear programming model when the number of slabs tends to infinity. Unfortunately, the convexity of this model breaks down when multiple materials are considered. The second convex optimization model can handle multiple materials by directly approximating the side slope areas using a quadratic regression model. Both models are convex quadratically constrained quadratic programs solved by CPLEX or Gurobi.