Functional Generative Design: An Evolutionary Approach to 3D-Printing

Consumer-grade printers are widely available, but their ability to print complex objects is limited. Therefore, new designs need to be discovered that serve the same function, but are printable. A representative such problem is to produce a working, reliable mechanical spring. The proposed methodology for discovering solutions to this problem consists of three components: First, an effective search space is learned through a variational autoencoder (VAE); second, a surrogate model for functional designs is built; and third, a genetic algorithm is used to simultaneously update the hyperparameters of the surrogate and to optimize the designs using the updated surrogate. Using a car-launcher mechanism as a test domain, spring designs were 3D-printed and evaluated to update the surrogate model. Two experiments were then performed: First, the initial set of designs for the surrogate-based optimizer was selected randomly from the training set that was used for training the VAE model, which resulted in an exploitative search behavior. On the other hand, in the second experiment, the initial set was composed of more uniformly selected designs from the same training set and a more explorative search behavior was observed. Both of the experiments showed that the methodology generates interesting, successful, and reliable spring geometries robust to the noise inherent in the 3D printing process. The methodology can be generalized to other functional design problems, thus making consumer-grade 3D printing more versatile.Comment: 8 pages, 12 figures, GECCO'1

Constraint Handling in Efficient Global Optimization

This is the author accepted manuscript. The final version is available from ACM via the DOI in this record.Real-world optimization problems are often subject to several constraints which are expensive to evaluate in terms of cost or time. Although a lot of effort is devoted to make use of surrogate models for expensive optimization tasks, not many strong surrogate-assisted algorithms can address the challenging constrained problems. Efficient Global Optimization (EGO) is a Kriging-based surrogate-assisted algorithm. It was originally proposed to address unconstrained problems and later was modified to solve constrained problems. However, these type of algorithms still suffer from several issues, mainly: (1) early stagnation, (2) problems with multiple active constraints and (3) frequent crashes. In this work, we introduce a new EGO-based algorithm which tries to overcome these common issues with Kriging optimization algorithms. We apply the proposed algorithm on problems with dimension d ≤ 4 from the G-function suite [16] and on an airfoil shape example.This research was partly funded by Tekes, the Finnish Funding Agency for Innovation (the DeCoMo project), and by the Engineering and Physical Sciences Research Council [grant numbers EP/N017195/1, EP/N017846/1]

Advances in Bayesian Optimization with Applications in Aerospace Engineering

Optimization requires the quantities of interest that define objective functions and constraints to be evaluated a large number of times. In aerospace engineering, these quantities of interest can be expensive to compute (e.g., numerically solving a set of partial differential equations), leading to a challenging optimization problem. Bayesian optimization (BO) is a class of algorithms for the global optimization of expensive-to-evaluate functions. BO leverages all past evaluations available to construct a surrogate model. This surrogate model is then used to select the next design to evaluate. This paper reviews two recent advances in BO that tackle the challenges of optimizing expensive functions and thus can enrich the optimization toolbox of the aerospace engineer. The first method addresses optimization problems subject to inequality constraints where a finite budget of evaluations is available, a common situation when dealing with expensive models (e.g., a limited time to conduct the optimization study or limited access to a supercomputer). This challenge is addressed via a lookahead BO algorithm that plans the sequence of designs to evaluate in order to maximize the improvement achieved, not only at the next iteration, but once the total budget is consumed. The second method demonstrates how sensitivity information, such as gradients computed with adjoint methods, can be incorporated into a BO algorithm. This algorithm exploits sensitivity information in two ways: first, to enhance the surrogate model, and second, to improve the selection of the next design to evaluate by accounting for future gradient evaluations. The benefits of the two methods are demonstrated on aerospace examples

Rank-Based Learning and Local Model Based Evolutionary Algorithm for High-Dimensional Expensive Multi-Objective Problems

Surrogate-assisted evolutionary algorithms have been widely developed to solve complex and computationally expensive multi-objective optimization problems in recent years. However, when dealing with high-dimensional optimization problems, the performance of these surrogate-assisted multi-objective evolutionary algorithms deteriorate drastically. In this work, a novel Classifier-assisted rank-based learning and Local Model based multi-objective Evolutionary Algorithm (CLMEA) is proposed for high-dimensional expensive multi-objective optimization problems. The proposed algorithm consists of three parts: classifier-assisted rank-based learning, hypervolume-based non-dominated search, and local search in the relatively sparse objective space. Specifically, a probabilistic neural network is built as classifier to divide the offspring into a number of ranks. The offspring in different ranks uses rank-based learning strategy to generate more promising and informative candidates for real function evaluations. Then, radial basis function networks are built as surrogates to approximate the objective functions. After searching non-dominated solutions assisted by the surrogate model, the candidates with higher hypervolume improvement are selected for real evaluations. Subsequently, in order to maintain the diversity of solutions, the most uncertain sample point from the non-dominated solutions measured by the crowding distance is selected as the guided parent to further infill in the uncertain region of the front. The experimental results of benchmark problems and a real-world application on geothermal reservoir heat extraction optimization demonstrate that the proposed algorithm shows superior performance compared with the state-of-the-art surrogate-assisted multi-objective evolutionary algorithms. The source code for this work is available at https://github.com/JellyChen7/CLMEA

Methods for constrained optimization of expensive mixed-integer multi-objective problems, with application to an internal combustion engine design problem

Engineering design optimization problems increasingly require computationally expensive high-fidelity simulation models to evaluate candidate designs. The evaluation budget may be small, limiting the effectiveness of conventional multi-objective evolutionary algorithms. Bayesian optimization algorithms (BOAs) are an alternative approach for expensive problems but are underdeveloped in terms of support for constraints and non-continuous design variables—both of which are prevalent features of real-world design problems. This study investigates two constraint handling strategies for BOAs and introduces the first BOA for mixed-integer problems, intended for use on a real-world engine design problem. The new BOAs are empirically compared to their closest competitor for this problem—the multi-objective evolutionary algorithm NSGA-II, itself equipped with constraint handling and mixed-integer components. Performance is also analysed on two benchmark problems which have similar features to the engine design problem, but are computationally cheaper to evaluate. The BOAs offer statistically significant convergence improvements of between 5.9% and 31.9% over NSGA-II across the problems on a budget of 500 design evaluations. Of the two constraint handling methods, constrained expected improvement offers better convergence than the penalty function approach. For the engine problem, the BOAs identify improved feasible designs offering 36.4% reductions in nitrogen oxide emissions and 2.0% reductions in fuel consumption when compared to a notional baseline design. The use of constrained mixed-integer BOAs is recommended for expensive engineering design optimization problems

Surrogate-assisted multiobjective optimization based on decomposition

International audienceA number of surrogate-assisted evolutionary algorithms are being developed for tackling expensive multiobjective optimization problems. On the one hand, a relatively broad range of techniques from both machine learning and multiobjective optimization can be combined for this purpose. Diferent taxonomies exist in order to better delimit the design choices, advantages and drawbacks of existing approaches. On the other hand, assessing the relative performance of a given approach is a diicult task, since it depends on the characteristics of the problem at hand. In this paper, we focus on surrogate-assisted approaches using objective space decomposition as a core component. We propose a reined and ine-grained classiication, ranging from EGO-like approaches to iltering or pre-screening. More importantly, we provide a comprehensive comparative study of a representative selection of state-of-the-art methods , together with simple baseline algorithms. We rely on selected benchmark functions taken from the bbob-biobj benchmarking test suite, that provides a variable range of objective function diiculties. Our empirical analysis highlights the efect of the available budget on the relative performance of each approach, and the impact of the training set and of the machine learning model construction on both solution quality and runtime eiciency