Realistic Constrained Multi-Objective Optimization Benchmark Problems from Design

Multi-objective optimization is increasingly used in engineering to design new systems and to identify design trade-offs. Yet, design problems often have objective functions and constraints that are expensive and highly non-linear. Combinations of these features lead to poor convergence and diversity loss with common algorithms that have not been specifically designed for constrained optimization. Constrained benchmark problems exist, but they do not necessarily represent the challenges of engineering problems. In this paper, a framework to design electro-mechanical actuators, called MODAct, is presented and 20 constrained multi-objective optimization test problems are derived from the framework with a specific focus on constraints. The full source code is made available to ease its use. The effects of the constraints are analyzed through their impact on the Pareto front as well as on the convergence performance. A constraint landscape analysis approach is followed and extended with three new metrics to characterize the search and objective spaces. The features of MODAct are compared to existing test suites to highlight the differences. In addition, a convergence analysis using NSGA-II, NSGA-III and C-TAEA on MODAct and existing test suites suggests that the design problems are indeed difficult due to the constraints. In particular, the number of simultaneously violated constraints in newly generated solutions seems key in understanding the convergence challenges. Thus, MODAct offers an efficient framework to analyze and handle constraints in future optimization algorithm design.

Automated Design: A Journey Across Modelling, Optimization, and Education

Cyril Picard

Machine intelligence greatly impacts almost all domains of our societies. It is profoundly changing the field of mechanical engineering with new technical possibilities and processes. The education of future engineers also needs to adapt in terms of techniques and even skills. Using the design of electro-mechanical actuators as a common thread, this work explores the many-facets of automated design: modeling, optimization, and education, and looks for the prerequisites essential to its successful application. The journey starts by building a modular and integrated model. It focuses on the prediction of system-level specifications that yield high added-value for decision-makers and shorten the path from the model to the final product. Combined with multi-objective evolutionary algorithms (MOEAs) and visualization tools, the model forms an automated design tool that helps engineers and decision-makers to rapidly get important insights into their design task. Its potential and benefits are validated through two specific applications. The results, however, also highlight a gap between the reported performance of optimizers on common benchmark problems and the actual performance on these problems. To further develop optimizers, appropriate and realistic benchmark problems are needed. A subset of the integrated design model is used to formulate a new test suite called MODAct, composed of 20 constrained multi-objective optimization problems (CMOPs) with variable levels of complexity. In addition, numerical approaches to evaluate the constraint landscape of CMOPs are introduced and applied to identify the differences in features of MODAct against 45 benchmark problems from literature. Further, the convergence performance of three algorithms on the same problems highlights the key role of constraints and, in particular, the number of simultaneously violated constraints in MODAct problems. In a next step, existing constraint handling strategies suitable for MOEAs along with a newly proposed technique for many-constraint problems are evaluated. Their parameters are tuned for different problems. The performance of the various configurations further highlights the difference between MODAct and other benchmark problems and show the highly competitive results of the proposed constraint handling technique on realistic design problems. As the technical limits are removed, the impact of automated design on the work of future engineers should be considered. On the one hand, the development of professional skills by students working on team project in different settings has been evaluated thanks to 205 students from three classes. Explicitly addressing these skills within the project seems key to support stronger and broader learning, suggesting changes that do not require a full curriculum redesign. On the other hand, nine groups (33 students) have been asked to design an actuator using a conventional approach followed by an automated design approach. The actuators suggested by students using the automated tool outperform the designs obtained through the traditional approach. Six groups even suggest solutions cheaper, three of which are also smaller, than the product of experienced industry engineers. Students proved thus capable of leveraging the tool within a short time. The analysis of their mistakes suggests possible improvements for future tools. As these students leave university, they carry the hope to see such methods spread in industry.

EPFL2021

A practical evolutionary method for the multi-objective optimisation of complex integrated energy systems including vehicle drivetrains

Adam Molyneaux

Concern for the environment has been steadily growing in recent years, and it is becoming more common to include environmental impact and pollution costs in the design problem along with construction, investment and operating costs. To further complicate matters governmental controls on emissions are still changing and the effect of increased emissions taxes may be critical in choosing a particular design solution. Thermo-economic and environmental analysis has been used previously at LENI to model investment, operating and pollution costs and aggregate them into a single objective that can be minimised. This has the drawback of requiring multiple optimisations in order to determine the sensitivity of the optimum solution to the presumed pollution costs. In addition, designers usually prefer a choice of different technological solutions as well as a clear idea of the trade-offs between multiple objectives without the need to define a common indicator (for example cost). Frequently, the thermodynamic and economic simulation of an energy system is non-linear, disjoint and with multiple local optima making it difficult to optimise with derivative based optimisation methods. This work presents the development of a multi-modal, multi-objective optimisation tool to respond to this need, and then demonstrates it on two complex problems – the design of a district heating system and the configuration of an advanced vehicle drivetrain. Multi-objective optimisation techniques aim to find the trade-off between two or more conflicting objectives. For example, if a design must be both efficient and low cost, then a multi-objective optimisation will find a range of solutions between the lowest cost but least efficient solution and the most efficient but most expensive solution, including some solutions that are fairly efficient and reasonable cost. Multi-modal optimisation techniques aim to keep different local optima. The optimisation tool developed here is the clustering pareto evolutionary algorithm (CPEA). As with other evolutionary algorithms (EAs) it works with a population of solutions, each individual representing a different trade-off between objectives. New solutions are produced using real variable crossover and mutation techniques and the population is ranked and thinned to avoid excessively large populations and maintain convergence pressure. The algorithm uses statistical clustering techniques on the independent variables to keep multiple different local optima simultaneously. The clusters maintain diversity in the population and identify local optima. In problems with many variables multi dimensional scaling (MDS) is used to reduce the number of variables before clustering. Applying the CPEA to the problem of designing a district heating system for minimum costs with and without pollution costs, it was possible to repeat previous work in a fraction of the time. For the same effort it was also possible to produce complete trade-off curves for cost and pollution, showing the dramatic change in optimal solution when pollution costs were included. The clustering and in particular the MDS were found to be key factors in the solution of this problem – without them the best overall solution was not found. A three objective problem was solved and the results compared favourably to a combined two objective problem, although convergence was found to be slower. A parallel version of the CPEA was also applied to the optimisation of a vehicle drivetrain simulation with respect to performance, emissions and costs over a test cycle. The multi-modal nature of the CPEA allowed the simultaneous solution of multiple hybrid and conventional solutions at no extra cost and improving overall convergence. The pollution costs calculated using the same level of taxation as in the district heating problem were found to be of little influence compared to the operating and investment costs, suggesting that pollution costs from the energy domain are unlikely to promote hybrid vehicle technology.

EPFL2002

Sensitivity Analysis and Optimization of a Standing Wave Ultrasonic Linear Motor

José Fernandez Lopez, Yves Perriard

This paper presents the sensitivity analysis of an ultrasonic linear motor using design of experiments (DOE) and the finite element (FE) optimization of its deformation amplitude. A first ultrasonic linear motor prototype has been built at the laboratory. A deformation amplitude of about 6.6 /spl mu/m can be obtained by applying a 100 V voltage. The goal is to obtain a bigger deformation amplitude by varying the motor parameters, in particular the vibratory piece dimensions. First of all, a parametrization of the motor structure is carried out. Then, with the aim of reducing the variation ranges of the input parameters - but also to avoid performing a large number of simulations - a preoptimization stage is necessary. Thus, sensitivity analysis is carried out using design of experiments, which is a good way to obtain the influence of the input parameters on the objective function. Factorial designs have been chosen to find out the effects of each input factor but also the effect of their interactions. This method then is compared with Doehlert design technique, which is generally used for optimization approaches. The results show that it is absolutely necessary to take into account the quadratic terms in the model because they represent an important effect. The use of design of experiments revealed to be an interesting way to analyze numerically the ultrasonic motor as a preoptimization stage and already allows one to improve the deformation amplitude but also to reduce the input parameter variation ranges. Different FE optimization methods are then applied, and results show that the deformation amplitude can be increased by a factor higher than 10 compared to the initial design.