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Publication# Multi-objective optimisation applied to industrial energy problems

Abstract

This thesis presents the development of a new multi-objective optimisation tool and applies it to a number of industrial problems related to optimising energy systems. Multi-objective optimisation techniques provide the information needed for detailed analyses of design trade-offs between conflicting objectives. For example, if a product must be both inexpensive and high quality, the multi-objective optimiser will provide a range of optimal options from the cheapest (but lowest quality) alternative to the highest quality (but most expensive), and a range of designs in between – those that are the most interesting to the decision-maker. The optimisation tool developed is the queueing multi-objective optimiser (QMOO), an evolutionary algorithm (EA). EAs are particularly suited to multi-objective optimisation because they work with a population of potential solutions, each representing a different trade-off between objectives. EAs are ideal to energy system optimisation because problems from that domain are often non-linear, discontinuous, disjoint, and multi-modal. These features make energy system optimisation problems difficult to resolve with other optimisation techniques. QMOO has several features that improve its performance on energy systems problems – features that are applicable to a wide range of optimisation problems. QMOO uses cluster analysis techniques to identify separate local optima simultaneously. This technique preserves diversity and helps convergence to difficult-to-find optima. Once normal dominance relations no longer discriminate sufficiently between population members certain individuals are chosen and removed from the population. Careful choice of the individuals to be removed ensures that convergence continues throughout the optimisation. Preserving of the "tail regions" of the population helps the algorithm to explore the full extent of the problem's optimal regions. QMOO is applied to a number of problems: coke factory placement in Shanxi Province, China; choice of heat recovery system operating temperatures; design of heat-exchanger networks; hybrid vehicle configuration; district heating network design, and others. Several of the problems were optimised previously using single-objective EAs. QMOO proved capable of finding entire ranges of solutions faster than the earlier methods found a single solution. In most cases, QMOO successfully optimises the problems without requiring any specific tuning to each problem. QMOO is also tested on a number of test problems found in the literature. QMOO's techniques for improving convergence prove effective on these problems, and its non-tuned performance is excellent compared to other algorithms found in the literature.

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Algorithm

In mathematics and computer science, an algorithm (ˈælɡərɪðəm) is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algo

Mathematical optimization

Mathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternative

Genetic algorithm

In computer science and operations research, a genetic algorithm (GA) is a metaheuristic inspired by the process of natural selection that belongs to the larger class of evolutionary algorithms (EA)

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We have developed a new derivative-free algorithm based on Radial Basis Functions (RBFs). Derivative-free optimization is an active field of research and several algorithms have been proposed recently. Problems of this nature in the industrial setting are quite frequent. The reason is that in a number of applications the optimization process contains simulation packages which are treated as black boxes. The development of our own algorithm was originally motivated by an application in biomedical imaging: the medical image registration problem. The particular characteristics of this problem have incited us to develop a new optimization algorithm based on trust-region methods. However it has been designed to be generic and to be applied to a wide range of problems. The main originality of our approach is the use of RBFs to build the models. In particular we have adapted the existing theory based on quadratic models to our own models and developed new procedures especially designed for models based on RBFs. We have tested our algorithm called BOOSTERS against state-of-the-art methods (UOBYQA, NEWUOA, DFO). On the medical image registration problem, BOOSTERS appears to be the method of choice. The tests on problems from the CUTEr collection show that BOOSTERS is comparable to, but not better than other methods on small problems (size 2-20). It is performing very well for medium size problems (20-80). Moreover, it is able to solve problems of dimension 200, which is considered very large in derivative-free optimization. We have also developed a new class of algorithms combining the robustness of derivative-free algorithms with the faster rate of convergence characterizing Newtonlike-methods. In fact, they define a new class of algorithms lying between derivative-free optimization and quasi-Newton methods. These algorithms are built on the skeleton of our derivative-free algorithm but they can incorporate the gradient when it is available. They can be interpreted as a way of doping derivative-free algorithms with derivatives. If the derivatives are available at each iteration, then our method can be seen as an alternative to quasi-Newton methods. At the opposite, if the derivatives are never evaluated, then the algorithm is totally similar to BOOSTERS. It is a very interesting alternative to existing methods for problems whose objective function is expensive to evaluate and when the derivatives are not available. In this situation, the gradient can be approximated by finite differences and its costs corresponds to n additional function evaluations assuming that Rn is the domain of definition of the objective function. We have compared our method with CFSQP and BTRA, two gradient-based algorithms, and the results show that our doped method performs best. We have also a theoretical analysis of the medical image registration problem based on maximization of mutual information. Most of the current research in this field is concentrated on registration based on nonlinear image transformation. However, little attention has been paid to the theoretical properties of the optimization problem. In our analysis, we focus on the continuity and the differentiability of the objective function. We show in particular that performing a registration without extension of the reference image may lead to discontinuities in the objective function. But we demonstrate that, under some mild assumptions, the function is differentiable almost everywhere. Our analysis is important from an optimization point of view and conditions the choice of a solver. The usual practice is to use generic optimization packages without worrying about the differentiability of the objective function. But the use of gradient-based methods when the objective function is not differentiable may result in poor performance or even in absence of convergence. One of our objectives with this analysis is also that practitioners become aware of these problems and to propose them new algorithms having a potential interest for their applications.

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.

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.