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From whatever domain they come, engineers are faced daily with optimization problems that requires conflicting objectives to be met. This monograph systematically presents several multiobjective optimization methods accompanied by many analytical examples. Each method or definition is clarified, when possible, by an illustration. Multiobjective Optimization treats not only engineering problems, e.g in mechanics, but also problems arising in operations research and management. It explains how to choose the most suitable method to solve a given problem and uses three primary application examples: optimization of the numerical simulation of an industrial process; sizing of a telecommunication network; and decision-aid tools for the sorting of bids. This book is intended for engineering students, and those in applied mathematics, algorithmics, economics (operational research), production management, and computer scientists.

Inhaltsverzeichnis

Frontmatter

Principles of multiobjective optimization methods

Frontmatter

1. Introduction: multiobjective optimization and domination

Abstract
An optimization problem is defined as the search for a minimum or a maximum (the optimum) of a function. We can also find optimization problems for which the variables of the function to be optimized are constrained to evolve in a precisely defined area of the search space. In this case, we have a particular kind of optimization called constrained optimization problem.
Yann Collette, Patrick Siarry

2. Scalar methods

Abstract
This approach to multiobjective optimization problem solving is the most obvious. We also call this method the “naive approach” to multiobjective optimization [Coello 98]. The goal, here, is to transform our problem so that it turns into a mono-objective optimization problem, for which there exist various methods of solution. The simplest way to proceed is to take each objective function, associate a weight with the objective function and then take a weighted sum of objective functions. Hence we obtain a new, unique objective function.
Yann Collette, Patrick Siarry

3. Interactive methods

Abstract
Interactive methods allow the user to find one and only one solution. They belong to the family of progressive methods and allow the decision maker to fine-tune his/her preferences with respect to a tradeoff between objective functions during the running of the optimization method. These methods are to be compared with the following methods:
  • A priori preference methods, where the decision maker chooses the tradeoff to be operated between objective functions before the optimization method is run.
  • A posteriori preference methods, where the decision maker does not choose any tradeoff before the optimization method is run. The optimization method computes all the Pareto optimal solutions, and the decision maker can perform comparisons between these solutions and choose one.
Yann Collette, Patrick Siarry

4. Fuzzy methods

Abstract
In everyday life, everything cannot be described in a binary way. For example, the transition between day and night is progressive; the action of the clutch of a car is progressive too.
Yann Collette, Patrick Siarry

5. Multiobjective methods using metaheuristics

Abstract
Metaheuristics, as stated in the preface, are general optimization methods dedicated to “hard optimization” problem [Sait et al. 99]. These methods are, in general, presented as concepts. As we shall see later, they are sometimes based on ideas that we can find in everyday life. The main metaheuristics are simulated annealing, tabu search and genetic algorithms.
Yann Collette, Patrick Siarry

6. Decision aid methods

Abstract
The methods we have presented so far have been based on the domination relation. This relation (which we can define in various ways: Pareto domination or lexicographic domination, for example) allows us to “filter” elements of a set, and to just keep all the elements we can compare themselves. However, there exists another way to obtain a set of solutions, which is based on the setting up of an order relation between these various elements. With the order relation so defined, we can obtain a set of solutions (with a partial order relation) or one and only one solution (with a complete order relation). The other major difference, with respect to the “classical” multiobjective optimization methods, comes from the fact that the decision aid methods work only on discrete sets of points (“classical” multiobjective optimization methods can work on continuous sets). Moreover, decision aid methods allow us to answer several problems, listed in Table 6.1.
Yann Collette, Patrick Siarry

Evaluation of methods, and criteria for choice of method

Frontmatter

7. Performance measurement

Abstract
To measure the performance of a multiobjective optimization method, we must have some “measurement instruments”. We have mainly used the performance indices presented in [Van Veldhuizen 99].
Yann Collette, Patrick Siarry

8. Test functions for multiobjective optimization methods

Abstract
We have seen that the field of multiobjective optimization is plentiful. The methods we can use are numerous.
Yann Collette, Patrick Siarry

9. An attempt to classify multiobjective optimization methods

Abstract
As we have seen through this book, there exists a huge number of multiobjective optimization methods. This situation is a problem when one has to choose an optimization method to solve a concrete problem. At present, few scientific papers deal with the classification of optimization methods.
Yann Collette, Patrick Siarry

Case studies

Frontmatter

10. Case study 1: qualification of scientific software

Abstract
When we have to program a scientific software package (e.g. [Ascend]) dedicated to the simulation of an industrial process (such as chemical distillation chain or energy production in a nuclear reactor), we cannot take into account all the parameters of the process. Therefore, the engineer must reduce the complexity of the process model so that it can be simulated. The various approximations that have to be made often induce a gap, which may or may not be important, between the results obtained using the simulation and the results obtained via measurements. So we use an “artifice” which allows us to fill the gap: we bias the software so that its results correspond to the measurements. This bias is applied via modification of the parameters of the model.
Yann Collette, Patrick Siarry

11. Case study 2: study of the extension of a telecommunication network

Abstract
A service network is continuously changing its shape. When it first become operational, it is just at its start of its life. The network will evolve in response to the increase in the demand that it must route from one point to another. Its evolution will be driven by the obsolescence of the equipment which makes up the network, and, even more so, by the strategic decisions of the operator that manages the network.
Yann Collette, Patrick Siarry

12. Case study 3: multicriteria decision tools to deal with bids

Abstract
EADS (EADS LV), which is a wholly owned subsidiary of the EADS (European Aeronautic Defence and Space Company) group, which was itself formed from a merger of Daimler Chrysler Aerospace AG (DASA), Construcciones Aeronauticas (CASA) and Aérospatiale Matra on July 10, 2000, has used throughout its life a multicriteria decision model based on the ELECTRE TRI method to decide whether or not to respond to calls for bids. This model had also been used by one of the predecessor organizations of EADS LV since January 1, 1996. The commercial results of the model, which is also used to decide whether or not to make spontaneous commercial offers, are saved in a database. EADS LV makes several hundred commercial offers every year. These offers either are unsolicited or are made in response to calls for bids or via official consultation.
Yann Collette, Patrick Siarry

13. Conclusion

Abstract
As we have seen throughout this book, multiobjective optimization is not an easy task.
Yann Collette, Patrick Siarry

Backmatter

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