Dieses reich bebilderte Sachbuch bietet einen einfachen, aber fundierten Einblick in das Gebiet der Informatik und erklärt Schritt für Schritt, wie Computer und Internet funktionieren. In 18 Kapiteln werden die Schlüsselbegriffe der Computertechnologie erläutert.

URL http://www.sciencemag.org/cgi/content/abstract/303/5659/799. [2] D. Heckerman, D. Geiger, and D. M. Chickering. Learning Bayesian net-

ABSTRACT Recently, there has been a large interest in set‐based evolutionary algorithms for multi objective optimization. They are based on the definition of indicators that characterize the quality of the current population while being compliant with the concept of Pareto‐optimality. It has been shown that the hypervolume indicator, which measures the dominated volume in the objective space, enables the design of efficient search algorithms and, at the same time, opens up opportunities to express user preferences in the search by means of weight functions. The present paper contains the necessary theoretical foundations and corresponding algorithms to (i) select appropriate weight functions, to (ii) transform user preferences into weight functions and to (iii) efficiently evaluate the weighted hypervolume indicator through Monte Carlo sampling. The algorithm W‐HypE , which implements the previous concepts, is introduced, and the effectiveness of the search, directed towards the user's preferred solutions, is shown using an extensive set of experiments including the necessary statistical performance assessment. Copyright © 2013 John Wiley & Sons, Ltd.

This report documents the programme and outcomes of the Dagstuhl Seminar 12041 Learning in Multiobjective Optimization . The purpose of the seminar was to bring together researchers from the two main communities studying multiobjective optimization, Multiple Criteria Decision Making and Evolutionary Multiobjective Optimization, to take part in a wide-ranging discussion of what constitutes learning in multiobjective optimization, how it can be facilitated, and how it can be measured. The outcome was a deeper, more integrated understanding of the whole problem-solving process in multiobjective optimization from the viewpoint of learning, and several concrete research projects directly addressing different aspects of learning. Seminar

This report documents the programme and outcomes of the Dagstuhl Seminar 12041 Learning in Multiobjective Optimization. The purpose of the seminar was to bring together researchers from the two main communities studying multiobjective optimization, Multiple Criteria Decision Making and Evolutionary Multiobjective Optimization, to take part in a wide-ranging discussion of what constitutes learning in multiobjective optimization, how it can be facilitated, and how it can be measured. The outcome was a deeper, more integrated understanding of the whole problem-solving process in multiobjective optimization from the viewpoint of learning, and several concrete research projects directly addressing different aspects of learning.

Many optimization problems are multiobjective in nature in the sense that multiple, conflicting criteria need to be optimized simultaneously. Due to the conflict between objectives, usually, no single optimal solution exists. Instead, the optimum corresponds to a set of so-called Pareto-optimal solutions for which no other solution has better function values in all objectives. Evolutionary Multiobjective Optimization (EMO) algorithms are widely used in practice for solving multiobjective optimization problems due to several reasons. As randomized blackbox algorithms, EMO approaches allow to tackle problems with nonlinear, nondifferentiable, or noisy objective functions. As set-based algorithms, they allow to compute or approximate the full set of Pareto-optimal solutions in one algorithm run---opposed to classical solution-based techniques from the multicriteria decision making (MCDM) field. Using EMO approaches in practice has two other advantages: they allow to learn about a problem formulation, for example, by automatically revealing common design principles among (Pareto-optimal) solutions (innovization) and it has been shown that certain single-objective problems become easier to solve with randomized search heuristics if the problem is reformulated as a multiobjective one (multiobjectivization). This tutorial aims at giving a broad introduction to the EMO field and at presenting some of its recent research results in more detail. More specifically, I am going to (i) introduce the basic principles of EMO algorithms in comparison to classical solution-based approaches, (ii) show a few practical examples which motivate the use of EMO in terms of the mentioned innovization and multiobjectivization principles, and (iii) present a general overview of state-of-the-art algorithms and techniques. Moreover, I will present some of the most important research results in areas such as indicator-based EMO, preference articulation, and performance assessment. Though classified as advanced, this tutorial is intended for both novices and regular users of EMO. Those without any knowledge will learn about the foundations of multiobjective optimization and the basic working principles of state-of-the-art EMO algorithms. Open questions, presented throughout the tutorial, can serve for all participants as a starting point for future research and/or discussions during the conference.

In the field of evolutionary multi-criterion optimization, the hypervolume indicator is the only single set quality measure that is known to be strictly monotonic with regard to Pareto dominance: whenever a Pareto set approximation entirely dominates another one, then the indicator value of the dominant set will also be better. This property is of high interest and relevance for problems involving a large number of objective functions. However, the high computational effort required for hypervolume calculation has so far prevented the full exploitation of this indicator's potential; current hypervolume-based search algorithms are limited to problems with only a few objectives. This paper addresses this issue and proposes a fast search algorithm that uses Monte Carlo simulation to approximate the exact hypervolume values. The main idea is not that the actual indicator values are important, but rather that the rankings of solutions induced by the hypervolume indicator. In detail, we present HypE, a hypervolume estimation algorithm for multi-objective optimization, by which the accuracy of the estimates and the available computing resources can be traded off; thereby, not only do many-objective problems become feasible with hypervolume-based search, but also the runtime can be flexibly adapted. Moreover, we show how the same principle can be used to statistically compare the outcomes of different multi-objective optimizers with respect to the hypervolume—so far, statistical testing has been restricted to scenarios with few objectives. The experimental results indicate that HypE is highly effective for many-objective problems in comparison to existing multi-objective evolutionary algorithms. HypE is available for download at http://www.tik.ee.ethz.ch/sop/download/supplementary/hype/ .

As a novel optimization method, chaos has gained lots of attentions and applications in the past few years. Chaos movement can go through all states unrepeated according to the rule of itself in some area. It was introduced into the optimization strategy to accelerate the optimum seeking operation in this study. A chaos based particle swarm optimization strategy was developed to solve multi-objective optimization problems. The proposed approach is validated using several benchmark test functions and metrics on evolutionary multi-objective optimization. Results demonstrate the effectiveness and efficiency of the proposed strategy and that can be considered a viable alternative to solve multi-objective optimization problems.

In recent years, indicator-based evolutionary algorithms, allowing to implicitly incorporate user preferences into the search, have become widely used in practice to solve multiobjective optimization problems. When using this type of methods, the optimization goal changes from optimizing a set of objective functions simultaneously to the single-objective optimization goal of finding a set of mu points that maximizes the underlying indicator. Understanding the difference between these two optimization goals is fundamental when applying indicator-based algorithms in practice. On the one hand, a characterization of the inherent optimization goal of different indicators allows the user to choose the indicator that meets her preferences. On the other hand, knowledge about the sets of mu points with optimal indicator values - the so-called optimal mu-distributions-can be used in performance assessment whenever the indicator is used as a performance criterion. However, theoretical studies on indicator-based optimization are sparse.One of the most popular indicators is the weighted hypervolume indicator. It allows to guide the search towards user-defined objective space regions and at the same time has the property of being a refinement of the Pareto dominance relation with the result that maximizing the indicator results in Pareto-optimal solutions only. In previous work, we theoretically investigated the unweighted hypervolume indicator in terms of a characterization of optimal mu-distributions and the influence of the hypervolume's reference point for general bi-objective optimization problems. In this paper, we generalize those results to the case of the weighted hypervolume indicator. In particular, we present general investigations for finite mu, derive a limit result for mu going to infinity in terms of a density of points and derive lower bounds (possibly infinite) for placing the reference point to guarantee the Pareto front's extreme points in an optimal mu-distribution. Furthermore, we state conditions about the slope of the front at the extremes such that there is no finite reference point that allows to include the extremes in an optimal mu-distribution-contradicting previous belief that a reference point chosen just above the nadir point or the objective space boundary is sufficient for obtaining the extremes. However, for fronts where there exists a finite reference point allowing to obtain the extremes, we show that for mu to infinity, a reference point that is slightly worse in all objectives than the nadir point is a sufficient choice. Last, we apply the theoretical results to problems of the ZDT, DTLZ, and WFG test problem suites. (C) 2011 Elsevier B.V. All rights reserved.

Assuming that evolutionary multiobjective optimization (EMO) mainly deals with set problems, one can identify three core questions in this area of research: 1) how to formalize what type of Pareto set approximation is sought; 2) how to use this information within an algorithm to efficiently search for a good Pareto set approximation; and 3) how to compare the Pareto set approximations generated by different optimizers with respect to the formalized optimization goal. There is a vast amount of studies addressing these issues from different angles, but so far only a few studies can be found that consider all questions under one roof. This paper is an attempt to summarize recent developments in the EMO field within a unifying theory of set-based multiobjective search. It discusses how preference relations on sets can be formally defined, gives examples for selected user preferences, and proposes a general preference-independent hill climber for multiobjective optimization with theoretical convergence properties. Furthermore, it shows how to use set preference relations for statistical performance assessment and provides corresponding experimental results. The proposed methodology brings together preference articulation, algorithm design, and performance assessment under one framework and thereby opens up a new perspective on EMO.

In recent years, the hypervolume indicator – a set quality measure considering the dominated portion of the objective space – has gained increasing attention in the context of multiobjective search. This is mainly due to the following feature: whenever one Pareto set approximation completely dominates another approximation, the hypervolume of the former will be greater than the hypervolume of the latter. Unfortunately, the calculation of the hypervolume measure is computationally highly demanding, and current algorithms are exponential in the number of objectives. This paper proposes a methodology based on Monte Carlo sampling to estimate the hypervolume contribution of single solutions regarding a specific Pareto set approximation. It is therefore designed to be used in the environmental selection process of an evolutionary algorithm, and allows substantial speedups in hypervolume-based search as the experimental results demonstrate.

Many-objective problems pose various challenges in terms of decision making and search. One approach to tackle the resulting problems is the automatic reduction of the number of objectives such that the information loss is minimized. While in a previous work we have investigated the issue of omitting objectives, we here address the generalized problem of aggregating objectives using weighted sums. To this end, heuristics are presented that iteratively remove two objectives and replace them by a new objective representing an optimally weighted combination of them. As shown in the paper, the new reduction method can substantially reduce the information loss and thereby can be highly useful when analyzing trade-off sets after optimization as well as during search to reduce the computation overhead related to hypervolume-based fitness assignment.

In the field of evolutionary multiobjective optimization, the hypervolume indicator is the only single set quality measure that is known to be strictly monotonic with regard to Pareto dominance. This property is of high interest and relevance for multiobjective search involving a large number of objective functions. However, the high computational effort required for calculating the indicator values has so far prevented to fully exploit the potential of hypervolume-based multiobjective optimization. This paper addresses this issue and proposes a fast search algorithm that uses Monte Carlo sampling to approximate the exact hypervolume values. In detail, we present HypE (Hypervolume Estimation Algorithm for Multiobjective Optimization), by which the accuracy of the estimates and the available computing resources can be traded off; thereby, not only many-objective problems become feasible with hypervolume-based search, but also the runtime can be flexibly adapted. The experimental results indicate that HypE is highly effective for many-objective problems in comparison to existing multiobjective evolutionary algorithms.

In the context of Systems Biology, computer simulations of gene regulatory networks provide a powerful tool to validate hypotheses and to explore possible system behaviors. Nevertheless, modeling a system poses some challenges of its own: especially the step of model calibration is often difficult due to insufficient data. For example when considering developmental systems, mostly qualitative data describing the developmental trajectory is available while common calibration techniques rely on high-resolution quantitative data. Focusing on the calibration of differential equation models for developmental systems, this study investigates different approaches to utilize the available data to overcome these difficulties. More specifically, the fact that developmental processes are hierarchically organized is exploited to increase convergence rates of the calibration process as well as to save computation time. Using a gene regulatory network model for stem cell homeostasis in Arabidopsis thaliana the performance of the different investigated approaches is evaluated, documenting considerable gains provided by the proposed hierarchical approach.

Multiobjective optimization in general aims at learning about the problem at hand. Usually the focus lies on objective space properties such as the front shape and the distribution of optimal solutions. However, structural characteristics in the decision space can also provide valuable insights. In certain applications, it may even be more important to find a structurally diverse set of close-to-optimal solutions than to identify a set of optimal but structurally similar solutions. Accordingly, multiobjective optimizers are required that are capable of considering both the objective space quality of a Pareto-set approximation and its diversity in the decision space. Although NSGA, one of the first multiobjective evolutionary algorithms, explicitly considered decision space diversity, only a few other studies address that issue. It therefore is an open research question how modern multiobjective evolutionary algorithms can be adapted to search for structurally diverse high-quality Pareto-set approximations. To this end we propose an approach to integrate decision space diversity into hypervolume-based multiobjective search. We present a modified hypervolume indicator and integrate it into an evolutionary algorithm. The proof-of-principle results show the potential of the approach and indicate further research directions for structure-oriented multiobjective search.

The use of quality indicators within the search has become a popular approach in the field of evolutionary multiobjective optimization. It relies on the concept to transform the original multiobjective problem into a set problem that involves a single objective function only, namely a quality indicator, reflecting the quality of a Pareto set approximation. Especially the hypervolume indicator has gained a lot of attention in this context since it is the only set quality measure known that guarantees strict monotonicity. Accordingly, various hypervolume-based search algorithms for approximating the Pareto set have been proposed, including sampling-based methods that circumvent the problem that the hypervolume is in general hard to compute. Despite these advances, there are several open research issues in indicator-based multiobjective search when considering real-world applications—the issue of robustness is one of them. For instance with mechanical manufacturing processes, there exist unavoidable inaccuracies that prevent a desired solution to be realized with perfect precision; therefore, a solution in terms of a concrete decision vector is not associated with just one one fixed vector of objective values, but rather with a range of objective values that reflect the variance when slightly changing the decision variables. As a consequence, the optimization model needs to account for such uncertainties and the search method is required to explicitly integrate robustness considerations. While in single-objective optimization, there are various studies dealing with the robustness issue, there are considerably fewer in the multiobjective optimization literature and none in the context of hypervolume-based multiobjective search. This study is set in the latter context and addresses the question of how to incorporate robustness when using the hypervolume indicator within an evolutionary algorithm. To this end, three common robustness concepts are translated to and tested for hypervolume-based search on the one hand, and an extension of the hypervolume indicator is proposed on the other hand that not only unifies those three concepts, but also enables to realize much more general trade-offs between objective values and robustness of a solution. Finally, the approaches are compared on two test problem suites as well as on a newly proposed real-world bridge construction problem.

Plants maintain stem cells in their meristems as a source for new undifferentiated cells throughout their life. Meristems are small groups of cells that provide the microenvironment that allows stem cells to prosper. Homeostasis of a stem cell domain within a growing meristem is achieved by signalling between stem cells and surrounding cells. We have here simulated the origin and maintenance of a defined stem cell domain at the tip of Arabidopsis shoot meristems, based on the assumption that meristems are self-organizing systems. The model comprises two coupled feedback regulated genetic systems that control stem cell behaviour. Using a minimal set of spatial parameters, the mathematical model allows to predict the generation, shape and size of the stem cell domain, and the underlying organizing centre. We use the model to explore the parameter space that allows stem cell maintenance, and to simulate the consequences of mutations, gene misexpression and cell ablations.

Many-objective problems represent a major challenge in the field of evolutionary multiobjective optimization--in terms of search efficiency, computational cost, decision making, visualization, and so on. This leads to various research questions, in particular whether certain objectives can be omitted in order to overcome or at least diminish the difficulties that arise when many, that is, more than three, objective functions are involved. This study addresses this question from different perspectives. First, we investigate how adding or omitting objectives affects the problem characteristics and propose a general notion of conflict between objective sets as a theoretical foundation for objective reduction. Second, we present both exact and heuristic algorithms to systematically reduce the number of objectives, while preserving as much as possible of the dominance structure of the underlying optimization problem. Third, we demonstrate the usefulness of the proposed objective reduction method in the context of both decision making and search for a radar waveform application as well as for well-known test functions.