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20
On SetBased Multiobjective Optimization
, 2008
"... Assuming that evolutionary multiobjective optimization (EMO) mainly deals with set problems, one can identify three core questions in this area of research: (i) how to formalize what type of Pareto set approximation is sought, (ii) how to use this information within an algorithm to efficiently sear ..."
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Cited by 24 (4 self)
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Assuming that evolutionary multiobjective optimization (EMO) mainly deals with set problems, one can identify three core questions in this area of research: (i) how to formalize what type of Pareto set approximation is sought, (ii) how to use this information within an algorithm to efficiently search for a good Pareto set approximation, and (iii) 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 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 setbased multiobjective search. It discusses how preference relations on sets can be formally defined, gives examples for selected user preferences, and proposes a general, preferenceindependent 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.
Approximating minimum multicuts by evolutionary multiobjective algorithms
 In Proc. of Parallel Problem Solving from Nature (PPSN’08
, 2008
"... Abstract. It has been shown that simple evolutionary algorithms are able to solve the minimum cut problem in expected polynomial time when using a multiobjective model of the problem. In this paper, we generalize these ideas to the NPhard minimum multicut problem. Given a set of k terminal pairs, ..."
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Abstract. It has been shown that simple evolutionary algorithms are able to solve the minimum cut problem in expected polynomial time when using a multiobjective model of the problem. In this paper, we generalize these ideas to the NPhard minimum multicut problem. Given a set of k terminal pairs, we prove that evolutionary algorithms in combination with a multiobjective model of the problem are able to obtain a kapproximation for this problem in expected polynomial time.
On the effects of adding objectives to plateau functions
 IEEE Transactions on Evolutionary Computation
, 2009
"... AbstractIn this paper, we examine how adding objectives to a given optimization problem affects the computational effort required to generate the set of Paretooptimal solutions. Experimental studies show that additional objectives may change the running time behavior of an algorithm drastically. ..."
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AbstractIn this paper, we examine how adding objectives to a given optimization problem affects the computational effort required to generate the set of Paretooptimal solutions. Experimental studies show that additional objectives may change the running time behavior of an algorithm drastically. Often it is assumed that more objectives make a problem harder as the number of different tradeoffs may increase with the problem dimension. We show that additional objectives, however, may be both beneficial and obstructive depending on the chosen objective. Our results are obtained by rigorous running time analyses that show the different effects of adding objectives to a wellknown plateau function. Additional experiments show that the theoretically shown behavior can be observed for problems with more than one objective. Index TermsMultiobjective optimization, running time analysis, theory. I. MOTIVATION I N RECENT YEARS, the number of publications on evolutionary multiobjective optimization has been rapidly growing; however, most of the studies investigate problems where the number of considered objectives is low, i.e., between two and four, while studies with many objectives are rare There is some evidence in the literature that additional objectives can make a problem harder. This discussion indicates that a general statement on the effect of increasing the number of objectives is not possible. For some problems, with a higher number of objectives it is more difficult to generate the Paretooptimal front; for other problems, it is easier. However, given the previous work, the question arises whether one and the same problem can be made both easier and harder depending on the added objective. This paper answers this question both experimentally and 10518215/$25.00
Additive Approximations of ParetoOptimal Sets by Evolutionary MultiObjective Algorithms
"... Often the Pareto front of a multiobjective optimization problem grows exponentially with the problem size. In this case, it is not possible to compute the whole Pareto front efficiently and one is interested in good approximations. We consider how evolutionary algorithms can achieve such approximat ..."
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Cited by 6 (1 self)
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Often the Pareto front of a multiobjective optimization problem grows exponentially with the problem size. In this case, it is not possible to compute the whole Pareto front efficiently and one is interested in good approximations. We consider how evolutionary algorithms can achieve such approximations by using different diversity mechanisms. We discuss some wellknown approaches such as the density estimator and the εdominance approach and point out how and when such mechanisms provably help to obtain good additive approximations of the Paretooptimal set.
Plateaus can be harder in multiobjective optimization
 In Proc. of CEC ’07
, 2007
"... In recent years a lot of progress has been made in understanding the behavior of evolutionary computation methods for single and multiobjective problems. Our aim is to analyze the diversity mechanisms that are implicitly used in evolutionary algorithms for multiobjective problems by rigorous runt ..."
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Cited by 6 (4 self)
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In recent years a lot of progress has been made in understanding the behavior of evolutionary computation methods for single and multiobjective problems. Our aim is to analyze the diversity mechanisms that are implicitly used in evolutionary algorithms for multiobjective problems by rigorous runtime analyses. We show that, even if the population size is small, the runtime can be exponential where corresponding singleobjective problems are optimized within polynomial time. To illustrate this behavior we analyze a simple plateau function in a first step and extend our result to a class of instances of the wellknown SetCover problem.
Multiobjectivizing the HP Model for Protein Structure Prediction
"... Abstract. The hydrophobicpolar (HP) model for protein structure prediction abstracts the fact that hydrophobic interactions are a dominant force in the protein folding process. This model represents a hard combinatorial optimization problem, which has been widely addressed using evolutionary alg ..."
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Abstract. The hydrophobicpolar (HP) model for protein structure prediction abstracts the fact that hydrophobic interactions are a dominant force in the protein folding process. This model represents a hard combinatorial optimization problem, which has been widely addressed using evolutionary algorithms and other metaheuristics. In this paper, the multiobjectivization of the HP model is proposed. This originally singleobjective problem is restated as a multiobjective one by decomposing the conventional objective function into two independent objectives. By using different evolutionary algorithms and a large set of test cases, the new alternative formulation was compared against the conventional singleobjective problem formulation. As a result, the proposed formulation increased the search performance of the implemented algorithms in most of the cases. Both two and threedimensional lattices are considered. To the best of authors ’ knowledge, this is the first study where multiobjective optimization methods are used for solving the HP model.
An Improved Multiobjectivization Strategy for HP ModelBased Protein Structure Prediction, in: Parallel Problem Solving from Nature
 of Lecture
"... Abstract. Through multiobjectivization, a singleobjective problem is restated in multiobjective form with the aim of enabling a more efficient search process. Recently, this transformation was applied with success to the hydrophobicpolar (HP) lattice model, which is an abstract representation of ..."
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Abstract. Through multiobjectivization, a singleobjective problem is restated in multiobjective form with the aim of enabling a more efficient search process. Recently, this transformation was applied with success to the hydrophobicpolar (HP) lattice model, which is an abstract representation of the protein structure prediction problem. The use of alternative multiobjective formulations of the problem has led to significantly better results. In this paper, an improved multiobjectivization for the HP model is proposed. By decomposing the HP model’s energy function, a twoobjective formulation for the problem is defined. A comparative analysis reveals that the new proposed multiobjectivization evaluates favorably with respect to both the conventional singleobjective and the previously reported multiobjective formulations. Statistical significance testing and the use of a large set of test cases support the findings of this study. Both twodimensional and threedimensional lattices are considered.
Benefits and drawbacks for the use of ǫdominance in evolutionary multiobjective optimization
 In Proc. of GECCO 2008
, 2008
"... Using diversity mechanisms in evolutionary algorithms for multiobjective optimization problems is considered as an important issue for the design of successful algorithms. This is in particular the case for problems where the number of nondominated feasible objective vectors is exponential with re ..."
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Using diversity mechanisms in evolutionary algorithms for multiobjective optimization problems is considered as an important issue for the design of successful algorithms. This is in particular the case for problems where the number of nondominated feasible objective vectors is exponential with respect to the problem size. In this case the goal is to compute a good approximation of the Pareto front. We investigate how this goal can be achieved by using the diversity mechanism of εdominance and point out where this concept is provably helpful to obtain a good approximation of an exponentially large Pareto front in expected polynomial time. Afterwards, we consider the drawbacks of this approach and point out situations where the use of εdominance slows down the optimization process significantly.
Approximating ParetoOptimal Sets Using Diversity Strategies in Evolutionary MultiObjective Optimization
"... Abstract Often the Pareto front of a multiobjective optimization problem grows exponentially with the problem size. In this case, it is not possible to compute the whole Pareto front efficiently and one is interested in good approximations. We consider how evolutionary algorithms can achieve such a ..."
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Abstract Often the Pareto front of a multiobjective optimization problem grows exponentially with the problem size. In this case, it is not possible to compute the whole Pareto front efficiently and one is interested in good approximations. We consider how evolutionary algorithms can achieve such approximations by using different diversity mechanisms. We discuss some wellknown approaches such as the density estimator and the εdominance approach and point out how and when such mechanisms provably help to obtain good approximations of the Paretooptimal set. 1
MultiObjective Optimization
, 2008
"... This work is a product of the Collaborative Research Center 531, “Computational Intelligence, ” at the Technische Universität Dortmund and was printed with financial ..."
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This work is a product of the Collaborative Research Center 531, “Computational Intelligence, ” at the Technische Universität Dortmund and was printed with financial