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814
Evolutionary Algorithms for Multiobjective Optimization: Methods and Applications
, 1999
"... Many realworld problems involve two types of problem difficulty: i) multiple, conflicting objectives and ii) a highly complex search space. On the one hand, instead of a single optimal solution competing goals give rise to a set of compromise solutions, generally denoted as Paretooptimal. In the a ..."
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Cited by 301 (12 self)
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Many realworld problems involve two types of problem difficulty: i) multiple, conflicting objectives and ii) a highly complex search space. On the one hand, instead of a single optimal solution competing goals give rise to a set of compromise solutions, generally denoted as Paretooptimal. In the absence of preference information, none of the corresponding tradeoffs can be said to be better than the others. On the other hand, the search space can be too large and too complex to be solved by exact methods. Thus, efficient optimization strategies are required that are able to deal with both difficulties. Evolutionary algorithms possess several characteristics that are desirable for this kind of problem and make them preferable to classical optimization methods. In fact, various evolutionary approaches to multiobjective optimization have been proposed since 1985, capable of searching for multiple Paretooptimal solutions concurrently in a single simulation run. However, in spite of this...
Combining convergence and diversity in evolutionary multiobjective optimization
 Evolutionary Computation
, 2002
"... Over the past few years, the research on evolutionary algorithms has demonstrated their niche in solving multiobjective optimization problems, where the goal is to �nd a number of Paretooptimal solutions in a single simulation run. Many studies have depicted different ways evolutionary algorithms c ..."
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Cited by 113 (11 self)
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Over the past few years, the research on evolutionary algorithms has demonstrated their niche in solving multiobjective optimization problems, where the goal is to �nd a number of Paretooptimal solutions in a single simulation run. Many studies have depicted different ways evolutionary algorithms can progress towards the Paretooptimal set with a widely spread distribution of solutions. However, none of the multiobjective evolutionary algorithms (MOEAs) has a proof of convergence to the true Paretooptimal solutions with a wide diversity among the solutions. In this paper, we discuss why a number of earlier MOEAs do not have such properties. Based on the concept ofdominance, new archiving strategies are proposed that overcome this fundamental problem and provably lead to MOEAs that have both the desired convergence and distribution properties. A number of modi�cations to the baseline algorithm are also suggested. The concept ofdominance introduced in this paper is practical and should make the proposed algorithms useful to researchers and practitioners alike.
Performance Assessment of Multiobjective Optimizers: An Analysis and Review
 IEEE Transactions on Evolutionary Computation
, 2002
"... An important issue in multiobjective optimization is the quantitative comparison of the performance of di#erent algorithms. In the case of multiobjective evolutionary algorithms, the outcome is usually an approximation of the Paretooptimal front, which is denoted as an approximation set, and the ..."
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Cited by 90 (2 self)
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An important issue in multiobjective optimization is the quantitative comparison of the performance of di#erent algorithms. In the case of multiobjective evolutionary algorithms, the outcome is usually an approximation of the Paretooptimal front, which is denoted as an approximation set, and therefore the question arises of how to evaluate the quality of approximation sets. Most popular are methods that assign each approximation set a vector of real numbers that reflect different aspects of the quality. Sometimes, pairs of approximation sets are considered too. In this study, we provide a rigorous analysis of the limitations underlying this type of quality assessment.
Indicatorbased selection in multiobjective search
 in Proc. 8th International Conference on Parallel Problem Solving from Nature (PPSN VIII
, 2004
"... Abstract. This paper discusses how preference information of the decision maker can in general be integrated into multiobjective search. The main idea is to first define the optimization goal in terms of a binary performance measure (indicator) and then to directly use this measure in the selection ..."
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Cited by 88 (6 self)
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Abstract. This paper discusses how preference information of the decision maker can in general be integrated into multiobjective search. The main idea is to first define the optimization goal in terms of a binary performance measure (indicator) and then to directly use this measure in the selection process. To this end, we propose a general indicatorbased evolutionary algorithm (IBEA) that can be combined with arbitrary indicators. In contrast to existing algorithms, IBEA can be adapted to the preferences of the user and moreover does not require any additional diversity preservation mechanism such as fitness sharing to be used. It is shown on several continuous and discrete benchmark problems that IBEA can substantially improve on the results generated by two popular algorithms, namely NSGAII and SPEA2, with respect to different performance measures. 1
Scalable Test Problems for Evolutionary MultiObjective Optimization
 Computer Engineering and Networks Laboratory (TIK), Swiss Federal Institute of Technology (ETH
, 2001
"... After adequately demonstrating the ability to solve di#erent twoobjective optimization problems, multiobjective evolutionary algorithms (MOEAs) must now show their e#cacy in handling problems having more than two objectives. In this paper, we have suggested three di#erent approaches for systema ..."
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Cited by 80 (13 self)
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After adequately demonstrating the ability to solve di#erent twoobjective optimization problems, multiobjective evolutionary algorithms (MOEAs) must now show their e#cacy in handling problems having more than two objectives. In this paper, we have suggested three di#erent approaches for systematically designing test problems for this purpose. The simplicity of construction, scalability to any number of decision variables and objectives, knowledge of exact shape and location of the resulting Paretooptimal front, and introduction of controlled di#culties in both converging to the true Paretooptimal front and maintaining a widely distributed set of solutions are the main features of the suggested test problems. Because of the above features, they should be found useful in various research activities on MOEAs, such as testing the performance of a new MOEA, comparing di#erent MOEAs, and better understanding of the working principles of MOEAs.
Scalable MultiObjective Optimization Test Problems
 in Congress on Evolutionary Computation (CEC’2002
, 2002
"... After adequately demonstrating the ability to solve different twoobjective optimization problems, multiobjective evolutionary algorithms (MOEAs) must now show their efficacy in handling problems having more than two objectives. In this paper, we suggest three different approaches for systematicall ..."
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Cited by 75 (7 self)
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After adequately demonstrating the ability to solve different twoobjective optimization problems, multiobjective evolutionary algorithms (MOEAs) must now show their efficacy in handling problems having more than two objectives. In this paper, we suggest three different approaches for systematically designing test problems for this purpose. The simplicity of construction, scalability to any number of decision variables and objectives, knowledge of exact shape and location of the resulting Paretooptimal front, and ability to control difficulties in both converging to the true Paretooptimal front and maintaining a widely distributed set of solutions are the main features of the suggested test problems. Because of these features, they should be found useful in various research activities on MOEAs, such as testing the performance of a new MOEA, comparing different MOEAs, and having a better understanding of the working principles of MOEAs.
A Computationally Efficient Evolutionary Algorithm for RealParameter Optimization
, 2002
"... Due to an increasing interest in solving realworld optimization problems using evolutionary algorithms (EAs), researchers have developed a number of realparameter genetic algorithms (GAs) in the recent past. In such studies, the main research effort is spent on developing an efficient recombina ..."
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Cited by 56 (7 self)
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Due to an increasing interest in solving realworld optimization problems using evolutionary algorithms (EAs), researchers have developed a number of realparameter genetic algorithms (GAs) in the recent past. In such studies, the main research effort is spent on developing an efficient recombination operator. Such recombination operators use probability distributions around the parent solutions to create an ospring. Some operators emphasize solutions at the center of mass of parents and some around the parents. In this paper, we propose a generic parentcentric recombination operator (PCX) and a steadystate, elitepreserving, scalable, and computationally fast populationalteration model (we called the G3 model). The performance of the G3 model with the PCX operator is investigated on three commonlyused test problems and is compared with a number of evolutionary and classical optimization algorithms including other realparameter GAs with UNDX and SPX operators, the correlated selfadaptive evolution strategy, the dierential evolution technique and the quasiNewton method. The proposed approach is found to be consistently and reliably performing better than all other methods used in the study. A scaleup study with problem sizes up to 500 variables shows a polynomial computational complexity of the proposed approach. This extensive study clearly demonstrates the power of the proposed technique in tackling realparameter optimization problems.
Multiobjective query processing for database systems
 In International Conference on Very Large Data Bases (VLDB
, 2004
"... Query processing in database systems has developed beyond mere exact matching of attribute values. Scoring database objects and retrieving only the top k matches or Paretooptimal result sets (skyline queries) are already common for a variety of applications. Specialized algorithms using either para ..."
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Cited by 49 (10 self)
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Query processing in database systems has developed beyond mere exact matching of attribute values. Scoring database objects and retrieving only the top k matches or Paretooptimal result sets (skyline queries) are already common for a variety of applications. Specialized algorithms using either paradigm can avoid naïve linear database scans and thus improve scalability. However, these paradigms are only two extreme cases of exploring viable compromises for each user‘s objectives. To find the correct result set for arbitrary cases of multiobjective query processing in databases we will present a novel algorithm for computing sets of objects that are nondominated with respect to a set of monotonic objective functions. Naturally containing top k and skyline retrieval paradigms as special cases, this algorithm maintains scalability also for all cases in between. Moreover, we will show the algorithm’s correctness and instanceoptimality in terms of necessary object accesses and how the response behavior can be improved by progressively producing result objects as quickly as possible, while the algorithm is still running. 1.
Running Time Analysis of a MultiObjective Evolutionary Algorithm on a Simple Discrete Optimization Problem
, 2002
"... For the first time, a running time analysis of a multiobjective evolutionary algorithm for a discrete optimization problem is given. To this end, a simple pseudoBoolean problem (Lotz: leading ones  trailing zeroes) is defined and a populationbased optimization algorithm (FEMO). We show, that the ..."
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Cited by 44 (7 self)
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For the first time, a running time analysis of a multiobjective evolutionary algorithm for a discrete optimization problem is given. To this end, a simple pseudoBoolean problem (Lotz: leading ones  trailing zeroes) is defined and a populationbased optimization algorithm (FEMO). We show, that the algorithm performs a black box optimization in #(n 2 log n) function evaluations where n is the number of binary decision variables. 1