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PESAII: Regionbased Selection in Evolutionary Multiobjective Optimization
 Proceedings of the Genetic and Evolutionary Computation Conference (GECCO’2001
, 2001
"... We describe a new selection technique for evolutionary multiobjective optimization algorithms in which the unit of selection is a hyperbox in objective space. In this technique, instead of assigning a selective fitness to an individual, selective fitness is assigned to the hyperboxes in object ..."
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Cited by 71 (9 self)
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We describe a new selection technique for evolutionary multiobjective optimization algorithms in which the unit of selection is a hyperbox in objective space. In this technique, instead of assigning a selective fitness to an individual, selective fitness is assigned to the hyperboxes in objective space which are currently occupied by at least one individual in the current approximation to the Pareto frontier. A hyperbox is thereby selected, and the resulting selected individual is randomly chosen from this hyperbox. This method of selection is shown to be more sensitive to ensuring a good spread of development along the Pareto frontier than individualbased selection. The method is implemented in a modern multiobjective evolutionary algorithm, and performance is tested by using Deb's test suite of `T' functions with varying properties. The new selection technique is found to give significantly superior results to the other methods compared, namely PAES, PESA, and SPEA; each is a modern multiobjective optimization algorithm previously found to outperform earlier approaches on various problems.
Ideal Evaluation from Coevolution
 Evolutionary Computation
, 2004
"... In many problems of interest, performance can be evaluated using tests, such as examples in concept learning, test points in function approximation, and opponents in gameplaying. Evaluation on all tests is often infeasible. Identification of an accurate evaluation or fitness function is a difficult ..."
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Cited by 68 (6 self)
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In many problems of interest, performance can be evaluated using tests, such as examples in concept learning, test points in function approximation, and opponents in gameplaying. Evaluation on all tests is often infeasible. Identification of an accurate evaluation or fitness function is a difficult problem in itself, and approximations are likely to introduce human biases into the search process. Coevolution evolves the set of tests used for evaluation, but has so far often led to inaccurate evaluation. We show that for any set of learners, a Complete Evaluation Set can be determined that provides ideal evaluation as specified by Evolutionary MultiObjective Optimization. This provides a principled approach to evaluation in coevolution, and thereby brings automatic ideal evaluation within reach. The Complete Evaluation Set is of manageable size, and progress towards it can be accurately measured. Based on this observation, an algorithm named DELPHI is developed. The algorithm is tested on problems likely to permit progress on only a subset of the underlying objectives. Where all comparison methods result in overspecialization, the proposed method and a variant achieve sustained progress in all underlying objectives. These findings demonstrate that ideal evaluation may be approximated by practical algorithms, and that accurate evaluation for testbased problems is possible even when the underlying objectives of a problem are unknown.
Pareto efficient multiobjective test case selection
 in Proc. 2007 Int’l Symp. Software Testing and Analysis (ISSTA
"... Previous work has treated test case selection as a single objective optimisation problem. This paper introduces the concept of Pareto efficiency to test case selection. The Pareto efficient approach takes multiple objectives such as code coverage, past faultdetection history and execution cost, and ..."
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Cited by 65 (18 self)
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Previous work has treated test case selection as a single objective optimisation problem. This paper introduces the concept of Pareto efficiency to test case selection. The Pareto efficient approach takes multiple objectives such as code coverage, past faultdetection history and execution cost, and constructs a group of nondominating, equivalently optimal test case subsets. The paper describes the potential benefits of Pareto efficient multiobjective test case selection, illustrating with empirical studies of two and three objective formulations.
A MultiObjective Algorithm based upon Particle Swarm Optimisation, an Efficient Data Structure and Turbulence.
, 2002
"... This paper introduces a MultiObjective Algorithm (MOA) based upon the Particle Swarm Optimisation (PSO) heuristic. ..."
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Cited by 59 (2 self)
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This paper introduces a MultiObjective Algorithm (MOA) based upon the Particle Swarm Optimisation (PSO) heuristic.
Evolving Objects: a general purpose evolutionary computation library
, 2001
"... This paper presents the evolving objects library (EOlib), an objectoriented framework for evolutionary computation (EC) that aims to provide a exible set of classes to build EC applications. EOlib design objective is to be able to evolve any object in which tness makes sense. ..."
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Cited by 59 (12 self)
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This paper presents the evolving objects library (EOlib), an objectoriented framework for evolutionary computation (EC) that aims to provide a exible set of classes to build EC applications. EOlib design objective is to be able to evolve any object in which tness makes sense.
Performance Scaling of MultiObjective Evolutionary Algorithms
, 2002
"... In real world problems, one is often faced with the problem of multiple, possibly competing, goals, which should be optimized simultaneously. These competing goals give rise to a set of compromise solutions, generally denoted as Paretooptimal. If none of the objectives have preference over the othe ..."
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Cited by 57 (5 self)
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In real world problems, one is often faced with the problem of multiple, possibly competing, goals, which should be optimized simultaneously. These competing goals give rise to a set of compromise solutions, generally denoted as Paretooptimal. If none of the objectives have preference over the other, none of these tradeoff solutions can be said to be better than any other solution in the set. Multiobjective Evolutionary Algorithms (MOEAs) can find these optimal tradeoffs in order to get a set of solutions that are optimal in an overall sense.
Evolutionary computation in structural design
 Journal of Engineering with Computers
, 2001
"... Evolutionary computation is emerging as a new engineering computational paradigm, which may significantly change the present structural design practice. For this reason, an extensive study of evolutionary computation in the context of structural design has been conducted in the Information Technolog ..."
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Cited by 54 (7 self)
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Evolutionary computation is emerging as a new engineering computational paradigm, which may significantly change the present structural design practice. For this reason, an extensive study of evolutionary computation in the context of structural design has been conducted in the Information Technology and Engineering School at George Mason University and its results are reported here. First, a general introduction to evolutionary computation is presented and recent developments in this field are briefly described. Next, the field of evolutionary design is introduced and its relevance to structural design is explained. Further, the issue of creativity/novelty is discussed and possible ways of achieving it during a structural design process are suggested. Current research progress in building engineering systems ’ representations, one of the key issues in evolutionary design, is subsequently discussed. Next, recent developments in constrainthandling methods in evolutionary optimization are reported. Further, the rapidly growing field of evolutionary multiobjective optimization is presented and briefly described. An emerging subfield of coevolutionary design is subsequently introduced and its current advancements reported. Next, a comprehensive review of the applications of evolutionary computation in structural design is provided and chronologically classified. Finally, a summary of the current research status and a discussion on the most promising paths of future research are also presented.
HypE: An Algorithm for Fast HypervolumeBased ManyObjective Optimization
, 2008
"... In the field of evolutionary multicriterion 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 also the indicator value of the ..."
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Cited by 54 (5 self)
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In the field of evolutionary multicriterion 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 also the indicator value of the former will 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 to fully exploit the potential of this indicator; current hypervolumebased 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 that not the actual indicator values are important, but rather the rankings of solutions induced by the hypervolume indicator. In detail, we present HypE, a 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 manyobjective problems become feasible with hypervolumebased 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 multiobjective 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 manyobjective problems in comparison to existing multiobjective evolutionary algorithms. HypE is available for download at
Running performance Metrics for evolutionary multiobjective optimization
, 2002
"... It is now well established that more than one performance metrics are necessary for evaluating a multiobjective evolutionary algorithm (MOEA). Although there exist a number of performance metrics in the MOEA literature, most of them are applied to the final nondominated set obtained by an MOEA to ..."
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Cited by 54 (3 self)
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It is now well established that more than one performance metrics are necessary for evaluating a multiobjective evolutionary algorithm (MOEA). Although there exist a number of performance metrics in the MOEA literature, most of them are applied to the final nondominated set obtained by an MOEA to evaluate its performance. In this paper, we suggest a couple of running metrics  one for measuring the convergence to a reference set and other for measuring the diversity in population members at every generation of an MOEA run. Either using a known Paretooptimal front or an agglomeration of generationwise populations, the suggested metrics reveal important insights and interesting dynamics of the working of an MOEA or help provide a comparative evaluation of two or more MOEAs.
A Nondominated Sorting Particle Swarm Optimizer for Multiobjective Optimization
 Lecture Notes in Computer Science, Proceedings of Genetic and Evolutionary Computation GECCO 2003, Vol. 2723, Part I
, 2003
"... Abstract. This paper introduces a modified PSO, Nondominated Sorting Particle Swarm Optimizer (NSPSO), for better multiobjective optimization. NSPSO extends the basic form of PSO by making a better use of particles ’ personal bests and offspring for more effective nondomination comparisons. Instead ..."
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Cited by 51 (7 self)
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Abstract. This paper introduces a modified PSO, Nondominated Sorting Particle Swarm Optimizer (NSPSO), for better multiobjective optimization. NSPSO extends the basic form of PSO by making a better use of particles ’ personal bests and offspring for more effective nondomination comparisons. Instead of a single comparison between a particle’s personal best and its offspring, NSPSO compares all particles’ personal bests and their offspring in the entire population. This proves to be effective in providing an appropriate selection pressure to propel the swarm population towards the Paretooptimal front. By using the nondominated sorting concept and two parameterfree niching methods, NSPSO and its variants have shown remarkable performance against a set of wellknown difficult test functions (ZDT series). Our results and comparison with NSGA II show that NSPSO is highly competitive with existing evolutionary and PSO multiobjective algorithms. 1