A faster algorithm for calculating hypervolume

While, Lyndon; Hingston, Philip; Barone, Luigi; Huband, S.

doi:10.1109/tevc.2005.851275

Cited by 838 publications

(303 citation statements)

References 22 publications

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“…The major drawback of the hypervolume indicator is its high computation effort; all known algorithms have a worst-case runtime complexity that is exponential in the number of objectives, more specifically O.N n 1 / where N is the number of solutions considered (Knowles 2002;While et al 2006). A different approach was presented by Fleischer (2003) who mistakenly claimed a polynomial worst-case runtime complexity - While (2005) showed that it is exponential in n as well.…”

Section: Related Workmentioning

confidence: 99%

“…The fitness values I k h .a; A; R/ can be calculated on the fly for all individuals a 2 A by a slightly extended version of the "hypervolume by slicing objectives" (Zitzler 2001;Knowles 2002;While et al 2006) algorithm, which traverse recursively one objective after another. It differs from existing methods in that it allows (1) to consider a set R of reference points and (5) to compute all fitness values, e.g., the I 1 h .a; P; R/ values for k D 1, in parallel for any number of objectives instead of subsequently as in Beume et al (2007).…”

Section: Extended Scheme For Environmental Selectionmentioning

confidence: 99%

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A Hypervolume-Based Optimizer for High-Dimensional Objective Spaces

Bader

Zitzler²

2010

Lecture Notes in Economics and Mathematical Systems

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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.

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Section: Related Workmentioning

confidence: 99%

Section: Extended Scheme For Environmental Selectionmentioning

confidence: 99%

A Hypervolume-Based Optimizer for High-Dimensional Objective Spaces

Bader

Zitzler²

2010

Lecture Notes in Economics and Mathematical Systems

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“…HV is a performance indicator to measure the quality of solution sets obtained by MOEAs in terms of both convergence and diversity [61]. The method for calculating HV value is the same to that adopted in [23].…”

Section: Approximate Non-dominated Sorting For Many-objective Optimizmentioning

confidence: 99%

Effectiveness and efficiency of non-dominated sorting for evolutionary multi- and many-objective optimization

Tian

Wang

Zhang

et al. 2017

Complex Intell. Syst.

119

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Since non-dominated sorting was first adopted in NSGA in 1995, most evolutionary algorithms have employed non-dominated sorting as one of the major criteria in their environmental selection for solving multi-and many-objective optimization problems. In this paper, we focus on analyzing the effectiveness and efficiency of nondominated sorting in multi-and many-objective evolutionary algorithms. The effectiveness of non-dominated sorting is verified by considering two popular evolutionary algorithms, NSGA-II and KnEA, which were designed for solving multiand many-objective optimization problems, respectively. The efficiency of non-dominated sorting is evaluated by comparing several state-of-the-art non-dominated sorting algorithms for multi-and many-objective optimization problems. These results provide important insights to adopt non-dominated sorting in developing novel multi-and many-objective evolutionary algorithms.

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“…A lot of research has focused on improving the computational complexity of this indicator [29,30,31,32]. The exact computation of the algorithm has been shown to be #P-hard [33] in the number of objectives.…”

Section: Multi-objective Art-based Edamentioning

confidence: 99%

Multi-Objective Optimization with an Adaptive Resonance Theory-Based Estimation of Distribution Algorithm: A Comparative Study

Martí

García

Berlanga

et al. 2011

Lecture Notes in Computer Science

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Abstract. The introduction of learning to the search mechanisms of optimization algorithms has been nominated as one of the viable approaches when dealing with complex optimization problems, in particular with multi-objective ones. One of the forms of carrying out this hybridization process is by using multi-objective optimization estimation of distribution algorithms (MOEDAs). However, it has been pointed out that current MOEDAs have a intrinsic shortcoming in their model-building algorithms that hamper their performance.In this work we argue that error-based learning, the class of learning most commonly used in MOEDAs is responsible for current MOEDA underachievement. We present adaptive resonance theory (ART) as a suitable learning paradigm alternative and present a novel algorithm called multi-objective ART-based EDA (MARTEDA) that uses a Gaussian ART neural network for model-building and an hypervolume-based selector as described for the HypE algorithm. In order to assert the improvement obtained by combining two cutting-edge approaches to optimization an extensive set of experiments are carried out. These experiments also test the scalability of MARTEDA as the number of objective functions increases.

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A faster algorithm for calculating hypervolume

Cited by 838 publications

References 22 publications

A Hypervolume-Based Optimizer for High-Dimensional Objective Spaces

A Hypervolume-Based Optimizer for High-Dimensional Objective Spaces

Effectiveness and efficiency of non-dominated sorting for evolutionary multi- and many-objective optimization

Multi-Objective Optimization with an Adaptive Resonance Theory-Based Estimation of Distribution Algorithm: A Comparative Study

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