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Keywords
(12)
Estimation Algorithm
Monte Carlo Sampling
Monte Carlo Simulation
Multi Objective Evolutionary Algorithm
Multi Objective Optimization
multiobjective evolutionary algorithm
multiobjective optimization
Objective Function
pareto set
Quality Measures
Search Algorithm
Statistical Test
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HypE: An Algorithm for Fast HypervolumeBased ManyObjective Optimization
HypE: An Algorithm for Fast HypervolumeBased ManyObjective Optimization,10.1162/EVCO_a_00009,Evolutionary Computation,Johannes Bader,Eckart Zitzler
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HypE: An Algorithm for Fast HypervolumeBased ManyObjective Optimization
(
Citations: 31
)
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Johannes Bader
,
Eckart Zitzler
Abstract—In the field of evolutionary multicriterion optimiza tion, 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 solu tions 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 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 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.
Journal:
Evolutionary Computation  EC
, vol. 19, no. 1, pp. 4576, 2011
DOI:
10.1162/EVCO_a_00009
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Citation Context
(23)
...The quality of the Paretoset approximations are assessed using the hypervolume indicator, where for less than 6 objectives the indicator values are calculated exactly and otherwise approximated by Monte Carlo sampling as described in [
2
]...
Johannes Bader
,
et al.
HypE: An Algorithm for Fast HypervolumeBased ManyObjective Optimizat...
...However, a faster method for hypervolume estimation using MonteCarlo sampling has been proposed recently [
32
], which...
Hemant Kumar Singh
,
et al.
A Pareto Corner Search Evolutionary Algorithm and Dimensionality Reduc...
...Furthermore, IH is the only unary measure which is consistent with the Pareto dominance relationship, i.e., if a set dominates another one, it always has a better IH [
46
]...
Yi Mei
,
et al.
DecompositionBased Memetic Algorithm for Multiobjective Capacitated A...
...Hypervolume Estimation Algorithm (HypE) [
24
]...
Mario GarzaFabre
,
et al.
Effective ranking + speciation = Manyobjective optimization
...In the past years several multiobjective evolutionary algorithms [1], [2], [3], [
4
] were proposed and used to deal with these problems...
Martin Pilat
,
et al.
ASMMOMA: Multiobjective memetic algorithm with aggregate surrogate mo...
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(
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Dimo Brockhoff
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Citations
(31)
HypE: An Algorithm for Fast HypervolumeBased ManyObjective Optimization
(
Citations: 31
)
Johannes Bader
,
Eckart Zitzler
Journal:
Evolutionary Computation  EC
, vol. 19, no. 1, pp. 4576, 2011
A Pareto Corner Search Evolutionary Algorithm and Dimensionality Reduction in ManyObjective Optimization Problems
(
Citations: 1
)
Hemant Kumar Singh
,
Amitay Isaacs
,
Tapabrata Ray
Journal:
IEEE Transactions on Evolutionary Computation  TEC
, vol. 15, no. 4, pp. 539556, 2011
DecompositionBased Memetic Algorithm for Multiobjective Capacitated Arc Routing Problem
(
Citations: 1
)
Yi Mei
,
Ke Tang
,
Xin Yao
Journal:
IEEE Transactions on Evolutionary Computation  TEC
, vol. 15, no. 2, pp. 151165, 2011
Effective ranking + speciation = Manyobjective optimization
Mario GarzaFabre
,
Gregorio ToscanoPulido
,
Carlos A. Coello Coello
,
Eduardo RodriguezTello
Published in 2011.
Hypervolumebased expected improvement: Monotonicity properties and exact computation
Michael T. M. Emmerich
,
Andre H. Deutz
,
Jan Willem Klinkenberg
Published in 2011.