A comparison of different algorithms for the calculation of dominated hypervolumes

Christopher, Priester; Narukawa, Kaname; Rodemann, Tobias

doi:10.1145/2463372.2463451

Cited by 11 publications

(5 citation statements)

References 11 publications

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“…This algorithm takes advantage of the bounding boxes to compute the exclusive contributions of points that are then used for the hypervolume computation. The asymptotic time does not seem to be very good, but experimental and theoretical evidence shows that is the fastest exact algorithm for high dimensions [16], [17]. For dimensions bigger than 10, however, the computation time increases toward unfeasible values.…”

Section: B Hypervolume Metricmentioning

confidence: 99%

MHACO: a Multi-Objective Hypervolume-Based Ant Colony Optimizer for Space Trajectory Optimization

Acciarini

Izzo

Mooij

2020

2020 IEEE Congress on Evolutionary Computation (CEC)

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In this paper, we combine the concepts of hypervolume, ant colony optimization and nondominated sorting to develop a novel multi-objective ant colony optimizer for global space trajectory optimization. In particular, this algorithm is first tested on three space trajectory bi-objective test problems: an Earth-Mars transfer, an Earth-Venus transfer and a bi-objective version of the Jupiter Icy Moons Explorer mission (the first largeclass mission of the European Space Agency's Cosmic Vision 2015-2025 programme). Finally, the algorithm is applied to a four-objectives low-thrust problem that describes the journey of a solar sail towards a polar orbit around the Sun. The results on both the test cases and the more complex problem are reported by comparing the novel algorithm performances with those of two popular multi-objective optimizers (i.e., a nondominated sorting genetic algorithm and a multi-objective evolutionary algorithm with decomposition) in terms of hypervolume metric. The numerical results of this study show that the multi-objective hypervolume-based ant colony optimization algorithm is not only competitive with the standard multi-objective algorithms when applied to the space trajectory test cases, but it can also provide better Pareto fronts in terms of hypervolume values when applied to the complex solar sailing mission.

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Section: B Hypervolume Metricmentioning

confidence: 99%

MHACO: a Multi-Objective Hypervolume-Based Ant Colony Optimizer for Space Trajectory Optimization

Acciarini

Izzo

Mooij

2020

2020 IEEE Congress on Evolutionary Computation (CEC)

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“…This partly explains the success of NSGA-II, which has excellent diversity retention and can be classed as a general solver. Despite this, most of the currently developed EAs utilize a "convergence first, diversity second" approach (Liu et al, 2017) where the mechanisms that promote convergence are preferred, while diversity is obtained using secondary methods such as crowding distance calculations (Deb et al, 2002), external archive refining (Zitzler et al, 2001), problem decomposition (Zhang and Li, 2007;Liu and Li, 2009;, or indicator-based solution selection (Zitzler and Simon, 2004;Beume et al, 2007;Priester et al, 2013). A recent methodology developed by Grudniewski and Sobey (2018), Sobey and Grudniewski (2018), multilevel selection genetic algorithm (MLSGA), introduces a multilevel selection (MLS) mechanism, via subpopulations called collectives.…”

Section: The Requirement For General Algorithmsmentioning

confidence: 99%

Coevolutionary strategies at the collective level for improved generalism

Grudniewski

Sobey

2023

DCE

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In many complex practical optimization cases, the dominant characteristics of the problem are often not known prior. Therefore, there is a need to develop general solvers as it is not always possible to tailor a specialized approach to each application. The previously developed multilevel selection genetic algorithm (MLSGA) already shows good performance on a range of problems due to its diversity-first approach, which is rare among evolutionary algorithms. To increase the generality of its performance, this paper proposes utilization of multiple distinct evolutionary strategies simultaneously, similarly to algorithm selection, but with coevolutionary mechanisms between the subpopulations. This distinctive approach to coevolution provides less regular communication between subpopulations with competition between collectives rather than individuals. This encourages the collectives to act more independently creating a unique subregional search, leading to the development of coevolutionary MLSGA (cMLSGA). To test this methodology, nine genetic algorithms are selected to generate several variants of cMLSGA, which incorporates these approaches at the individual level. The mechanisms are tested on 100 different functions and benchmarked against the 9 state-of-the-art competitors to evaluate the generality of each approach. The results show that the diversity divergence in the principles of working of the selected coevolutionary approaches is more important than their individual performances. The proposed methodology has the most uniform performance on the divergent problem types, from across the tested state of the art, leading to an algorithm more likely to solve complex problems with limited knowledge about the search space, but is outperformed by more specialized solvers on simpler benchmarking studies.

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“…The main advantage of HV is its strictly Pareto compliance property [27]. However, it is difficult to compute the exact value of HV for a large solution set with many objectives, although some fast computational methods have been proposed for approximating HV [28], [29], [30], [31], [32]. For example, Sharpe-Ratio [33], [34] is such an indicator with interesting properties and not as time consuming as hypervolume indicator.…”

Section: B Related Studies On Quality Indicatorsmentioning

confidence: 99%

A Kernel-Based Indicator for Multi/Many-Objective Optimization

Cai

Xiao

et al. 2022

IEEE Trans. Evol. Computat.

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How to evaluate Pareto front approximations generated by multi/many-objective optimizers is a critical issue in the field of multiobjective optimization. Currently, there exist two types of comprehensive quality indicators (i.e., volume-based and distance-based indicators). Distance-based indicators, such as Inverted Generational Distance (IGD), are usually computed by summing up the distance of each reference point to its nearest solution. Their high computational efficiency leads to their prevalence in many-objective optimization. However, in the existing distance-based indicators, the distributions of the solution sets are usually neglected, leading to their lacks of ability to well distinguish between different solution sets. This phenomenon may become even more severe in high-dimensional space. To address such an issue, a kernel-based indicator (KBI) is proposed as a comprehensive indicator. Different from other distancebased indicators, a kernel-based maximum mean discrepancy is adopted in KBI for directly measuring the difference that can characterize the convergence, spread and uniformity of two sets, i.e., the solution set and reference set, by embedding them in Reproducing Kernel Hilbert Space (RKHS). As a result, KBI not only reflects the distance between the solution set and the reference set, but also can reflect the distribution of the solution set itself. In addition, to maintain the desirable weak Pareto compliance property of KBI, a nondominated set reconstruction approach is also proposed to shift the original solution set. The detailed theoretical and experimental analysis of KBI is provided in this paper. The properties of KBI have also been analyzed by the optimal µ-distribution.

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A comparison of different algorithms for the calculation of dominated hypervolumes

Cited by 11 publications

References 11 publications

MHACO: a Multi-Objective Hypervolume-Based Ant Colony Optimizer for Space Trajectory Optimization

MHACO: a Multi-Objective Hypervolume-Based Ant Colony Optimizer for Space Trajectory Optimization

Coevolutionary strategies at the collective level for improved generalism

A Kernel-Based Indicator for Multi/Many-Objective Optimization

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