Using the Averaged Hausdorff Distance as a Performance Measure in Evolutionary Multiobjective Optimization

Schütze, Oliver; Esquivel, Xavier; Lara, Adriana; Coello, Carlos A. Coello

doi:10.1109/tevc.2011.2161872

Cited by 430 publications

(237 citation statements)

References 36 publications

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“…The IGD and ADRS indicators have the same complexity of DOA, but they are ≻≻-c only [11]. The Δp indicator [39] can be considered as the combination of slight variation Generational Distance and the IGD indicator [25]. Therefore, it presents the advanta limitations of these indicators, that is it accounts for all the features but it is ≻≻-complete on The Completeness and Potential Function indicators are as ≻-complete as the DOA in Nevertheless, the Completeness indicator cannot be directly computed, but can be estim drawing samples from the feasible set and computing completeness for these samp confidence interval for the true value can be evaluated with any reliability value, given suf large samples [26].…”

Section: Indicatormentioning

confidence: 99%

“…[39,40] The Inverted Generational Distance indicator (IGD) [29] and a similar indicator using a weighted-scalar distance function called Average Distance from Reference Set indicator (ADRS) [30], the Completeness indicator [31,32], the Potential Function indicator [27] and the Hypervolume indicator [1] account for all the features but they present some drawbacks.…”

Section: Indicatormentioning

confidence: 99%

“…The ∆ p indicator [39] can be considered as the combination of slight variations of the Generational Distance and the IGD indicator [25]. Therefore, it presents the advantage and limitations of these indicators, that is it accounts for all the features but it is -complete only.…”

Section: Indicatormentioning

confidence: 99%

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A Weakly Pareto Compliant Quality Indicator

Dilettoso

Rizzo

2017

MCA

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Abstract:In multi-and many-objective optimization problems, the optimization target is to obtain a set of non-dominated solutions close to the Pareto-optimal front, well-distributed, maximally extended and fully filled. Comparing solution sets is crucial in evaluating the performance of different optimization algorithms. The use of performance indicators is common in comparing those sets and, subsequently, optimization algorithms. Therefore, an effective performance indicator must encompass these features as a whole and, above all, it must be Pareto dominance compliant. Unfortunately, some of the known indicators often fail to properly reflect the quality of a solution set or cost a lot to compute. This paper demonstrates that the Degree of Approximation (DOA) quality indicator is a weakly Pareto compliant unary indicator that gives a good estimation of the match between the approximated front and the Pareto-optimal front.

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Section: Indicatormentioning

confidence: 99%

Section: Indicatormentioning

confidence: 99%

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A Weakly Pareto Compliant Quality Indicator

Dilettoso

Rizzo

2017

MCA

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“…There are many performance measures for comparisons among algorithms, like Inverted Generational Distance (IGD) [44], Hypervolume (HV) [45], Spread [46], Δ [47], and so on. Because all comparative algorithms in their literature employ either IGD or HV or both of them, they are also chosen to assess the performance of the proposed algorithm and its comparisons.…”

Section: Performance Measurementioning

confidence: 99%

Latest Stored Information Based Adaptive Selection Strategy for Multiobjective Evolutionary Algorithm

Gao

Qing-hua

Fan

et al. 2017

Mathematical Problems in Engineering

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The adaptive operator selection (AOS) and the adaptive parameter control are widely used to enhance the search power in many multiobjective evolutionary algorithms. This paper proposes a novel adaptive selection strategy with bandits for the multiobjective evolutionary algorithm based on decomposition (MOEA/D), named latest stored information based adaptive selection (LSIAS). An improved upper confidence bound (UCB) method is adopted in the strategy, in which the operator usage rate and abandonment of extreme fitness improvement are introduced to improve the performance of UCB. The strategy uses a sliding window to store recent valuable information about operators, such as factors, probabilities, and efficiency. Four common used DE operators are chosen with the AOS, and two kinds of assist information on operator are selected to improve the operators search power. The operator information is updated with the help of LSIAS and the resulting algorithmic combination is called MOEA/D-LSIAS. Compared to some well-known MOEA/D variants, the LSIAS demonstrates the superior robustness and fast convergence for various multiobjective optimization problems. The comparative experiments also demonstrate improved search power of operators with different assist information on different problems.

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“…The first treats diversity as a property of a set and evolves sets with a good diversity. The diversity can be measured according to the accumulated distances between the members of the set [8], [9], or indirectly by the hypervolume measure [10] or the averaged Hausdorff distance ∆ p [11]. Algorithms in the second category treat diversity as a property of each individual according to the density of solutions surrounding it.…”

Section: Introductionmentioning

confidence: 99%

PSA Based Multi Objective Evolutionary Algorithms

Domínguez-Medina¹,

Avigad

Freitas

et al. 2014

EVOLVE - A Bridge Between Probability, Set Oriented Numerics, and Evolutionary Computation III

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It has generally been acknowledged that both proximity to the Pareto front and a certain diversity along the front, should be targeted when using evolutionary multiobjective optimization. Recently, a new partitioning mechanism, the Part and Select Algorithm (PSA), has been introduced. It was shown that this partitioning allows for the selection of a well-diversified set out of an arbitrary given set, while maintaining low computational cost. When embedded into an evolutionary search (NSGA-II), the PSA has significantly enhanced the exploitation of diversity. In this paper, the ability of the PSA to enhance evolutionary multiobjective algorithms (EMOAs) is further investigated. Two research directions are explored here. The first one deals with the integration of the PSA within an EMOA with a novel strategy. Contrary to most EMOAs, that give a higher priority to proximity over diversity, this new strategy promotes the balance between the two. The suggested algorithm allows some dominated solutions to survive, if they contribute to diversity. It is shown that such an approach substantially reduces the risk of the algorithm to fail in finding the Pareto front. The second research direction explores the use of the PSA as an archiving selection mechanism, to improve the averaged Hausdorff distance obtained by existing EMOAs. It is shown that the integration of the PSA into NSGA-II-I and ∆ p -EMOA as an archiving mechanism leads to algorithms that are superior to base EMOAS on problems with disconnected Pareto fronts.

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Using the Averaged Hausdorff Distance as a Performance Measure in Evolutionary Multiobjective Optimization

Cited by 430 publications

References 36 publications

A Weakly Pareto Compliant Quality Indicator

A Weakly Pareto Compliant Quality Indicator

Latest Stored Information Based Adaptive Selection Strategy for Multiobjective Evolutionary Algorithm

PSA Based Multi Objective Evolutionary Algorithms

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