Why Unary Quality Indicators Are Not Inferior to Binary Quality Indicators

Lizárraga, Giovanni; Gomez, Marco Jimenez; Castañon, Mauricio Garza; Acevedo-Dávila, J. L.; Rionda, Salvador Botello

doi:10.1007/978-3-642-05258-3_57

Cited by 4 publications

(6 citation statements)

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“…Moreover, Pareto dominance is sufficient but not necessary to consider an APF preferable to another: there are pairs of APFs with considerable quality difference which are considered, by Pareto dominance relations, as not comparable [16]. Hence, if a comparison method based on UQI were -compatible, the indicator could not provide any preference in the case of two incomparable APFs.…”

Section: Compatibility and Completenessmentioning

confidence: 99%

“…Therefore, DOA can be used to evaluate the performance of optimization algorithms instead of the Hypervolume since it is proven that DOA is ≻-complete (then DOA is a weakly Pareto compliant UQI). A unary QI (UQI) estimates a non-dominated solution set quality by means of a real number [16]; then it is useful to estimate the effectiveness of a MOOA. Several known UQIs have no or limited completeness as regards Pareto dominance relations and are unable to take into account all the features listed previously.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, defining n a (n a < n) as the number of functions for which the f k,a − f k,i ≥ 0 (f k,a ≥ f k,i , k = 1,..,n a and f k,a < f k,i , k = n a + 1,..,n) expression (16) can be rewritten as:…”

Section: The Weakly Pareto Compliant Quality 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: Compatibility and Completenessmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Weakly Pareto Compliant Quality Indicator

Dilettoso

Rizzo

2017

MCA

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“…Let ► be an arbitrary dominance relation among those defined in It has been demonstrated [11] that a comparison method based on a UQI (or on a finite combination of UQIs) that is both ⊳-compatible and ⊳-complete cannot exist. Moreover, Pareto dominance is sufficient but not necessary to consider an APF preferable to another: there are pairs of APFs with considerable quality difference which are considered, by Pareto dominance relations, as not comparable [16]. Hence, if a comparison method based on UQI were ⊳-compatible, the indicator could not provide any preference in the case of two incomparable APFs.…”

Section: Compatibility and Completenessmentioning

confidence: 99%

“…Each goal represents a desired feature of the APF: in the following we refer to them as closeness, distribution, extension and cardinality, respectively. A unary QI (UQI) estimates one non-dominated solutions set quality by means of a real number [16]; then it is useful to estimate the effectiveness of a MOOA.…”

Section: Introductionmentioning

confidence: 99%

A Weakly Pareto Compliant Quality Indicator

Dilettoso

Rizzo

2016

Preprint

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In multi-objective optimization problems, the optimization target is to obtain a set of non-dominated solutions. Comparing solution sets is crucial in evaluating the performances of different optimization algorithms. The use of performance indicators is common in comparing those sets and, subsequently, optimization algorithms. A good solution set must be close to the Pareto-optimal front, well-distributed, maximally extended and fully filled. Therefore, an effective performance indicator must encompass these features as a whole and 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. Moreover, DOA computation is easy and fast.

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