Measuring the quality of discrete representations of efficient sets in multiple objective mathematical programming

Sayın, Serpil

doi:10.1007/s101070050011

Cited by 73 publications

(106 citation statements)

References 18 publications

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“…Thus, we cannot conclude whether one set is better or worse than another by just looking at the order of the indicator values. A similar argument as for the generational distance applies to the coverage error indicator presented in [16]; the only difference is that the coverage error denotes the minimum distance to the Pareto-optimal front instead of the average distance.…”

Section: Incompatibilitymentioning

confidence: 99%

Performance assessment of multiobjective optimizers: an analysis and review

Zitzler

Thiele

Laumanns

et al. 2003

IEEE Trans. Evol. Computat.

3,640

1,766

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An important issue in multiobjective optimization is the quantitative comparison of the performance of different algorithms. In the case of multiobjective evolutionary algorithms, the outcome is usually an approximation of the Pareto-optimal front, which is denoted as an approximation set, and therefore the question arises of how to evaluate the quality of approximation sets. Most popular are methods that assign each approximation set a vector of real numbers that reflect different aspects of the quality. Sometimes, pairs of approximation sets are considered too. In this study, we provide a rigorous analysis of the limitations underlying this type of quality assessment. To this end, a mathematical framework is developed which allows to classify and discuss existing techniques.

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Section: Incompatibilitymentioning

confidence: 99%

Performance assessment of multiobjective optimizers: an analysis and review

Zitzler

Thiele

Laumanns

et al. 2003

IEEE Trans. Evol. Computat.

3,640

1,766

View full text Add to dashboard Cite

show abstract

“…The first three measures were proposed by Sayın (2000) and the representation error was introduced in (Ruzika, 2007). The coverage error quantifies how accurate the representation represents the whole nondominated set.…”

Section: Definitionmentioning

confidence: 99%

“…This stopping condition can also be implemented in our new algorithm, and the needed analogue results for three objectives are also proven. However, since we experienced that the volume of boxes is not a robust and reliable quality measure, as lowerdimensional boxes would get an empty volume and boxes with two huge sides and one very small side would not be penalized, the focus in this document lies on the coverage error introduced in (Sayın, 2000). Furthermore, it will also be explained how the other quality measures, i. e. cardinality and uniformity, can be treated in the theoretical analysis of the algorithm.…”

Section: Our Contributionmentioning

confidence: 99%

A coverage-based Box-Algorithm to compute a representation for optimization problems with three objective functions

Kühn

Ruzika

2016

J Glob Optim

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Abstract. A new algorithm for optimization problems with three objective functions is presented which computes a representation for the set of nondominated points. This representation is guaranteed to have a desired coverage error and a bound on the number of iterations needed by the algorithm to meet this coverage error is derived. Since the representation does not necessarily contain nondominated points only, ideas to calculate bounds for the representation error are given. Moreover, the incorporation of domination during the algorithm and other quality measures are discussed.

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“…3 above, we can clearly find out the computational effort increases at a linear rate with the number of points in the solution set. Take Sayin 's [20] metric fo r examp le, this is a kind of algorith m based on the distances of two points in the population and thus has a computational co mplexity of O (N 2 ). Therefore, when it comes to dealing with quantities of data using diversity performance metric, entropy met ric has an absolutely advantage over other metrics.…”

Section: Run Time Analysismentioning

confidence: 99%

Diversity Based on Entropy: A Novel Evaluation Criterion in Multi-objective Optimization Algorithm

Wang¹,

Chen²

2012

IJISA

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Abstract-Quality assessment of Multi-objective Optimization algorith ms has been a major concern in the scientific field during the last decades. The entropy metric is introduced and highlighted in co mputing the diversity of Mult i-objective Optimization A lgorith ms. In this paper, the definit ion of the entropy metric and the approach of diversity measurement based on entropy are presented. This measurement is adopted to not only Multi-objective Evolutionary Algorithm but also Multi-objective Immune A lgorith m. Besides, the key techniques of entropy metric, such as the appropriate princip le of grid method, the reasonable parameter selection and the simp lificat ion of density function, are discussed and analyzed. Moreover, experimental results prove the validity and efficiency of the entropy metric. The computational effort of entropy increases at a linear rate with the number of points in the solution set, which is indeed superior to other quality indicators. Co mpared with Generational Distance, it is proved that the entropy metric have the capability of describing the d iversity performance on a quantitative basis. Therefore, the entropy criterion can serve as a high-efficient d iversity criterion of Mu ltiobjective optimization algorithms.

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Measuring the quality of discrete representations of efficient sets in multiple objective mathematical programming

Cited by 73 publications

References 18 publications

Performance assessment of multiobjective optimizers: an analysis and review

Performance assessment of multiobjective optimizers: an analysis and review

A coverage-based Box-Algorithm to compute a representation for optimization problems with three objective functions

Diversity Based on Entropy: A Novel Evaluation Criterion in Multi-objective Optimization Algorithm

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