Theory and Algorithms for Finding Knees

Shukla, Pradyumn Kumar; Braun, Marlon Alexander; Schmeck, Hartmut

doi:10.1007/978-3-642-37140-0_15

Cited by 13 publications

(7 citation statements)

References 23 publications

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“…Therefore, we reformulated the notion to make it compatible with minimization and to avoid scalarization values of zero. Finally, proper utility [25] is a concept that has only recently emerged. It is founded on the concept of proper Pareto optimality [18,29] and describes desirability in terms of tradeoffs.…”

Section: Definition 3 (Scalarization Function)mentioning

confidence: 99%

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Obtaining Optimal Pareto Front Approximations using Scalarized Preference Information

Braun

Shukla

Schmeck

2015

Proceedings of the 2015 Annual Conference on Genetic and Evolutionary Computation

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Scalarization techniques are a popular method for articulating preferences in solving multi-objective optimization problems. These techniques, however, have so far proven to be ill-suited in finding a preference-driven approximation that still captures the Pareto front in its entirety. Therefore, we propose a new concept that defines an optimal distribution of points on the front given a specific scalarization function. It is proven that such an approximation exists for every real-valued problem irrespective of the shape of the corresponding front under some very mild conditions. We also show that our approach works well in obtaining an equidistant approximation of the Pareto front if no specific preference is articulated. Our analysis is complemented by the presentation of a new algorithm that implements the aforementioned concept. We provide in-depth simulation results to demonstrate the performance of our algorithm. The analysis also reveals that our algorithm is able to outperform current state-of-the-art algorithms on many popular benchmark problems.

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Section: Definition 3 (Scalarization Function)mentioning

confidence: 99%

“…Other scalarization techniques have been used in conjunction with minimum threshold levels, underneath which all solutions are considered to be equal. Traditional evolutionary selection mechanisms have then been applied to find an approximation of the preferred set [11,25]. Nevertheless, choosing a threshold level can be difficult.…”

Section: Introductionmentioning

confidence: 99%

Obtaining Optimal Pareto Front Approximations using Scalarized Preference Information

Braun

Shukla

Schmeck

2015

Proceedings of the 2015 Annual Conference on Genetic and Evolutionary Computation

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“…After grouping the solution in K groups, a selection method should be used to pick up a representative solution of each cluster. Several single solution selection methods were proposed to rank each solution in a given Pareto optimal set by calculating a corresponding rank [40–42]. This rank is then used to choose the best solution.…”

Section: Proposed Parameter Optimisation Frameworkmentioning

confidence: 99%

Bio‐inspired metaheuristic framework for clustering optimisation in VANETs

Alsuhli

Fahmy²,

Khattab³

2020

IET intell. transp. syst

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“…This algorithm is based on NSGA-II [5] and PKEA [11] and uses a cone based approach to focus on different regions of the Pareto front.…”

Section: Cone Utility Based Genetic Al-gorithmmentioning

confidence: 99%

On homogenization of coal in longitudinal blending beds

Shukla

Cipold²,

Bachmann³

et al. 2014

Proceedings of the 2014 Annual Conference on Genetic and Evolutionary Computation

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Coal blending processes mainly use static and non-reactive blending methods like the well-known Chevron stacking. Although real-time quality measurement techniques such as online X-ray fluorescence measurements are available, the possibility to explore a dynamic adaptation of the blending process to the current quality data obtained using these techniques has not been explored. A dynamic adaptation helps to mix the coal from different mines in an optimal way and deliver a homogeneous product. The paper formulates homogenization of coal in longitudinal blending beds as a bi-objective problem of minimizing the variance of the cross-sectional quality and minimizing the height variance of the coal heap in the blending bed. We propose a cone based evolutionary algorithm to explore different trade-off regions of the Pareto front. A pronounced knee region on the Pareto front is found and is investigated in detail using a knee search algorithm. There are many interesting problem insights that are gained by examining the solutions found in different regions. In addition, all the knee solutions outperform the traditional Chevron stacking method.

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Theory and Algorithms for Finding Knees

Cited by 13 publications

References 23 publications

Obtaining Optimal Pareto Front Approximations using Scalarized Preference Information

Obtaining Optimal Pareto Front Approximations using Scalarized Preference Information

Bio‐inspired metaheuristic framework for clustering optimisation in VANETs

On homogenization of coal in longitudinal blending beds

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