Kriging-model-based multi-objective robust optimization and trade-off-rule mining using association rule with aspiration vector

Sugimura, Kazuyuki; Jeong, Shinkyu; Obayashi, Shigeru; Kimura, Takeshi

doi:10.1109/cec.2009.4982990

Cited by 16 publications

(11 citation statements)

References 18 publications

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“…As a result, different representations have been proposed in literature. Most notable are rule-based [8], self-organizing maps [6] and dendograms [10].…”

Section: Knowledge Representationmentioning

confidence: 99%

Design knowledge extraction in multi-objective optimization problems

Bandaru

Deb

2011

Proceedings of the 13th Annual Conference Companion on Genetic and Evolutionary Computation

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This work concerns the post-optimal analysis of the tradeoff front of a multi-objective optimization problem to extract useful design knowledge pertaining to these high-performing solutions. The expected knowledge basically consists of statistically significant relationships between the objective functions and decision variables. These relationships are represented in an intuitive and easy-to-use mathematical form. Since a number of such relationships may exist, for efficiency it is desirable that they are obtained in a single knowledge extraction step. Further, problem knowledge can be explored at two levels: lower and higher. At the lower-level, our interest is in finding a subset of the trade-off solutions to which the obtained relationships are exclusive. The higherlevel knowledge addresses the effect of varying the problem parameters (that are kept constant in one run) on the tradeoff front and therefore on the relationships. These concepts are explained through different examples.

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“…As a result, different representations have been proposed in literature. Most notable are rule-based [8], self-organizing maps [6] and dendograms [10].…”

Section: Knowledge Representationmentioning

confidence: 99%

Design knowledge extraction in multi-objective optimization problems

Bandaru

Deb

2011

Proceedings of the 13th Annual Conference Companion on Genetic and Evolutionary Computation

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“…Sugimura et al . () also assumed that there are design variables and mines for design rules that specify which variable settings lead to which fitness levels. Preliminary work of the author (Ulrich et al ., ) applies biclustering to the (binary) decision space to identify characteristic subsets of decision variables, called modules.…”

Section: Related Workmentioning

confidence: 99%

Pareto‐Set Analysis: Biobjective Clustering in Decision and Objective Spaces

Ulrich

2012

Multi Criteria Decision Anal

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Multiobjective problems usually contain conflicting objectives. Therefore, there is no single best solution but a set of solutions that represent different tradeoffs between these objectives. Knowledge of this front can help in understanding the optimization problem better, as promising designs can be identified, and it can be seen what the achievable tradeoffs between the objective values are. Although for real‐world problems, this interpretation of the front is usually not straightforward. This paper proposes a method to help the decision maker by clustering a given set of tradeoff solutions. It does so by extending the standard approach of clustering the solutions in objective space, such that it finds clusters that are compact and well separated both in decision space and in objective space. It is not the goal of the method to provide the decision maker with a single preferred solution. Instead, it helps the decision maker by structuring the tradeoff solutions such that he or she can learn about the problem. More precisely, a good clustering of the tradeoff solutions both in decision space and in objective space elicits information from the front about what design types lead to what regions in objective space. The novelty of the presented approach over existing work is its general nature, as it does not require the identification of distinct design variables or feature vectors. Instead, the proposed method only requires that a distance measure between a given pair of solutions can be calculated both in decision space and in objective space. As good clusters in decision space do not necessarily correspond to good clusters in objective space, we formulate this clustering problem as a biobjective optimization problem and propose PAN, a multiobjective evolutionary algorithm, to generate promising partitionings. Tests on artificial datasets are used to identify a suitable representation and a suitable partitioning goodness measure for PAN. Results from applying PAN to a knapsack problem and a bridge construction problem show that PAN is able to find multiple tradeoffs between good clustering in decision space and in objective space. Copyright © 2012 John Wiley & Sons, Ltd.

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“…The proofof-concept was first shown by Deb [4] through a process called innovization which we discuss later in Section I-A. The trade-off-rule mining approach [5] uses an aspiration vector to extract trade-off control principles from the Pareto front in the form of association rules. Sugimura et al [6] employed the rough set theory for achieving the same.…”

Section: Introductionmentioning

confidence: 99%

Automated discovery of vital knowledge from Pareto-optimal solutions: First results from engineering design

Bandaru

Deb

2010

IEEE Congress on Evolutionary Computation

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Real world multi-objective optimization problems are often solved with the only intention of selecting a single trade-off solution by taking up a decision-making task. The computational effort and time spent on obtaining the entire Pareto front is thus not justifiable. The Pareto solutions as a whole contain within them a lot more information than that is used. Extracting this knowledge would not only give designers a better understanding of the system, but also bring worth to the resources spent. The obtained knowledge acts as governing principles which can help solve other similar systems easily. We propose a genetic algorithm based unsupervised approach for learning these principles from the Pareto-optimal dataset of the base problem. The methodology is capable of discovering analytical relationships of a certain type between different problem entities.

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Kriging-model-based multi-objective robust optimization and trade-off-rule mining using association rule with aspiration vector

Cited by 16 publications

References 18 publications

Design knowledge extraction in multi-objective optimization problems

Design knowledge extraction in multi-objective optimization problems

Pareto‐Set Analysis: Biobjective Clustering in Decision and Objective Spaces

Automated discovery of vital knowledge from Pareto-optimal solutions: First results from engineering design

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