Machine learning based decision support for many-objective optimization problems

Duro, João A.; Saxena, Dhish Kumar; Deb, Kalyanmoy; Zhang, Qingfu

doi:10.1016/j.neucom.2014.06.076

Cited by 25 publications

(34 citation statements)

References 30 publications

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“…In that: (i) an MOEA termination guided by the ratio of dominated solutions may lead to a poor POFapproximation and also poor POF-representation [30], and (ii) if the MOEA is allowed to run beyond the inferred termination, significant improvements in the POFrepresentation could be achieved, which paves way for effective objective-reduction [30]- [32] in MaOPs.…”

Section: Past Research On Termination Criterion Formentioning

confidence: 99%

“…Further research in this direction could provide interesting insights and results. • unraveling the timing of objective-reduction [30], [31] based decision-support for MaOPs: the importance of applying objective reduction techniques to derive a decision support characterized by objectivity, repeatability, consistency, and coherence [32] is being recognized.…”

Section: Potential Future Directionsmentioning

confidence: 99%

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Entropy-Based Termination Criterion for Multiobjective Evolutionary Algorithms

Saxena

Sinha

Duro

et al. 2016

IEEE Trans. Evol. Computat.

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Multi-objective Evolutionary Algorithms evolve a population of solutions through successive generations towards the Pareto-optimal Front. One of the most critical questions faced by the researchers and practitioners in this domain, relates to the number of generations that may be sufficient for an algorithm to offer a good approximation of the Pareto-optimal Front, for a given problem. Ironically, till date this question largely remains unanswered and the number of generations are arbitrarily fixed a priori, with potentially punitive implications. If the a priori fixed generations are insufficient, then the algorithm reports suboptimal solutions. In contrast, if the a priori fixed generations are far-too-many, it implies waste of computational resources. This paper proposes a novel entropy based dissimilarity measure that helps identify on-the-fly the number of generations beyond which an algorithm stabilizes, implying that either a good approximation has been obtained, or that it can not be obtained due to the stagnation of the algorithm in the search space. Given that, in either case no further improvement in the approximation can be obtained, despite additional computational expense, the proposed dissimilarity measure provides a termination criterion and facilitates a termination detection algorithm. The generality, on-the-fly implementation, low computational complexity, and the demonstrated efficacy of the proposed termination detection algorithm, on a wide range of multi-and many-objective test problems, define the novel contribution of this paper.

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Section: Past Research On Termination Criterion Formentioning

confidence: 99%

Section: Potential Future Directionsmentioning

confidence: 99%

Entropy-Based Termination Criterion for Multiobjective Evolutionary Algorithms

Saxena

Sinha

Duro

et al. 2016

IEEE Trans. Evol. Computat.

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“…To reduce cognitive burden for the DM when the number of objectives is large, Sinha, Saxena, Deb, and Tiwari (2013) proposed to perform dimensionality reduction before engaging the DM in ranking the solutions according to his/her preferences. Duro, Saxena, Deb, and Zhang (2010) suggested a machine learning-based decision support framework for many-objective optimization problems to address different features of DM preferences, such as objectivity, repeatability, consistency, and coherence. In all cases, the quality of the methods proposed, concerning the correspondence between the solutions produced and the preferences of the DM, was assessed empirically.…”

Section: Introductionmentioning

confidence: 99%

Methodology to select solutions for multiobjective optimization problems: Weighted stress function method

Ferreira

Fonseca

Denysiuk

et al. 2017

J. Multi-Crit. Decis. Anal.

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The weighted stress function method is proposed here as a new way of identifying the best solution from a set of nondominated solutions according to the decision maker's preferences, expressed in terms of weights. The method was tested using several benchmark problems from the literature, and the results obtained were compared with those of other methods, namely, the reference point evolutionary multiobjective optimization (EMO), the weighted Tchebycheff metric, and a goal programming method. The weighted stress function method can be seen to exhibit a more direct correspondence between the weights set by the decision maker and the final solutions obtained than the other methods tested.KEYWORDS evolutionary algorithm, multiobjective optimization, preference-based search

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“…In terms of the latter, the selection operation either becomes ineffective or computationally too demanding. For instance: (a) the most commonly used primary selection, as in NSGA-II [4], is based on Pareto-dominance which fails to induce an effective partial order on the solutions as the number of objectives increases [5], (b) there is huge computational cost involved in dealing with a large number of weight vectors in decomposition based MOEAs, such as MOEA/D [6], and (c) the indicator based MOEAs, such as HypE [7] become impractical since indicators like hypervolume are computationally too demanding. This paper distinguishes between: (δ-I) the capability of a decision support framework to reveal the preference-structure of different objectives in a given input solution set (non-dominated solutions obtained from an MOEA), and (δ-II) the capability to determine the timing of decision support, implying, the capability to determine the number of generations along an MOEA run at/after which, the corresponding non-dominated solution set could be treated as the most appropriate input solution set for application of the machine learning based framework for revelation of the objectives' preference-structure.…”

Section: Introductionmentioning

confidence: 99%

“…This paper distinguishes between: (δ-I) the capability of a decision support framework to reveal the preference-structure of different objectives in a given input solution set (non-dominated solutions obtained from an MOEA), and (δ-II) the capability to determine the timing of decision support, implying, the capability to determine the number of generations along an MOEA run at/after which, the corresponding non-dominated solution set could be treated as the most appropriate input solution set for application of the machine learning based framework for revelation of the objectives' preference-structure. While the former has been demonstrated in [5], this paper focuses on the latter-a more fundamental aspect of when to time the decision support. The criticality of the latter aspect can be gauged from the fact that it is analogous to the fundamental and largely unaddressed question (until [9]) of when to terminate an MOEA in the absence of a termination criterion that is robust in terms of its: (a) generality, implying that it does not require an a priori knowledge of the POF, and neither depends on MOEA-specific operators, nor on the MOEA-related performance indicators, (b) on-the-fly implementation, and (c) computational efficiency enabling efficient scalability with the number of objectives.…”

Section: Introductionmentioning

confidence: 99%

Timing the Decision Support for Real-World Many-Objective Optimization Problems

Duro

Saxena

2017

Lecture Notes in Computer Science

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Lately, there is growing emphasis on improving the scalability of multi-objective evolutionary algorithms (MOEAs) so that manyobjective problems (characterized by more than three objectives) can be effectively dealt with. Alternatively, the utility of integrating decision maker's (DM's) preferences into the optimization process so as to target some most preferred solutions by the DM (instead of the whole Paretooptimal front), is also being increasingly recognized. The authors here, have earlier argued that despite the promises in the latter approach, its practical utility may be impaired by the lack of-objectivity, repeatability, consistency, and coherence in the DM's preferences. To counter this, the authors have also earlier proposed a machine learning based decision support framework to reveal the preference-structure of objectives. Notably, the revealed preference-structure may be sensitive to the timing of application of this framework along an MOEA run. In this paper the authors counter this limitation, by integrating a termination criterion with an MOEA run, towards determining the appropriate timing for application of the machine learning based framework. Results based on three real-world many-objective problems considered in this paper, highlight the utility of the proposed integration towards an objective, repeatable, consistent, and coherent decision support for many-objective problems.

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Machine learning based decision support for many-objective optimization problems

Cited by 25 publications

References 30 publications

Entropy-Based Termination Criterion for Multiobjective Evolutionary Algorithms

Entropy-Based Termination Criterion for Multiobjective Evolutionary Algorithms

Methodology to select solutions for multiobjective optimization problems: Weighted stress function method

Timing the Decision Support for Real-World Many-Objective Optimization Problems

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