Objective Reduction in Many-Objective Optimization: Linear and Nonlinear Algorithms

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

doi:10.1109/tevc.2012.2185847

Cited by 259 publications

(141 citation statements)

References 30 publications

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“…In case there is a strong correlation between objectives, some objectives can be removed [35]. To this end, statistical machine techniques, such as feature selection [36], principal component analysis (PCA) [37], [38], and maximum variance unfolding (MVU) [39] can be employed for objective reduction. In practice, users are often interested in only a part of the Pareto optimal solutions [40].…”

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confidence: 99%

Diversity Assessment in Many-Objective Optimization

Wang

Jin

Yao

2017

IEEE Trans. Cybern.

213

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Abstract-Maintaining diversity is one important aim of multiobjective optimization. However, diversity for many-objective optimization problems is less straightforward to define than for multi-objective optimization problems. Inspired by measures for biodiversity, we propose a new diversity metric for manyobjective optimization, which is an accumulation of the dissimilarity in the population, where an Lp-norm-based (p < 1) distance is adopted to measure the dissimilarity of solutions. Empirical results demonstrate our proposed metric can more accurately assess the diversity of solutions in various situations. We compare the diversity of the solutions obtained by four popular many-objective evolutionary algorithms using the proposed diversity metric on a large number of benchmark problems with two to ten objectives. The behaviors of different diversity maintenance methodologies in those algorithms are discussed in depth based on the experimental results. Finally, we show that the proposed diversity measure can also be employed for enhancing diversity maintenance or reference set generation in many-objective optimization.

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confidence: 99%

Diversity Assessment in Many-Objective Optimization

Wang

Jin

Yao

2017

IEEE Trans. Cybern.

213

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“…The conflict might be global or local (the range of conflict) (Freitas et al 2013), and linear or nonlinear (the structure of correlation) (Saxena et al 2013). …”

Section: Conflicting Objectivesmentioning

confidence: 99%

“…The objective reduction approach based on PCA (Saxena et al 2013) is a well-known one. Therefore, we compare our objective selection method with the PCA method (using the same setting as in Saxena et al 2013). As NCIE is a nonlinear metric, we also compare it with the kernel PCA (KPCA) method (with Gaussian kernel function).…”

Section: Objective Selectionmentioning

confidence: 99%

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Objective reduction based on nonlinear correlation information entropy

Wang

Yao

2015

Soft Comput

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It is hard to obtain the entire solution set of a many-objective optimization problem (MaOP) by multiobjective evolutionary algorithms (MOEAs) because of the difficulties brought by the large number of objectives. However, the redundancy of objectives exists in some problems with correlated objectives (linearly or nonlinearly). Objective reduction can be used to decrease the difficulties of some MaOPs. In this paper, we propose a novel objective reduction approach based on nonlinear correlation information entropy (NCIE). It uses the NCIE matrix to measure the linear and nonlinear correlation between objectives and a simple method to select the most conflicting objectives during the execution of MOEAs. We embed our approach into both Pareto-based and indicator-based MOEAs to analyze the impact of our reduction method on the performance of these algorithms. The results show that our approach significantly improves the performance of Pareto-based MOEAs on both reducible and irreducible MaOPs, but does not much help the performance of indicator-based MOEAs.

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“…Also for the DTLZ and WFG functions, there is no function having a convex Pareto front; however, a convex Pareto front may bring more difficulty (than a concave Pareto front) for decomposition-based algorithms in terms of solutions' uniformity maintenance [20]. In addition, the DTLZ and WFG functions which are used as MaOPs with a degenerate Pareto front (i.e., DTLZ5, DTLZ6 and WFG3) have a nondegenerate part of the Pareto front when the number of objectives is larger than four [10,21,22]. This naturally affects the performance investigation of evolutionary algorithms on degenerate MaOPs.…”

Section: Introductionmentioning

confidence: 99%

A benchmark test suite for evolutionary many-objective optimization

Cheng

Tian

et al. 2017

Complex Intell. Syst.

401

118

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In the real world, it is not uncommon to face an optimization problem with more than three objectives. Such problems, called many-objective optimization problems (MaOPs), pose great challenges to the area of evolutionary computation. received little attention. Several test problem suites which were designed for multi-objective optimization have still been dominantly used in many-objective optimization. In this paper, we carefully select (or modify) 15 test problems with diverse properties to construct a benchmark test suite, aiming to promote the research of evolutionary many-objective optimization (EMaO) via suggesting a set of test problems with a good representation of various real-world scenarios.Also, an open-source software platform with a user-friendly GUI is provided to facilitate the experimental execution and data observation.

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Objective Reduction in Many-Objective Optimization: Linear and Nonlinear Algorithms

Cited by 259 publications

References 30 publications

Diversity Assessment in Many-Objective Optimization

Diversity Assessment in Many-Objective Optimization

Objective reduction based on nonlinear correlation information entropy

A benchmark test suite for evolutionary many-objective optimization

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