Generating Well-Spaced Points on a Unit Simplex for Evolutionary Many-Objective Optimization

Blank, Julian; Deb, Kalyanmoy; Dhebar, Yashesh; Bandaru, Sunith; Seada, Haitham

doi:10.1109/tevc.2020.2992387

Cited by 49 publications

(21 citation statements)

References 29 publications

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“…Given a weight vector w(t) = (w 1 (t), w 2 (t)) T , it changes gradually and periodically with the process of the evolution as {w 1 (t) = | sin(2πt)/F |, w 2 (t) = 1.0 − w 1 (t)} where F is a parameter that controls the change frequency, t is the number of generation and | • | returns the absolute value. More recently, Blank et al [32] proposed to use the Riesz s-energy metric to iteratively generate a set of well-spaced weight vectors in high-dimensional spaces.…”

Section: Fixed Methodsmentioning

confidence: 99%

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Decomposition Multi-Objective Evolutionary Optimization: From State-of-the-Art to Future Opportunities

2021

Preprint

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Decomposition has been the mainstream approach in the classic mathematical programming for multi-objective optimization and multi-criterion decision-making. However, it was not properly studied in the context of evolutionary multi-objective optimization until the development of multi-objective evolutionary algorithm based on decomposition (MOEA/D). In this article, we present a comprehensive survey of the development of MOEA/D from its origin to the current state-of-the-art approaches. In order to be self-contained, we start with a step-by-step tutorial that aims to help a novice quickly get onto the working mechanism of MOEA/D. Then, selected major developments of MOEA/D are reviewed according to its core design components including weight vector settings, subproblem formulations, selection mechanisms and reproduction operators. Besides, we also overviews some further developments for constraint handling, computationally expensive objective functions, preference incorporation, and real-world applications. In the final part, we shed some lights on emerging directions for future developments.

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Section: Fixed Methodsmentioning

confidence: 99%

“…Fixed methods MOGLS [13,17,25], MOEA/D-RW [26] Random method NSGA-III [27], MOEA/DD [28] Multi-layer method UMOEA/D [29,30], UMODE/D [31] Uniform design Riesz s-energy function [32], RMA [16] Others…”

Section: Subcategory Algorithm Name Core Techniquementioning

confidence: 99%

Decomposition Multi-Objective Evolutionary Optimization: From State-of-the-Art to Future Opportunities

2021

Preprint

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“…Extensive hyperparameter tuning was conducted to narrow down on the final values of hyperparameters used in this study Li et al 2019b). In addition to parameters like population size, number of generations, and mutation probabilities, both these algorithms also require reference directions that are created using Das & Dennis (1998) and the Riesz s-energy approaches (Blank et al 2021). The number of reference directions should be such that H ≈ P, where P is the population size .…”

Section: Optimisation Algorithmsmentioning

confidence: 99%

Multiobjective optimisation and cluster analysis in placement of best management practices in an urban flooding scenario

Dwivedula

Madhuri

Raju

et al. 2021

Water Science and Technology

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Urban floods cause massive damage to infrastructure and loss of life. This research is being carried out to study how Best Management Practices (BMPs) can mitigate the negative effects of urban floods during extreme rainfall events. Strategically placing BMPs throughout open areas and rooftops in urban areas serves multiple purposes of storage of rainwater, removal of pollutants from surface runoff and sustainable utilisation of land. This situation is framed as a multiobjective optimisation problem to analyse the trade-offs between multiple goals of runoff reduction, construction cost and pollutant load reduction. Output includes a wide range of choices to choose from for decision makers. Proposed methodology is demonstrated with a case study of Greater Hyderabad Municipal Corporation (GHMC), India. Historical extreme rainfall event of 237.5 mm which occurred in year 2016 and extreme rainfall event of 1,740.62 mm corresponding to Representative Concentration Pathway (RCP) 2.6 were considered for analysis. Two multiobjective optimisation algorithms, namely, Non-dominated Sorting Genetic Algorithm – III (NSGA-III) and Constrained Two-Archive Evolutionary Algorithm (C-TAEA) are employed to solve the BMP placement problem, following which the resulting pareto-fronts are ensembled. K-Medoids-based cluster analysis is performed on the resulting ensembled pareto-front. The proposed ensembled approach identified ten possible BMP configurations with costs ranging from Rs. to surface runoff reduction ranging from to and pollutant load removal ranging from tonnes. Use of BMPs in future event has the potential to reduce surface runoff from , while simultaneously removing tonnes of pollutants for cost ranging from The proposed framework forms an effective and novel way to characterise and solve BMP optimisation problems in context of climate change, presenting a view of the urban flooding scenario today, and the likely course of events in the future.

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“…For task k, the items to be initialized include: the set of weight vectors W k , the internal neighborhood structure B k of each subproblem, the task index Φ k of the external neighborhood of each subproblem, the external neighborhood structure B k of each subproblem, and the sub-population P k and the ideal point Z k . For the weight vectors, we use the method mentioned in [40] to initialize them. The internal neighborhood of each subproblem is defined as the T closest weight vectors based on the Euclidean distance between the weight vectors [17].…”

Section: A Algorithm Frameworkmentioning

confidence: 99%

Multiobjective Multitasking Optimization Based on Decomposition with Dual Neighborhoods

Wang¹,

Dong²,

Tang³

et al. 2021

Preprint

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This paper proposes a multiobjective multitasking optimization evolutionary algorithm based on decomposition with dual neighborhood. In our proposed algorithm, each subproblem not only maintains a neighborhood based on the Euclidean distance among weight vectors within its own task, but also keeps a neighborhood with subproblems of other tasks. Gray relation analysis is used to define neighborhood among subproblems of different tasks. In such a way, relationship among different subproblems can be effectively exploited to guide the search. Experimental results show that our proposed algorithm outperforms four state-of-the-art multiobjective multitasking evolutionary algorithms and a traditional decomposition-based multiobjective evolutionary algorithm on a set of test problems.

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Generating Well-Spaced Points on a Unit Simplex for Evolutionary Many-Objective Optimization

Cited by 49 publications

References 29 publications

Decomposition Multi-Objective Evolutionary Optimization: From State-of-the-Art to Future Opportunities

Decomposition Multi-Objective Evolutionary Optimization: From State-of-the-Art to Future Opportunities

Multiobjective optimisation and cluster analysis in placement of best management practices in an urban flooding scenario

Multiobjective Multitasking Optimization Based on Decomposition with Dual Neighborhoods

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