Investigating the Normalization Procedure of NSGA-III

Blank, Julian; Deb, Kalyanmoy; Roy, Proteek Chandan

doi:10.1007/978-3-030-12598-1_19

Cited by 58 publications

(26 citation statements)

References 19 publications

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“…Algorithm Reference GA DE [38] NSGA-II [12] RNSGA-II [14] NSGA-III [10,26,4] UNSGA-III [43] RNSGA-III [47] MOEAD [52] to 1. This can be achieved by supplying this as a parameter in the initialization method as shown in Section 3.…”

Section: Algorithmsmentioning

confidence: 99%

Pymoo: Multi-Objective Optimization in Python

2020

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A B S T R A C TPython has become the programming language of choice for research and industry projects related to data science, machine learning, and deep learning. Since optimization is an inherent part of these research fields, more optimization related frameworks have arisen in the past few years. Only a few of them support optimization of multiple conflicting objectives at a time, but do not provide comprehensive tools for a complete multi-objective optimization task. To address this issue, we have developed pymoo, a multi-objective optimization framework in Python. We provide a guide to getting started with our framework by demonstrating the implementation of an exemplary constrained multiobjective optimization scenario. Moreover, we give a high-level overview of the architecture of pymoo to show its capabilities followed by an explanation of each module and its corresponding sub-modules. The implementations in our framework are customizable and algorithms can be modified/extended by supplying custom operators. Moreover, a variety of single, multi and many-objective test problems are provided and gradients can be retrieved by automatic differentiation out of the box. Also, pymoo addresses practical needs, such as the parallelization of function evaluations, methods to visualize low and high-dimensional spaces, and tools for multi-criteria decision making. For more information about pymoo, readers are encouraged to visit: https://pymoo.org

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Section: Algorithmsmentioning

confidence: 99%

Pymoo: Multi-Objective Optimization in Python

2020

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“…iii. Many-objective NSGA-II called as NSGA-III [ [43]- [45]] to optimize workplace design for three or more tasks.…”

Section: Workplace Optimizationmentioning

confidence: 99%

“…As a result of this selection method, there will be a situation where a front needs to be split because not all solutions will be selected. In the case of optimizing a two-tasks workplace, solutions are selected based on crowding distance [42]; otherwise, the reference direction selection method [45] is used. Accordingly, the parent population (Pt+1) is formulated, and the process continues until it reaches the number of generations (G) defined by the user in order to identify optimal Pareto solutions.…”

Section: Workplace Optimizationmentioning

confidence: 99%

Parameterized Design Optimization Framework for Worker-Friendly Workplaces in Modular Construction

Zaalouk

Han

2021

J. Constr. Eng. Manage.

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Workers in modular construction suffer frequent exposure to ergonomic risks that lead to work-related musculoskeletal disorders (WMSDs). Addressing ergonomic risk factors is thus critical to enhance the productivity of production lines and reduce social expenses for workers' recovery. Towards this goal, an ergonomic-driven workplace design approach is essential to not only prevent risks through design changes proactively but also accommodate medical restrictions for workers getting back on the job during the health recovery period. However, a lack of methods to identify root causes of ergonomic risks among various workplace design parameters (WDPs) and design optimal workplace settings for complex and multiple tasks leads to difficulties in adopting this twofold design approach. To address this limitation, this thesis proposes a parameterized workplace design optimization framework that involves four procedures: (i) performing design initiation to identify WDPs and accordingly create design alternatives using the definitive screening design (DSD) method; (ii) building interactive worker-workplace simulation models to acquire workers' body posture data and assess ergonomic risks among the different design alternatives; (iii) developing predictive surrogate models of the tasks using DSD statistical analysis; and (iv) optimizing workplace settings using the genetic algorithm to minimize ergonomic risk scores. The proposed framework is demonstrated through a case study to design a drywall preparation workplace in a real modular construction plant.

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“…Second, we translate each objective f j (x) by subtracting z min j , denoted as f j (x) = f j (x) − z min j . Third, we determine M extreme points to constitute a M-dimensional hyperplane that makes the Achievement Scalarization Function (ASF) minimum (Blank, Deb, and Roy, 2019), expressed as z j,max = f n (x) | min n∈F1 {ASF j } where j ∈ {1, 2, . .…”

Section: Normalization Of Population Membersmentioning

confidence: 99%

“…vector composed of the maximum value of each function to generate, intercept, and then normalize the functions (the last generation positive intercept can be utilized as well). Recently, authors have revealed how to handle degenerate cases and negative intercepts (Blank et al, 2019) to avoid the algorithm getting stuck, but that solution remains as future research.…”

Section: Normalization Of Population Membersmentioning

confidence: 99%

EF1-NSGA-III: An evolutionary algorithm based on the first front to obtain non-negative and non-repeated extreme points

2020

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Multi-Objective and Many-objective Optimization problems have been extensively solved through evolutionary algorithms over a few decades. Despite the fact that NSGA-II and NSGA-III are frequently employed as a reference for a comparative evaluation of new evolutionary algorithms, the latter is proprietary. In this paper, we used the basic framework of the NSGA-II, which is very similar to the NSGA-III, with significant changes in its selection operator. We took the first front generated at the non-dominating sort procedure to obtain nonnegative and nonrepeated extreme points. This opensource version of the NSGA-III is called EF1-NSGA-III, and its implementation does not start from scratch; that would be reinventing the wheel. Instead, we took the NSGA-II code from the authors in the repository of the Kanpur Genetic Algorithms Laboratory to extend the EF1-NSGA-III. We then adjusted its selection operator from diversity, based on the crowding distance, to the one found on reference points and preserved its parameters. After that, we continued with the adaptive EF1-NSGA-III (A-EF1-NSGA-III), and the efficient adaptive EF1-NSGA-III (A2-EF1-NSGA-III), while also contributing to explain how to generate different types of reference points. The proposed algorithms resolve optimization problems with constraints of up to 10 objective functions. We tested them on a wide range of benchmark problems, and they showed notable improvements in terms of convergence and diversity by using the Inverted Generational Distance (IGD) and the HyperVolume (HV) performance metrics. The EF1-NSGA-III aims to resolve the power consumption for Centralized Radio Access Networks and the BiObjective Minimum DiameterCost Spanning Tree problems.

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Investigating the Normalization Procedure of NSGA-III

Cited by 58 publications

References 19 publications

Pymoo: Multi-Objective Optimization in Python

Pymoo: Multi-Objective Optimization in Python

Parameterized Design Optimization Framework for Worker-Friendly Workplaces in Modular Construction

EF1-NSGA-III: An evolutionary algorithm based on the first front to obtain non-negative and non-repeated extreme points

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