A Comprehensive Review on NSGA-II for Multi-Objective Combinatorial Optimization Problems

Verma, Shanu; Pant, Millie; Snášel, Václav

doi:10.1109/access.2021.3070634

Cited by 397 publications

(105 citation statements)

References 220 publications

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“…In this model, ELI and accessibility were introduced into modified GDP, while NDVI was used in modified ESV; the modification not only give economic and ecological objective a quantitative meaning, but also the ability of spatial location preference for enabling agglomeration, whereas the above objectives had only a quantitative function in the previous study [13,20]. Additionally, original NSGA-II used a neighbor-change method to reduce the fragmentation [40,42]. In our model, spatial allocation with implicit economic relationships was enhanced through a two-step mutation operator to limit fragmentation.…”

Section: Discussionmentioning

confidence: 99%

“…The Pareto frontier obtains a set of preferred solution sets by non-dominated sorting and selects the results according to the planner's needs [39]. The non-dominated sorting genetic algorithm II (NSGA-II) is a classic metaheuristic algorithm based on GA, and it can obtain Pareto set by non-dominated sorting; it has been widely used for optimizations, due to its good robustness and global search capability [40][41][42]. For example, it has been successfully applied to land use planning and integrated optimization using system dynamics models [43][44][45].…”

Section: Introductionmentioning

confidence: 99%

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Land Use Optimization for Coastal Urban Agglomerations Based on Economic and Ecological Gravitational Linkages and Accessibility

Pan

Yan

et al. 2022

Land

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Urban agglomerations (UA) are attracting increasing research attention as a global emergent phenomenon, whereby regional collaborative linkages between cities attracts and agglomerates development. However, these studies also acknowledge that ecological values may be negatively impacted by re-development, ecological fragmentation, and proximity or downstream impacts. Sustainable development, therefore, requires balancing forces from economic attraction and ecological repulsion. Forces similar to economic ones may also operate in attracting ecological enhancement towards higher-valued ecological regions; however, research regarding the role of the self-collaborative gravity-like forces shaping UA is limited in land use optimization. To assist planners, this study developed a new multi-objective land use optimization of UA that explored the intensity of economic ties and ecological gradients using the multi-objective NSGA-II algorithm. In this model, economic linkage intensity (ELI) and accessibility were used to calculate a modified GDP (gross domestic product), while the NDVI (normalized difference vegetation index) was used for the modified ESV (ecosystem services value). Spatial allocation with implicit economic accessibility relationships was enhanced through a two-step mutation operator, including a “gravity flip” spatial orientation factor. Compared to the standard NSGA-II algorithm, models of future land use of the Guangdong-Hong Kong-Macao Greater Bay Area (GBA) in 2030 have shown that the modified GDP value in our model increased by 7.41%, while the conversion rate of high-density vegetation reduced by 7.92%. The results highlighted the importance of linkage and accessibility factors in enhancing the clustering of cities. In tandem, the modified ESV also enhances ecosystem services contributions of higher value vegetated land through decentralized built-up developments. The proposed model provides managers with a comprehensive and efficient land use solution model that accounts for intrinsic linkage factors shaping the development of compact urban agglomerations.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Land Use Optimization for Coastal Urban Agglomerations Based on Economic and Ecological Gravitational Linkages and Accessibility

Pan

Yan

et al. 2022

Land

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“…The traditional particle swarm and ant colony algorithms easily become local when dealing with multiobjective problems, and the Pareto solution’s convergence effect is poor [ 32 , 33 ]. Therefore, this study selects three algorithms with good performance when dealing with constrained multiobjective optimization problems to solve the model [ 34 , 35 , 36 ]: the nondominated sorting genetic algorithm-II (NSGA-II), nondominated sorting genetic algorithm-III (NSGA-III), and a multiobjective evolutionary algorithm based on decomposition (MOEA/D).…”

Section: Methodsmentioning

confidence: 99%

“…The crowding method was used instead of the fitness sharing strategy, which was necessary to ensure the diversity of individuals. The algorithm frameworks of NSGA-III and NSGA-II are roughly the same, but the selection mechanism is different [ 35 ]. NSGA-II uses crowding to select individuals with the same non-dominated level, while NSGA-III selects individuals based on reference points.…”

Section: Methodsmentioning

confidence: 99%

Optimized Selection of Water Resource Allocation Schemes Based on Improved Connection Entropy in Beijing’s Southern Plain

Men

Yin

2022

Entropy

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Increased urbanization has caused problems such as increasing water consumption and the continuous deterioration of the groundwater environment. It is necessary to consider the groundwater quality in the water resource optimization system and increase the rate of reclaimed water development to reduce the amount of groundwater exploitation and achieve sustainable development of water resources. This study used the Daxing District, a region of Beijing’s southern plain, as an example to evaluate water quality by analyzing water quality data of surface and groundwater from 2012 to 2016 and actual water-use schemes from 2006 to 2016. Three groundwater extraction modes were set up based on NO3–N concentrations, water resources were optimized under three extraction modes, and water resource optimization schemes were determined based on the improved connection entropy. The results show that (1) the surface water quality was poor, and the proportion of V4 type water in the indexes of NH3–N and chemical oxygen demand (COD) was the largest. The surface water can only be used for agricultural irrigation. The pollution sources contributing most to NH3–N and COD were domestic and agricultural pollution sources. (2) The groundwater quality was good. The NO3–N index was primarily type I–III water, accounting for 95.20% of the total samples. Severe NH3–N pollution areas were mainly in the northern region, and most regional groundwater can be used for various purposes. (3) Taking 2016 as an example, three groundwater exploitation modes were set to optimize water resource allocation, and the results showed that the rate of groundwater development and NO3–N pollution decreased significantly after optimization. (4) Connection entropy is an evaluation method that combines connection numbers and entropy, including identify, difference, and opposition entropy. As connection entropy being a kind of complete entropy, which can reflect the difference of the system in different states, based on the improved connection entropy, the connection entropies of optimal water resource allocation and actual water-use schemes were calculated. The connection entropy of groundwater exploitation mode 3 was less than that of groundwater exploitation modes 1 and 2 and actual water-use schemes from 2006 to 2016. Therefore, exploitation mode 3′s water resource optimization scheme was recommended. In the paper, satisfactory results have been obtained. As a kind of complete entropy, connection entropy has great research value in dealing with complex hydrological problems. This study’s research methods and outcomes can provide methodological and theoretical lessons for water management in freshwater-deficient areas.

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“…The confidence interval (CI) width represents the certainty of probability prediction, which is also an important objective to consider. As one of the most popular multiobjective optimization algorithms, the non-dominated sorting genetic algorithm (NSGA-II) reduces the complexity of genetic algorithms with fast calculation and good convergence [27][28][29].…”

Section: Introductionmentioning

confidence: 99%

An Ensemble Prognostic Method of Francis Turbine Units Using Low-Quality Data under Variable Operating Conditions

Duan

Liu

Zhou

et al. 2022

Sensors

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The prognostic is the key to the state-based maintenance of Francis turbine units (FTUs), which consists of performance state evaluation and degradation trend prediction. In practical engineering environments, there are three significant difficulties: low data quality, complex variable operation conditions, and prediction model parameter optimization. In order to effectively solve the above three problems, an ensemble prognostic method of FTUs using low-quality data under variable operation conditions is proposed in this study. Firstly, to consider the operation condition parameters, the running data set of the FTU is constructed by the water head, active power, and vibration amplitude of the top cover. Then, to improve the robustness of the proposed model against anomaly data, the density-based spatial clustering of applications with noise (DBSCAN) is introduced to clean outliers and singularities in the raw running data set. Next, considering the randomness of the monitoring data, the healthy state model based on the Gaussian mixture model is constructed, and the negative log-likelihood probability is calculated as the performance degradation indicator (PDI). Furthermore, to predict the trend of PDIs with confidence interval and automatically optimize the prediction model on both accuracy and certainty, the multiobjective prediction model is proposed based on the non-dominated sorting genetic algorithm and Gaussian process regression. Finally, monitoring data from an actual large FTU was used for effectiveness verification. The stability and smoothness of the PDI curve are improved by 3.2 times and 1.9 times, respectively, by DBSCAN compared with 3-sigma. The root-mean-squared error, the prediction interval normalized average, the prediction interval coverage probability, the mean absolute percentage error, and the R2 score of the proposed method achieved 0.223, 0.289, 1.000, 0.641%, and 0.974, respectively. The comparison experiments demonstrate that the proposed method is more robust to low-quality data and has better accuracy, certainty, and reliability for the prognostic of the FTU under complex operating conditions.

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A Comprehensive Review on NSGA-II for Multi-Objective Combinatorial Optimization Problems

Cited by 397 publications

References 220 publications

Land Use Optimization for Coastal Urban Agglomerations Based on Economic and Ecological Gravitational Linkages and Accessibility

Land Use Optimization for Coastal Urban Agglomerations Based on Economic and Ecological Gravitational Linkages and Accessibility

Optimized Selection of Water Resource Allocation Schemes Based on Improved Connection Entropy in Beijing’s Southern Plain

An Ensemble Prognostic Method of Francis Turbine Units Using Low-Quality Data under Variable Operating Conditions

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