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Metaheuristic Multimodal Optimization
Published in Erik Cuevas, Alma Rodríguez, ®, 2020
As the name suggests, on the crowding model, diversity is added through the incorporation of a mechanism that tries to avoid the clustering of individuals. In this mechanism DeJong introduced the concept of population segment and a clustering strategy. Such elements were first included in a conventional genetic algorithm. Under the approach, only a portion G of the population (called generation gap) is used to generate new individuals in each iteration. In the method, when a new individual is generated, its inclusion in the portion G is performed by the following process. First, a number of CF (“crowding factor”) elements are selected randomly from the sub-population G. Then, the new individual is compared with these CF elements, in terms of similarity. Therefore, the new individual will replace the random element with which presents a greater similarity. In this study, DeJong uses as parameters G = 0.1 and CF = 2 or 3.
Genetic Algorithms
Published in Jay Liebowitz, The Handbook of Applied Expert Systems, 2019
There are two classes of niching methods: crowding and sharing. Crowding methods restrict individual replacement to reduce competition between genotypes that greatly differ within a niche. When a new genotype is introduced into the population, it replaces an individual who most resembles it. Sharing methods reduce a genotype’s fitness when similar genotypes exist within a particular niche. Using the sharing method incurs an additional computational cost, since genotypes must be compared to each other.
Overview of Multiobjective Optimization
Published in K.S. Tang, T.M. Chan, R.J. Yin, K.F. Man, Multiobjective Optimization Methodology, 2018
K.S. Tang, T.M. Chan, R.J. Yin, K.F. Man
Recognizing the difficulties of specifying the sharing parameter for the preservation of population diversity, a crowded-comparison approach is proposed in NSGA2. It involves two processes: the crowding-distance assignment and the crowded-comparison operation.
Logistics and supply chain management reorganisation via talent portfolio management to enhance human capital and resilience
Published in International Journal of Logistics Research and Applications, 2023
Yin-Hung Chen, Chia-An Chen, Chen-Fu Chien
To enhance the likelihood of convergence and preserve the advantages of superior chromosomes, the elitism strategy is used by combining the original population with the newly generated offspring. After decoding the chromosomes back to realistic solutions, the fast nondominated sorting and crowding distance calculation method can be employed to evaluate the solutions under multiple objectives. The nondominated sorting approach in NSGA-II counts the total quantity of solutions dominated by each solution and records the solutions that are dominated by it. The nondominated fronts are identified in a layer-by-layer manner, and the optimal Pareto front can be obtained. To maintain solution diversity and provide additional criteria for chromosome selection when different solutions are located at the same non-transcendental level, a crowding distance method is proposed. The crowding distance is the sum of the average distance of every attribute to adjacent solutions. A larger crowding distance represents a greater difference between the specific solution and other solutions, which can prevent the algorithm from stuck in local optima during iterations and facilitate exploration.
Bi-objective coordinated production and transportation scheduling problem with sustainability: formulation and solution approaches
Published in International Journal of Production Research, 2023
Ece Yağmur, Saadettin Erhan Kesen
Evaluate objective values: While evaluating the quality of the solutions in the population, the Pareto levels of the individuals are first determined. Pareto level of a particular solution is determined by the number of solutions that dominate it. In other words, if an individual cannot be dominated by other individuals, this individual is called non-dominant solution, and its Pareto level is assigned to zero. Once the Pareto levels of all individuals are assigned, these individuals are sorted according to their increasing Pareto levels. Following the non-dominated sorting process, the diversity among these solutions is measured by using the crowding distance. The larger crowding distance allows searching for the solution in relatively unexplored regions by going as far as possible from existing solutions. In the selection process, individuals on the low Pareto front with high crowding distance are selected as a parent by binary tournament selection process.
Design optimisation of railway pantograph-catenary systems with multiple objectives
Published in Vehicle System Dynamics, 2022
Hanlei Wang, Dingyang Zheng, Pu Huang, Wenyi Yan
For a multi-objective optimisation problem, finding the set of Pareto optimal solutions is the focus. The NSGA-II algorithm introduces fast non-dominated sorting, crowding distance, the elitist principle based on the genetic algorithm to solve this problem. Fast non-dominated sorting is to stratify the population based on the level of the noninferior of each individual, which could guide the search in the direction of the Pareto optimal solutions quickly and reduce computational complexity. Since a multi-objective optimisation problem usually has many optimised solutions, how to choose more suitable results in the Pareto optimal solutions is very critical. The crowding distance represents the degree of deviation of a certain data from other data. The larger the crowding distance, the fewer the number of similar individuals in the vicinity of the current individual, which also means that this individual is worthier to be retained, which can increase the diversity of optimisation results. The elitist principle is to compare parents and offspring at the same time and select the top performers as the new parents.