A New Algorithm Using the Non-Dominated Tree to Improve Non-Dominated Sorting

2018 ◽  
Vol 26 (1) ◽  
pp. 89-116 ◽  
Author(s):  
Patrik Gustavsson ◽  
Anna Syberfeldt
Keyword(s):  
Genetic Algorithm ◽  
Evolutionary Algorithms ◽  
Large Population ◽  
Divide And Conquer ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Sorting Algorithms ◽  
Population Sizes ◽  
Speed Up

Non-dominated sorting is a technique often used in evolutionary algorithms to determine the quality of solutions in a population. The most common algorithm is the Fast Non-dominated Sort (FNS). This algorithm, however, has the drawback that its performance deteriorates when the population size grows. The same drawback applies also to other non-dominating sorting algorithms such as the Efficient Non-dominated Sort with Binary Strategy (ENS-BS). An algorithm suggested to overcome this drawback is the Divide-and-Conquer Non-dominated Sort (DCNS) which works well on a limited number of objectives but deteriorates when the number of objectives grows. This article presents a new, more efficient algorithm called the Efficient Non-dominated Sort with Non-Dominated Tree (ENS-NDT). ENS-NDT is an extension of the ENS-BS algorithm and uses a novel Non-Dominated Tree (NDTree) to speed up the non-dominated sorting. ENS-NDT is able to handle large population sizes and a large number of objectives more efficiently than existing algorithms for non-dominated sorting. In the article, it is shown that with ENS-NDT the runtime of multi-objective optimization algorithms such as the Non-Dominated Sorting Genetic Algorithm II (NSGA-II) can be substantially reduced.

Multi-Objective Optimization of Manufacturing Processes Using Evolutionary Algorithms

2012 ◽  
pp. 44-66
Author(s):  
M. Kanthababu
Keyword(s):  
Genetic Algorithm ◽  
Evolutionary Algorithms ◽  
Multiple Objectives ◽  
Manufacturing Processes ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Local Optima ◽  
Multi Objective ◽  
Research Areas

Recently evolutionary algorithms have created more interest among researchers and manufacturing engineers for solving multiple-objective problems. The objective of this chapter is to give readers a comprehensive understanding and also to give a better insight into the applications of solving multi-objective problems using evolutionary algorithms for manufacturing processes. The most important feature of evolutionary algorithms is that it can successfully find globally optimal solutions without getting restricted to local optima. This chapter introduces the reader with the basic concepts of single-objective optimization, multi-objective optimization, as well as evolutionary algorithms, and also gives an overview of its salient features. Some of the evolutionary algorithms widely used by researchers for solving multiple objectives have been presented and compared. Among the evolutionary algorithms, the Non-dominated Sorting Genetic Algorithm (NSGA) and Non-dominated Sorting Genetic Algorithm-II (NSGA-II) have emerged as most efficient algorithms for solving multi-objective problems in manufacturing processes. The NSGA method applied to a complex manufacturing process, namely plateau honing process, considering multiple objectives, has been detailed with a case study. The chapter concludes by suggesting implementation of evolutionary algorithms in different research areas which hold promise for future applications.

Multi-Objective Evolutionary Algorithms

2016 ◽  
pp. 301-345
Author(s):  
A. K. Nandi ◽  
K. Deb
Keyword(s):  
Genetic Algorithm ◽  
Evolutionary Algorithms ◽  
Optimization Problem ◽  
Performance Metrics ◽  
Research Work ◽  
Primary Objective ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Mould Material ◽  
Multi Objective

The primary objective in designing appropriate particle reinforced polyurethane composite which will be used as a mould material in soft tooling process is to minimize the cycle time of soft tooling process by providing faster cooling rate during solidification of wax/plastic component. This chapter exemplifies an effective approach to design particle reinforced mould materials by solving the inherent multi-objective optimization problem associated with soft tooling process using evolutionary algorithms. In this chapter, first a brief introduction of multi-objective optimization problem with the key issues is presented. Then, after a short overview on the working procedure of genetic algorithm, a well- established multi-objective evolutionary algorithm, namely NSGA-II along with various performance metrics are described. The inherent multi-objective problem in soft tooling process is demonstrated and subsequently solved using an elitist non-dominated sorting genetic algorithm, NSGA-II. Multi-objective optimization results obtained using NSGA-II are analyzed statistically and validated with real industrial application. Finally the fundamental results of this approach are summarized and various perspectives to the industries along with scopes for future research work are pointed out.

Multi-Objective Evolutionary Algorithms

2017 ◽  
pp. 185-229
Author(s):  
A. K. Nandi ◽  
K. Deb
Keyword(s):  
Genetic Algorithm ◽  
Evolutionary Algorithms ◽  
Optimization Problem ◽  
Performance Metrics ◽  
Research Work ◽  
Primary Objective ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Mould Material ◽  
Multi Objective

The primary objective in designing appropriate particle reinforced polyurethane composite which will be used as a mould material in soft tooling process is to minimize the cycle time of soft tooling process by providing faster cooling rate during solidification of wax/plastic component. This chapter exemplifies an effective approach to design particle reinforced mould materials by solving the inherent multi-objective optimization problem associated with soft tooling process using evolutionary algorithms. In this chapter, first a brief introduction of multi-objective optimization problem with the key issues is presented. Then, after a short overview on the working procedure of genetic algorithm, a well- established multi-objective evolutionary algorithm, namely NSGA-II along with various performance metrics are described. The inherent multi-objective problem in soft tooling process is demonstrated and subsequently solved using an elitist non-dominated sorting genetic algorithm, NSGA-II. Multi-objective optimization results obtained using NSGA-II are analyzed statistically and validated with real industrial application. Finally the fundamental results of this approach are summarized and various perspectives to the industries along with scopes for future research work are pointed out.

An Efficient Non-dominated Sorting Method for Evolutionary Algorithms

2008 ◽  
Vol 16 (3) ◽  
pp. 355-384 ◽  
Author(s):  
Hongbing Fang ◽  
Qian Wang ◽  
Yi-Cheng Tu ◽  
Mark F. Horstemeyer
Keyword(s):  
Evolutionary Algorithms ◽  
Divide And Conquer ◽  
Computational Time ◽  
Sorting Algorithm ◽  
Objective Functions ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Overall Efficiency ◽  
Dominance Tree ◽  
The Cost

We present a new non-dominated sorting algorithm to generate the non-dominated fronts in multi-objective optimization with evolutionary algorithms, particularly the NSGA-II. The non-dominated sorting algorithm used by NSGA-II has a time complexity of O(MN2) in generating non-dominated fronts in one generation (iteration) for a population size N and M objective functions. Since generating non-dominated fronts takes the majority of total computational time (excluding the cost of fitness evaluations) of NSGA-II, making this algorithm faster will significantly improve the overall efficiency of NSGA-II and other genetic algorithms using non-dominated sorting. The new non-dominated sorting algorithm proposed in this study reduces the number of redundant comparisons existing in the algorithm of NSGA-II by recording the dominance information among solutions from their first comparisons. By utilizing a new data structure called the dominance tree and the divide-and-conquer mechanism, the new algorithm is faster than NSGA-II for different numbers of objective functions. Although the number of solution comparisons by the proposed algorithm is close to that of NSGA-II when the number of objectives becomes large, the total computational time shows that the proposed algorithm still has better efficiency because of the adoption of the dominance tree structure and the divide-and-conquer mechanism.

Multi-Objective Optimization of Manufacturing Processes Using Evolutionary Algorithms

2012 ◽  
pp. 352-376 ◽  
Author(s):  
M. Kanthababu
Keyword(s):  
Genetic Algorithm ◽  
Evolutionary Algorithms ◽  
Multiple Objectives ◽  
Manufacturing Processes ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Local Optima ◽  
Multi Objective ◽  
Research Areas

Recently evolutionary algorithms have created more interest among researchers and manufacturing engineers for solving multiple-objective problems. The objective of this chapter is to give readers a comprehensive understanding and also to give a better insight into the applications of solving multi-objective problems using evolutionary algorithms for manufacturing processes. The most important feature of evolutionary algorithms is that it can successfully find globally optimal solutions without getting restricted to local optima. This chapter introduces the reader with the basic concepts of single-objective optimization, multi-objective optimization, as well as evolutionary algorithms, and also gives an overview of its salient features. Some of the evolutionary algorithms widely used by researchers for solving multiple objectives have been presented and compared. Among the evolutionary algorithms, the Non-dominated Sorting Genetic Algorithm (NSGA) and Non-dominated Sorting Genetic Algorithm-II (NSGA-II) have emerged as most efficient algorithms for solving multi-objective problems in manufacturing processes. The NSGA method applied to a complex manufacturing process, namely plateau honing process, considering multiple objectives, has been detailed with a case study. The chapter concludes by suggesting implementation of evolutionary algorithms in different research areas which hold promise for future applications.

Multi-objective optimization of injection-molded plastic parts using entropy weight, random forest, and genetic algorithm methods

2020 ◽  
Vol 40 (4) ◽  
pp. 360-371
Author(s):  
Yanli Cao ◽  
Xiying Fan ◽  
Yonghuan Guo ◽  
Sai Li ◽  
Haiyue Huang
Keyword(s):  
Genetic Algorithm ◽  
Random Forest ◽  
Regression Model ◽  
Process Parameters ◽  
Multi Objective Optimization ◽  
Entropy Weight ◽  
Multi Objective ◽  
Injection Molded ◽  
Plastic Parts

AbstractThe qualities of injection-molded parts are affected by process parameters. Warpage and volume shrinkage are two typical defects. Moreover, insufficient or excessively large clamping force also affects the quality of parts and the cost of the process. An experiment based on the orthogonal design was conducted to minimize the above defects. Moldflow software was used to simulate the injection process of each experiment. The entropy weight was used to determine the weight of each index, the comprehensive evaluation value was calculated, and multi-objective optimization was transformed into single-objective optimization. A regression model was established by the random forest (RF) algorithm. To further illustrate the reliability and accuracy of the model, back-propagation neural network and kriging models were taken as comparative algorithms. The results showed that the error of RF was the smallest and its performance was the best. Finally, genetic algorithm was used to search for the minimum of the regression model established by RF. The optimal parameters were found to improve the quality of plastic parts and reduce the energy consumption. The plastic parts manufactured by the optimal process parameters showed good quality and met the requirements of production.

scholarly journals Cluster-Based Optimization of an Evacuation Process Using a Parallel Bi-Objective Real-Coded Genetic Algorithm

2020 ◽  
Vol 20 (3) ◽  
pp. 45-63
Author(s):  
Andranik S. Akopov ◽  
Levon A. Beklaryan ◽  
Armen L. Beklaryan
Keyword(s):  
Genetic Algorithm ◽  
Individual Characteristics ◽  
Nsga Ii ◽  
Human Agent ◽  
Performance Metric ◽  
Novel Approach ◽  
Distributed Processes ◽  
Real Coded Genetic Algorithm ◽  
Decision Making System

AbstractThis work presents a novel approach to the design of a decision-making system for the cluster-based optimization of an evacuation process using a Parallel bi-objective Real-Coded Genetic Algorithm (P-RCGA). The algorithm is based on the dynamic interaction of distributed processes with individual characteristics that exchange the best potential decisions among themselves through a global population. Such an approach allows the HyperVolume performance metric (HV metric) as reflected in the quality of the subset of the Pareto optimal solutions to be improved. The results of P-RCGA were compared with other well-known multi-objective genetic algorithms (e.g., -MOEA, NSGA-II, SPEA2). Moreover, P-RCGA was aggregated with the developed simulation of the behavior of human agent-rescuers in emergency through the objective functions to optimize the main parameters of the evacuation process.

Kinematic Multi-Objective Optimization of Circular-Toothed Gerotor Pumps by Genetic Algorithm

2017 ◽  
Author(s):  
Andrew J. Robison ◽  
Andrea Vacca
Keyword(s):  
Genetic Algorithm ◽  
Design Method ◽  
Third Party ◽  
Low Flow ◽  
Objective Functions ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Generation Algorithm ◽  
Multi Objective ◽  
Pareto Curve

A gerotor gear generation algorithm has been developed that evaluates key performance objective functions to be minimized or maximized, and then an optimization algorithm is applied to determine the best design. Because of their popularity, circular-toothed gerotors are the focus of this study, and future work can extend this procedure to other gear forms. Parametric equations defining the circular-toothed gear set have been derived and implemented. Two objective functions were used in this kinematic optimization: maximize the ratio of displacement to pump radius, which is a measure of compactness, and minimize the kinematic flow ripple, which can have a negative effect on system dynamics and could be a major source of noise. Designs were constrained to ensure drivability, so the need for additional synchronization gearing is eliminated. The NSGA-II genetic algorithm was then applied to the gear generation algorithm in modeFRONTIER, a commercial software that integrates multi-objective optimization with third-party engineering software. A clear Pareto front was identified, and a multi-criteria decision-making genetic algorithm was used to select three optimal designs with varying priorities of compactness vs low flow variation. In addition, three pumps used in industry were scaled and evaluated with the gear generation algorithm for comparison. The scaled industry pumps were all close to the Pareto curve, but the optimized designs offer a slight kinematic advantage, which demonstrates the usefulness of the proposed gerotor design method.

Modified Non-Dominated Sorting Genetic Algorithm (MNSGA-II) Applied in Multi-Objective Optimization of a Coal-Fired Boiler Combustion

2013 ◽  
Vol 694-697 ◽  
pp. 2850-2855
Author(s):  
Ting Fang Yu ◽  
Xia Wang ◽  
Chun Hua Peng
Keyword(s):  
Genetic Algorithm ◽  
Heat Loss ◽  
Bp Neural Network ◽  
Nox Emissions ◽  
Multi Objective Optimization ◽  
Good Tool ◽  
Nsga Ii ◽  
Multi Objective ◽  
Comparison Operator ◽  
Bp Model

This paper discussed application of modified non-dominated sorting genetic algorithm-II (MNSGA-II) to multi-objective optimization of a coal-fired boiler combustion, the two objectives considered are minimization of overall heat loss and NOx emissions from coal-fired boiler. In the first step, BP neural network was proposed to establish a mathematical model predicting the NOx emissions & overall heat loss from the boiler. Then, BP model and the non-dominated sorting genetic algorithm II (NSGA-II) were combined to gain the optimal operating parameters. According to the problems such as premature convergence and uneven distribution of Pareto solutions exist in the application of NSGA-II, corresponding improvements in the crowded-comparison operator and crossover operator were performed. The optimal results show that MNSGA-II can be a good tool to solve the problem of multi-objective optimization of a coal-fired combustion, which can reduce NOx emissions and overall heat loss effectively for the coal-fired boiler. Compared with NSGA-II, the Pareto set obtained by the MNSGA-II shows a better distribution and better quality.

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