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

Patrik Gustavsson1, Anna Syberfeldt2

  • 1School of Engineering, University of Skövde, Skövde, 54134, Sweden patrik.gustavsson@his.se.

Evolutionary Computation
|January 20, 2017
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Summary
This summary is machine-generated.

A new Efficient Non-dominated Sort with Non-Dominated Tree (ENS-NDT) algorithm improves evolutionary computation. ENS-NDT efficiently handles large populations and many objectives, outperforming existing non-dominated sorting methods.

Keywords:
Evolutionary computationPareto optimalityk-d treemulti-objective evolutionary algorithmsnon-dominated sortingruntime complexity.

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Area of Science:

  • Evolutionary Algorithms
  • Multi-objective Optimization
  • Computational Intelligence

Background:

  • Non-dominated sorting is crucial for evaluating solutions in evolutionary algorithms.
  • Existing methods like Fast Non-dominated Sort (FNS) and Efficient Non-dominated Sort with Binary Strategy (ENS-BS) struggle with large population sizes.
  • Divide-and-Conquer Non-dominated Sort (DCNS) is effective for few objectives but degrades with more.

Purpose of the Study:

  • Introduce a novel, efficient non-dominated sorting algorithm, Efficient Non-dominated Sort with Non-Dominated Tree (ENS-NDT).
  • Address the performance limitations of current algorithms concerning population size and number of objectives.
  • Enhance the efficiency of multi-objective optimization algorithms.

Main Methods:

  • Developed the Efficient Non-dominated Sort with Non-Dominated Tree (ENS-NDT) algorithm.
  • Extended the Efficient Non-dominated Sort with Binary Strategy (ENS-BS) approach.
  • Utilized a novel Non-Dominated Tree (NDTree) data structure to accelerate sorting.

Main Results:

  • ENS-NDT demonstrates superior efficiency in handling large populations and numerous objectives compared to existing algorithms.
  • The novel NDTree structure significantly speeds up the non-dominated sorting process.
  • Substantial runtime reductions were observed for multi-objective optimization algorithms like NSGA-II when using ENS-NDT.

Conclusions:

  • ENS-NDT offers a more scalable and efficient solution for non-dominated sorting in evolutionary computation.
  • The algorithm effectively overcomes the limitations of previous methods regarding population size and objective count.
  • Implementing ENS-NDT can lead to significant performance improvements in complex multi-objective optimization tasks.