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Effect of Objective Normalization and Penalty Parameter on Penalty Boundary Intersection Decomposition-Based

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This summary is machine-generated.

Normalization instabilities in evolutionary multiobjective optimization (EMO) can impact performance. This study theoretically analyzes these effects on PBI-based algorithms, offering insights for better optimization.

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Area of Science:

  • Computational Intelligence
  • Optimization Algorithms
  • Evolutionary Computation

Background:

  • Objective normalization is crucial for evolutionary multiobjective or many-objective optimization (EMO/EMaO) algorithms.
  • The Penalty Boundary Intersection (PBI) metric in decomposition-based EMO/EMaO algorithms is sensitive to normalization due to distance calculations.

Purpose of the Study:

  • To theoretically analyze the impact of normalization instabilities on the performance of PBI-based MOEA/D and a proposed PBI-based NSGA-III.
  • To understand the nature of normalization effects and guide the selection of penalty parameter values in PBI-based decomposition algorithms.

Main Methods:

  • Theoretical analysis of normalization instabilities in PBI-based evolutionary algorithms.
  • Experimental validation using DTLZ and WFG benchmark problems with 3 to 15 objectives (convex and non-convex).

Main Results:

  • Demonstrated the significant effect of normalization instabilities on the performance of PBI-based MOEA/D and NSGA-III.
  • Provided theoretical insights into the behavior of PBI-based decomposition algorithms under normalization variations.

Conclusions:

  • Normalization strategy is critical for the performance of PBI-based decomposition algorithms in EMO/EMaO.
  • The study offers theoretical conclusions and experimental evidence to guide the development and application of these algorithms.