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Benchmark Problems and Performance Indicators for Search of Knee Points in Multiobjective Optimization.

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    Summary
    This summary is machine-generated.

    This study introduces novel multiobjective optimization problems with complex knee regions to evaluate evolutionary algorithms. New performance indicators are also proposed to assess knee point identification capabilities in high-dimensional spaces.

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    Area of Science:

    • Optimization Theory
    • Computational Intelligence
    • Algorithm Design

    Background:

    • Decision-makers struggle to articulate preferences in multiobjective optimization, especially with many objectives.
    • Identifying knee points on the Pareto front is crucial but challenging in high-dimensional objective spaces.
    • Existing test suites lack problems with complex knee regions, hindering algorithm development.

    Purpose of the Study:

    • To propose a new set of multiobjective optimization test problems featuring complex knee regions.
    • To assess the capability of evolutionary algorithms in accurately identifying knee points.
    • To introduce novel performance indicators for evaluating knee point localization.

    Main Methods:

    • Designed multiobjective test problems incorporating features of knee points (symmetry, differentiability, degeneration).
    • Integrated challenges like multimodality, variable linkage, nonuniformity, and Pareto front scalability.
    • Developed new performance indicators tailored for evaluating knee point identification.

    Main Results:

    • Introduced scalable test problems for both decision and objective spaces.
    • Proposed performance indicators specifically for assessing knee point location accuracy.
    • Created a means to develop and evaluate preference-based evolutionary algorithms.

    Conclusions:

    • The proposed test problems and performance indicators address the need for better assessment of knee point identification in multiobjective optimization.
    • This work facilitates the development and evaluation of algorithms for preference-based evolutionary approaches.
    • It offers a valuable resource for advancing research in multi- and many-objective optimization.