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Objective-Domain Dual Decomposition: An Effective Approach to Optimizing Partially Differentiable Objective

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    This study introduces a novel dual-decomposition method for optimization problems with mixed differentiability. A new simulated water-stream algorithm (SWA) effectively solves these complex multiobjective optimization problems.

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    Area of Science:

    • Optimization Theory
    • Computational Mathematics

    Background:

    • Many real-world optimization problems involve objective functions that are partially differentiable or differentiable only within specific domains.
    • Existing methods struggle to efficiently handle such mixed differentiability, limiting their applicability.

    Purpose of the Study:

    • To develop a robust approach for optimization problems with partially differentiable or domain-specific differentiable objective functions.
    • To introduce a novel algorithm capable of solving the resulting multiobjective optimization problems (MOPs).

    Main Methods:

    • A dual-decomposition strategy combining objective and domain decomposition to isolate non-differentiable components.
    • Formulation of the problem as a multiobjective optimization problem (MOP).
    • Development of the simulated water-stream algorithm (SWA), a population-based approach inspired by natural water streams, integrating deterministic and heuristic search.

    Main Results:

    • The proposed dual-decomposition approach effectively handles mixed differentiability in optimization.
    • The simulated water-stream algorithm (SWA) demonstrates promising performance in solving the formulated MOPs.
    • Experimental comparisons indicate SWA outperforms existing counterparts.

    Conclusions:

    • The dual-decomposition method offers a powerful framework for tackling complex optimization challenges.
    • The SWA is an effective and efficient algorithm for solving optimization problems with mixed differentiability.
    • This research advances the field of optimization by providing new tools for challenging problem classes.