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Fast Pareto Optimization Using Sliding Window Selection for Problems with Determinstic and Stochastic Constraints.

Frank Neumann1, Carsten Witt2

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Evolutionary Computation
|October 31, 2025
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Summary
This summary is machine-generated.

This study introduces a sliding window technique to speed up evolutionary algorithms for submodular optimization problems. The new method significantly reduces computation time while maintaining performance guarantees for both bi-objective and 3-objective formulations.

Keywords:
ConstraintsPareto optimizationevolutionary multi-objective algorithmsruntime analysis

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Area of Science:

  • Artificial Intelligence
  • Optimization Theory
  • Computational Science

Background:

  • Submodular optimization is crucial in AI, machine learning, data science, and social networks.
  • Evolutionary multi-objective algorithms like GSEMO (or POMC) are used for constrained submodular optimization.
  • Algorithm runtime is often limited by population size, which increases with problem complexity.

Purpose of the Study:

  • Introduce a sliding window speed-up technique for evolutionary algorithms solving submodular optimization.
  • Analyze the technique's impact on deterministic bi-objective formulations and stochastic 3-objective formulations.
  • Improve the runtime efficiency of algorithms like GSEMO without sacrificing theoretical performance guarantees.

Main Methods:

  • Developed and applied a sliding window speed-up technique to evolutionary multi-objective algorithms.
  • Theoretically analyzed the technique for deterministic bi-objective submodular optimization.
  • Investigated the technique's effectiveness for stochastic 3-objective submodular optimization.
  • Conducted experimental evaluations on the maximum coverage problem.

Main Results:

  • The sliding window technique eliminates population size as a critical runtime factor for GSEMO.
  • Achieved same theoretical performance guarantees as previous methods with reduced computation time.
  • Demonstrated significant improvements in results for bi-objective and 3-objective formulations across various instances and constraints.
  • The technique enables more tailored parent selection, enhancing optimization progress.

Conclusions:

  • The sliding window technique offers a significant speed-up for evolutionary algorithms in submodular optimization.
  • This approach is effective for both deterministic and stochastic constraint settings in bi-objective and 3-objective problems.
  • The method enhances computational efficiency and maintains theoretical performance guarantees, making it valuable for complex AI problems.