Self-Adaptive Spherical Search With a Low-Precision Projection Matrix for Real-World Optimization.

Area of Science:

• Optimization algorithms
• Evolutionary computation
• Mathematical modeling

Background:

• Evolutionary algorithms (EAs) commonly use hypercube (HC) search models.
• Hyper-spherical (HS) models, like that in spherical search (SS), show promise but face computational challenges.
• Existing SS algorithms perform well on constrained and unconstrained optimization but are computationally intensive.

Purpose of the Study:

• To improve the computational efficiency of the spherical search (SS) algorithm.
• To enhance the search capability of the SS algorithm through self-adaptation.
• To validate the performance of the improved SS algorithm on diverse optimization problems.

Main Methods:

• Developed an efficient technique to construct HS loci by approximating the orthogonal projection matrix.
• Introduced a self-adaptation mechanism for dynamic control parameter tuning.
• Validated the algorithm on numerous real-world and benchmark optimization problems.

Main Results:

• The proposed technique significantly reduces the computational burden of HS locus generation.
• Empirical results show improved performance of the SS algorithm with less computational effort.
• The self-adaptation technique enhances the algorithm's search capability.

Conclusions:

• The enhanced SS algorithm offers improved efficiency and effectiveness for optimization tasks.
• The algorithm performs comparably or superiorly to state-of-the-art methods across various problems.
• This work provides a more computationally feasible and robust HS-based optimization approach.