Fractal Hypersphere Partitioning for Deterministic Nonlinear Optimization
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Solution Overview
Problem
Current optimization methods for large-scale nonlinear problems with many technical parameters face challenges in achieving accurate and reliable solutions within reasonable computation times, particularly due to the stochastic nature of existing algorithms and the curse of dimensionality, which limits their applicability in safety-critical applications.
Innovation Solution
A computer-implemented method using fractal geometric partitioning of the search space into overlapping hyperspheres, where the quality of each hypersphere is calculated, and the hypersphere with the best quality is selected to determine the optimum solution, allowing for deterministic optimization and efficient computation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If stochastic optimization algorithms are used to solve large-scale nonlinear problems, then the ability to handle complex search spaces is improved, but the reliability and repeatability of solutions deteriorate
Solution Approach 1:
The patent divides the search space into multiple hypercubes through systematic partitioning, transforming a single complex optimization problem into multiple smaller sub-problems. Each hypercube is then processed independently, allowing deterministic exploration of different regions while maintaining overall reliability through structured coverage of the entire search space.
2Adaptability or versatility
If the number of technical parameters increases to handle large-scale problems, then the comprehensiveness of the optimization problem coverage is improved, but the algorithm complexity increases exponentially
Solution Approach 1:
The patent implements a nested hierarchical structure where the search space is divided into hypercubes, which are further subdivided into sub-hypercubes, and continues recursively to lower levels. This nested partitioning allows systematic exploration of high-dimensional spaces by breaking down complex multi-parameter problems into manageable hierarchical levels, avoiding exponential complexity growth.
3Productivity
If gradient based algorithms are used for optimization, then the computational efficiency is improved, but the ability to find global optima in high-dimensional spaces deteriorates due to prevalence of saddle points
Solution Approach 1:
The patent transitions from gradient-based continuous optimization to a discrete dimensional partitioning approach by dividing the search space into hypercubes along coordinate axes. This dimensional transformation allows systematic exploration of the search space through grid-based partitioning, avoiding the saddle point problem inherent in gradient methods while maintaining computational tractability through structured dimension-wise processing.
Data Source
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AI summary
The invention relates to a computer implemented method to optimize operation of a technical system by solving deterministically a nonlinear optimization problem implying technical constraints relating to technical parameters under which the said technical system operates, the technical parameters being of a number greater than 50, characterized in that the method comprises fractal geometric partitioning of a search space into a plurality of hyperspheres as a geometrical unitary pattern and wherein the hyperspheres partitioning said search space are overlapping; calculating a quality for each hypersphere; selecting from the plurality of hyperspheres, the hypersphere with the best quality; and further comprises determining an optimum solution of the said selected hypersphere, the solution comprising values of the technical parameters to be implemented in the said technical system.