Restricted Search in High-Dimensional Optimization Spaces
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Solution Overview
Problem
Multi-criteria decision making tools face scalability issues in high-dimensional spaces, particularly due to the need for a priori preference or biasing information that can lead to missed solutions in optimization processes.
Innovation Solution
The method involves determining sub-dimensional subsets to define a restricted search space for unbiased optimization, where chromosome data structures are selected based on domination and diversity characteristics, allowing for an unbiased search within specific regions of interest.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Speed
If a priori preference or biasing information is introduced to guide optimization, then convergence speed improves, but solution completeness deteriorates as certain objectives are sustainedly favored leading to missed solutions
Solution Approach 1:
The patent segments the high-dimensional search space into multiple sub-dimensional subspaces, each representing a specific region of interest. By dividing the optimization problem into smaller dimensional subsets, the system can perform targeted searches in each subspace without imposing a priori preferences, thus maintaining solution completeness while improving convergence speed within each segment.
Solution Approach 2:
The patent transforms the high-dimensional optimization problem by projecting it into multiple lower-dimensional subspaces. This dimensionality reduction allows the optimization algorithm to explore each subspace more thoroughly without the computational burden and biasing effects of operating in the full high-dimensional space, thereby preserving solution completeness while enhancing convergence.
2Productivity
If the search space is restricted to specific regions of interest, then computational efficiency improves, but the ability to find globally optimal solutions may deteriorate
Solution Approach 1:
The patent divides the total search space into multiple sub-dimensional subspaces that collectively cover the entire domain. By segmenting the space and performing optimization in each subspace, the system achieves computational efficiency through focused searches while maintaining global optimality through comprehensive coverage of all regions.
Solution Approach 2:
The patent creates a universal optimization framework that can handle multiple objectives and multiple subspaces simultaneously. The system performs optimization across all sub-dimensional subspaces using consistent criteria, ensuring that the solution is globally optimal while maintaining computational efficiency through the modular subspace structure.
3Reliability
If unbiased optimization is performed across the entire search space, then solution completeness improves, but computational complexity increases making problems intractable
Solution Approach 1:
The patent segments the large search space into smaller sub-dimensional subspaces, reducing the computational complexity of searching each individual subspace. This segmentation allows unbiased optimization to be performed across the entire domain by systematically exploring each segment, thereby maintaining solution completeness while making the overall problem computationally tractable.
Solution Approach 2:
The patent performs optimization in a staged manner by first exploring sub-dimensional subspaces and then aggregating results. This partial action approach allows the system to achieve comprehensive coverage of the search space without the overwhelming computational burden of simultaneous global optimization, making previously intractable problems solvable.
Data Source
AI summary
Embodiments of the invention may provide systems and methods for supporting restricted search capabilities in high-dimensional spaces. These example restricted search capabilities may allow for an unbiased search that is simply restricted to those regions of interest to a decision maker. It will be appreciated that a restricted search does not mean that additional constraints, such as preference or biasing information, are utilized to reduce the search space into some feasible sub-space of the original optimization problem. Instead, the example restricted search may limit the search to a certain sub-space of the full multi-dimensional tradeoff space.