Interval Computing Subdomain Sampling Optimization
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Solution Overview
Problem
Interval computations are inefficient due to the inefficiency of the branch-and-prune technique, which consumes resources and is time-consuming when dealing with large subdomain boxes that do not contain solutions, as it performs exhaustive searches until the entire subdomain space is examined.
Innovation Solution
The system employs subdomain sampling by generating boxes of different sizes across the domain, evaluating these sampling subdomains, sorting results, and selecting the largest box size that achieves tight bounds, then discretizing the domain into subdomains of that size for effective interval computations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If the branch-and-prune technique is used to evaluate functions over large subdomain boxes, then the method can handle complex domains, but the computational efficiency deteriorates due to exhaustive searches and time-consuming evaluations on subdomains that do not contain solutions
Solution Approach 1:
The patent performs preliminary action by evaluating the function at sample points within each subdomain before initiating the full branch-and-prune process. This preliminary evaluation determines whether the subdomain contains a solution, allowing the algorithm to skip exhaustive searches on subdomains that clearly do not contain solutions, thereby improving computational efficiency while maintaining the ability to handle complex domains
Solution Approach 2:
The patent extracts and removes ineffective computations by using preliminary sample evaluations to identify and exclude subdomains that do not contain solutions from the main branch-and-prune process. This extraction of useless computations eliminates the time-consuming exhaustive searches on empty subdomains, directly addressing the productivity issue while preserving the method's adaptability to complex domains
2Reliability
If interval techniques are applied to large subdomain boxes, then the method can provide bounds on solutions, but the effectiveness deteriorates because the interval techniques become effective only after sufficient subdivision into smaller boxes
Solution Approach 1:
The patent performs preliminary action by pre-evaluating sample points in each subdomain to determine the appropriate initial box size for interval technique application. This allows the algorithm to start interval computations at an optimized scale where the techniques are most effective, rather than beginning with large boxes and waiting for recursive subdivision to make the techniques effective
Solution Approach 2:
The patent changes the parameter of box size dynamically based on preliminary evaluation results. By determining the optimal initial box size through sample point analysis, the algorithm adjusts the scale at which interval techniques are applied, enabling effective bound computation on appropriately sized subdomains without requiring extensive prior subdivision
3Reliability
If the branch-and-prune technique performs exhaustive searches on subdomains, then the method guarantees to find all solutions, but the computation time increases significantly for subdomains that do not contain solutions
Solution Approach 1:
The patent extracts and removes the time-consuming exhaustive search step for subdomains that do not contain solutions by using preliminary sample evaluations as a filter. This extraction allows the algorithm to maintain the guarantee of finding all solutions through branch-and-prune while eliminating the wasteful time spent on empty subdomains, directly addressing the time loss issue
Solution Approach 2:
The patent performs preliminary action by evaluating sample points before the main search process to identify and pre-filter out subdomains that do not contain solutions. This preliminary filtering action ensures that the subsequent exhaustive search is only performed on promising subdomains, maintaining solution completeness while significantly reducing the time lost on empty subdomains
Data Source
AI summary
One embodiment of the present invention provides a system that uses a computer to evaluate a function within a domain using an interval computing technique. During operation, the system receives the function and the domain over which the function is to be evaluated. Next, the system creates a set of sampling subdomains within the domain by generating a set of boxes of different sizes which are located at different positions across the domain. The system then performs evaluations on the set of sampling subdomains to generate evaluation results. Next, the system sorts the evaluation results based on box size. The system then selects a box size from the different box sizes by identifying a largest box size which achieves tight bounds on the evaluation results. The system next discretizes the domain into subdomains of the selected box size. Finally, the system uses the interval computing technique to evaluate the function on each of the subdomains wherein the interval computing technique recursively subdivides and evaluates the function on the subdomains.