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An area-based computational algorithm for robust extrema detection in noisy environments
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AI
DOI：10.1016/j.ins.2025.123019.png)
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Abstract
En 中文
A variety of point-based heuristics and metaheuristics have been developed to approximate the global optimum of univariate functions. However, these Point-Based Search (PBS) algorithms often converge to local optima and fail to detect all extrema due to limited domain exploration. This study proposes an Area-Based Search (ABS) algorithm that systematically partitions the domain into uniformly spaced subintervals and evaluates the area under the curve in each segment. Subintervals with significantly larger or smaller areas than their neighbors are likely to contain local maxima or minima, respectively. We validate this idea on multimodal test functions using a Monte Carlo simulation framework with 1,000 trials. Across all noise levels in a standard benchmark function, ABS consistently detects all 16 local and global extrema. Intuitively, coverage measures the fraction of true extrema that an algorithm successfully recovers within a prescribed positional tolerance. Compared to Genetic Algorithms (GA), ABS achieves up to 37% higher detection accuracy under noise, with an average coverage improvement of 4.75% across all test cases. Additionally, ABS exhibited a 30.41% lower position error and a 36.89% lower value error than GA. The deterministic nature of ABS, with only one tunable resolution parameter, supports its use in noisy environments requiring full-spectrum extrema detection.
Keywords:
Area-based method
Function optimization
Extrema detection
Univariate analysis
Point-based heuristics
Search algorithms
Journal
IF:
6.8
Papers:
540
Citations:
6.2W