Carbon Footprint Efficiency Ratio: A Unified Indicator for Green Evaluation of Evolutionary Algorithms

초록

Evolutionary algorithms (EAs) are widely adopted for black-box optimization, yet evaluation protocols remain largely accuracy-centric and often omit computational energy use, hindering carbon-aware deployment in green computing settings. We propose the Carbon Footprint Efficiency Ratio (CFER) to quantify optimization benefit per unit carbon emission and enable a unified assessment of carbon efficiency. To compute CFER without dedicated power-monitoring hardware, we develop a device-independent energy estimation model based on the Multimodal Energy Consumption Factor (MECF). Using a dataset constructed from 13 benchmark functions and 8 classical EAs, MECF is identified via outlier removal and Huber regression, achieving a mean estimation error of 1.80% and a maximum error of 2.51%. On the CEC2020 test suite, CFER-based comparisons reveal rankings that differ substantially from accuracy-only evaluations, highlighting algorithms that improve carbon efficiency with only marginal accuracy loss. Beyond metric-based assessment, we introduce a CFER-aware green optimization mechanism as an algorithm-agnostic plug-in control layer. Driven by real-time carbon estimation and marginal CFER feedback, it adaptively budgets computation through carbon-budget termination and population shrinking under low marginal carbon efficiency. Integrated into GA, DE, and PSO for uncrewed aerial vehicle (UAV) three-dimensional path planning, the resulting CFER-aware variants reduce CO2 emissions by 45.91%, 28.28%, and 59.14%, respectively, while increasing CFER by 78.59%, 32.45%, and 133.70%, respectively, yielding an improved performance-carbon trade-off with minor performance-score degradation. Overall, the proposed framework supports carbon-aware evaluation, algorithm selection, and adaptive computation budgeting for green AI systems.

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