Green Optimization: Energy-aware Design of Metaheuristics by Using Machine Learning Surrogates to Cope with Real Problems

• First study of surrogate-assisted optimization covering energy, time, and memory • Surrogate models reduce energy use by up to 98 • Well-trained surrogates raise training cost but save energy when used during search • Iterative retraining enhances surrogate accuracy and efficiency in optimization • Surrogates cut execution time in optimization but increase memory consumption Addressing real-world optimization challenges requires not only advanced metaheuristics but also continuous refinement of their internal mechanisms. This paper explores the integration of machine learning in the form of neural surrogate models into metaheuristics through a recent lens: energy consumption. While surrogates are widely used to reduce the computational cost of expensive objective functions, their combined impact on energy efficiency, algorithmic performance, and solution accuracy remains largely unquantified. We provide a critical investigation into this intersection, aiming to advance the design of energy-aware, surrogate-assisted search algorithms. Our experiments reveal substantial benefits: employing a pre-trained surrogate can reduce energy consumption by up to 98%, execution time by approximately 98%, and memory usage by around 99% in our setting. Moreover, increasing the training dataset size may further enhance these gains up to a point by lowering the per-use computational cost, while static pre-training versus continuous (iterative) retraining exhibit different advantages depending on whether we aim at time/energy or accuracy and overall computational cost across instances, respectively. Surrogates may negatively impact cost and accuracy in some cases, and then they cannot be blindly adopted. These findings support a more holistic approach to surrogate-assisted optimization, integrating energy with time and predictive accuracy into performance assessments.