Energy-Aware Metaheuristics

TL;DR

This paper introduces a framework for designing energy-aware metaheuristics that adaptively select operators based on an expected improvement per Joule score, achieving comparable results with less energy.

Contribution

The paper proposes a unified operator-level model and a robust EI/J score for energy-aware metaheuristics, demonstrated on three algorithms and multiple problems.

Findings

Energy-aware solvers reach similar fitness with less energy.

EI/J scores stabilize early, guiding operator selection.

Self-identification of the most efficient operator per problem.

Abstract

This paper presents a principled framework for designing energy-aware metaheuristics that operate under fixed energy budgets. We introduce a unified operator-level model that quantifies both numerical gain and energy usage, and define a robust Expected Improvement per Joule (EI/J) score that guides adaptive selection among operator variants during the search. The resulting energy-aware solvers dynamically choose between operators to self-control exploration and exploitation, aiming to maximize fitness gain under limited energy. We instantiate this framework with three representative metaheuristics - steady-state GA, PSO, and ILS - each equipped with both lightweight and heavy operator variants. Experiments on three heterogeneous combinatorial problems (Knapsack, NK-landscapes, and Error-Correcting Codes) show that the energy-aware variants consistently reach comparable fitness while requiring substantially less energy than their non-energy-aware baselines. EI/J values stabilize early and yield clear operator-selection patterns, with each solver reliably self-identifying the most improvement-per-Joule - efficient operator across problems.