Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Energy-Aware Metaheuristics

Tomohiro Harada, Enrique Alba, Gabriel Luque

TL;DR

This work targets energy-constrained optimization by introducing Expected Improvement per Joule (EI/J), a principled metric that couples numerical gain with energy cost to drive online operator selection. An energy-aware scheduler based on Thompson sampling selects among lightweight and heavyweight operators for GA, PSO, and ILS, with a budget-aware penalty to respect energy caps. Empirical results on Knapsack, NK-landscapes, and ECC show the EI/J framework preserves or improves solution quality while substantially reducing energy usage compared to non-energy-aware baselines, with EI/J stabilizing early and revealing the most efficient operators. The approach is broadly applicable to other operator-driven metaheuristics and opens avenues for bandit or RL-based energy-aware control in larger-scale or parallel settings.

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.

Energy-Aware Metaheuristics

TL;DR

This work targets energy-constrained optimization by introducing Expected Improvement per Joule (EI/J), a principled metric that couples numerical gain with energy cost to drive online operator selection. An energy-aware scheduler based on Thompson sampling selects among lightweight and heavyweight operators for GA, PSO, and ILS, with a budget-aware penalty to respect energy caps. Empirical results on Knapsack, NK-landscapes, and ECC show the EI/J framework preserves or improves solution quality while substantially reducing energy usage compared to non-energy-aware baselines, with EI/J stabilizing early and revealing the most efficient operators. The approach is broadly applicable to other operator-driven metaheuristics and opens avenues for bandit or RL-based energy-aware control in larger-scale or parallel settings.

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.
Paper Structure (31 sections, 15 equations, 16 figures, 3 tables, 4 algorithms)

This paper contains 31 sections, 15 equations, 16 figures, 3 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. Background and Related Work
  3. Expected Improvement per Joule (EI/J)
  4. Motivation
  5. Definition
  6. Estimation of Expected Improvement
  7. Estimation of Expected Energy Cost
  8. Thompson Sampling-based EI/J
  9. Energy-aware Prioritisation under Limited Budget
  10. Operator selection rule
  11. Energy-Aware Metaheuristic Design
  12. Energy-Aware EI/J Scheduler
  13. Energy-aware GA, PSO, and ILS
  14. Computational Overhead and Stability
  15. Experimental Setup
  16. ...and 16 more sections

Figures (16)

  • Figure 1: KP
  • Figure 2: NK
  • Figure 3: ECC
  • Figure 5: SSGA
  • Figure 6: PSO
  • ...and 11 more figures