Energy-Aware Metaheuristics

Enrique Alba; Gabriel Luque; Tomohiro Harada

arxiv: 2602.06595 · v4 · submitted 2026-02-06 · 💻 cs.NE

Energy-Aware Metaheuristics

Enrique Alba , Tomohiro Harada , Gabriel Luque This is my paper

Pith reviewed 2026-05-16 06:53 UTC · model grok-4.3

classification 💻 cs.NE

keywords energy-aware metaheuristicsExpected Improvement per Jouleoperator selectioncombinatorial optimizationgenetic algorithmsparticle swarm optimizationiterated local searchenergy efficiency

0 comments

The pith

Energy-aware metaheuristics select operators with an Expected Improvement per Joule score to reach comparable fitness while using substantially less energy.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper develops a framework for metaheuristics that must respect fixed energy budgets during search. It models both the fitness gain and the energy cost of each operator variant and uses an Expected Improvement per Joule metric to decide which variant to apply at each step. The approach is shown on steady-state genetic algorithms, particle swarm optimization, and iterated local search, each equipped with lightweight and heavy operator options. Experiments on knapsack, NK-landscapes, and error-correcting codes problems demonstrate that the energy-aware versions achieve fitness levels comparable to standard solvers yet consume markedly less total energy. The selection process stabilizes early and produces consistent patterns that favor the more efficient operator for each problem and solver.

Core claim

The paper claims that a unified operator-level model of numerical gain and energy usage, together with an EI/J selection score, lets metaheuristics dynamically balance exploration and exploitation so as to maximize fitness gain under a fixed energy budget. When the framework is instantiated in GA, PSO, and ILS, the resulting solvers match the final fitness of their non-aware baselines on three heterogeneous combinatorial problems while requiring substantially less energy, with EI/J values stabilizing early and revealing clear, reliable operator preferences.

What carries the argument

The Expected Improvement per Joule (EI/J) score, which ranks operator variants by expected fitness improvement divided by their measured energy cost and drives adaptive selection throughout the run.

If this is right

Energy-aware variants of steady-state GA, PSO, and ILS reach comparable fitness with substantially less energy on knapsack, NK-landscapes, and error-correcting codes problems.
EI/J values stabilize early and produce stable operator-selection patterns across different problems.
Each solver self-identifies its most improvement-per-joule efficient operator variant without external tuning.
The framework supports dynamic switching between lightweight and heavy operator variants to control exploration versus exploitation under energy limits.
The same operator-selection logic applies uniformly to three representative metaheuristics.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The EI/J approach could be tested on continuous or multi-objective problems to check whether similar energy savings appear outside combinatorial domains.
Hardware-specific calibration of the energy model would likely be required when moving the solvers to new platforms or embedded devices.
Battery-powered or mobile optimization tasks could run longer under the same energy budget without loss of solution quality.
Adding time or memory budgets alongside the energy limit could yield multi-resource-aware versions of the same framework.

Load-bearing premise

The operator-level energy model must accurately predict real hardware energy consumption, and the EI/J score must reliably choose operators without causing premature convergence or missing better solutions.

What would settle it

Run both energy-aware and baseline solvers on identical hardware while measuring actual power draw with a wattmeter; if the observed energy savings diverge significantly from the model's predictions or if final fitness is lower, the central claim is falsified.

Figures

Figures reproduced from arXiv: 2602.06595 by Enrique Alba, Gabriel Luque, Tomohiro Harada.

**Figure 2.** Figure 2: Transitions of expected improvement and expected energy (KP) [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

**Figure 3.** Figure 3: Transitions of expected improvement and expected energy (NK) [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

**Figure 4.** Figure 4: Transitions of expected improvement and expected energy (ECC) [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗

**Figure 5.** Figure 5: Operator selection ratios across energy budget (%) [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗

**Figure 6.** Figure 6: Trajectories of average fitness via cumulative energy consumption (J [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗

read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The EI/J operator-selection rule is a straightforward addition to metaheuristics, but the energy savings rest on an internal model that was never checked against real hardware measurements.

read the letter

The paper's main move is to define an Expected Improvement per Joule score that picks among operator variants during search so the algorithm stays inside a fixed energy budget. They wrap this around steady-state GA, PSO, and ILS, each with a light and a heavy operator version, and test on Knapsack, NK-landscapes, and error-correcting codes. The energy-aware runs reach roughly the same final fitness while reporting lower total energy than the plain baselines, and the EI/J values settle early into stable operator preferences. That multi-problem coverage and the explicit tie between gain and energy cost are the parts that feel new relative to the usual fitness-only selection rules in the metaheuristic literature. The experiments are presented cleanly enough to show the mechanism working across quite different combinatorial structures. The central weakness is that the energy figures come from the authors' own operator-level model rather than from power measurements on the same hardware. Without RAPL traces, external meters, or even a calibration step against real joules, the reported savings stay inside the simulation and could shrink or disappear once the model is replaced by actual consumption numbers, especially on data-dependent problems like Knapsack. The abstract also gives no error bars, run counts, or statistical tests, so the claim of consistent gains is hard to weigh. This work is aimed at people who already build or tune metaheuristics and now have to respect energy caps in embedded or green-computing settings. A reader looking for a simple adaptive rule to trade exploration cost against improvement would get usable ideas from the EI/J formulation. It should go to peer review. The framework is concrete, the tests span multiple domains, and the validation gap on energy is fixable with added measurements rather than a fatal flaw in the logic.

Referee Report

1 major / 2 minor

Summary. The manuscript introduces a framework for energy-aware metaheuristics that employs an operator-level energy model to define an Expected Improvement per Joule (EI/J) score for adaptive selection among lightweight and heavy operator variants. It instantiates the approach in steady-state GA, PSO, and ILS, and reports experiments on Knapsack, NK-landscapes, and Error-Correcting Codes problems in which the energy-aware versions reach fitness values comparable to non-energy-aware baselines while using substantially less energy according to the model.

Significance. If the operator energy model proves accurate under hardware measurement, the EI/J-driven selection mechanism would offer a concrete, self-adapting way to trade exploration cost against fitness gain under fixed energy budgets. The consistent operator-selection patterns observed across three heterogeneous problems suggest the metric can stabilize early and identify efficient operators without explicit tuning, which would be a useful addition to the metaheuristics literature.

major comments (1)

[Energy model and experimental results] The central claim that energy-aware variants require substantially less energy rests on an operator-level energy model whose per-operator joule estimates are never validated against physical hardware (no RAPL counters, external power meters, or cycle-accurate profiling are referenced). Because EI/J is computed directly from these model values, any systematic deviation between model and real consumption (especially data-dependent costs in Knapsack or NK-landscapes) renders the reported savings an internal artifact rather than a demonstrated physical reduction.

minor comments (2)

[Experiments] The abstract and results sections report consistent gains but omit error bars, standard deviations, and any statistical significance tests (e.g., Wilcoxon or t-tests) comparing energy-aware versus baseline runs; these details are required to substantiate the “comparable fitness” claim.
[Operator energy model] The manuscript does not supply the concrete numerical values or functional forms used to assign energy costs to each operator variant, making independent reproduction or sensitivity analysis impossible.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive assessment of our framework's potential significance and for highlighting the need to clarify the energy model's status. We address the major comment below and will revise the manuscript to strengthen the presentation of results and limitations.

read point-by-point responses

Referee: The central claim that energy-aware variants require substantially less energy rests on an operator-level energy model whose per-operator joule estimates are never validated against physical hardware (no RAPL counters, external power meters, or cycle-accurate profiling are referenced). Because EI/J is computed directly from these model values, any systematic deviation between model and real consumption (especially data-dependent costs in Knapsack or NK-landscapes) renders the reported savings an internal artifact rather than a demonstrated physical reduction.

Authors: We agree that the energy savings are demonstrated relative to the proposed operator-level model rather than through direct physical hardware measurements. The model assigns joule costs based on standard per-operation estimates (arithmetic, memory access, and control-flow costs drawn from established computational energy literature) applied uniformly to lightweight versus heavy operator variants. While we acknowledge that unmodeled data-dependent effects could alter absolute values, the framework's value lies in the relative ranking that EI/J induces, which produces stable operator-selection patterns and comparable fitness across three distinct problem classes. In revision we will: (1) explicitly qualify every energy claim as model-based, (2) add a limitations subsection discussing possible discrepancies and data dependency, and (3) outline concrete next steps for RAPL-based or external-meter validation. These changes address the concern directly while preserving the contribution of the adaptive EI/J mechanism. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The abstract introduces an operator-level energy model and EI/J score to guide operator selection, then reports experimental outcomes on three problems where energy-aware variants achieve comparable fitness with lower energy (per the model). No equations are present that reduce the final claims to definitional inputs by construction, no fitted parameters are renamed as predictions, and no self-citations or uniqueness theorems appear in the provided text. The fitness results remain an independent objective separate from the energy metric used for selection, making the framework self-contained without circular reduction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The framework rests on the new EI/J metric and the assumption that operators have independently measurable energy costs; no free parameters are explicitly fitted in the abstract description.

axioms (1)

domain assumption Metaheuristics can be decomposed into discrete operators whose numerical gain and energy consumption can be quantified separately
Foundation of the operator-level model introduced in the abstract

invented entities (1)

Expected Improvement per Joule (EI/J) score no independent evidence
purpose: To guide dynamic selection among operator variants under energy limits
New metric defined in the paper to combine gain and energy

pith-pipeline@v0.9.0 · 5460 in / 1126 out tokens · 22572 ms · 2026-05-16T06:53:30.290987+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

EI/J(ο)= μΔf(ο) / μE(ο) ... Thompson sampling ... budget-aware penalty π(ο, Bt)
IndisputableMonolith/Foundation/AlphaCoordinateFixation.lean J_uniquely_calibrated_via_higher_derivative unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

energy consumption measured ... via pyRAPL ... operator-level energy profiles

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

40 extracted references · 40 canonical work pages · 1 internal anchor

[1]

Amr Abdelhafez, Enrique Alba, and Gabriel Luque. 2019. A component-based study of energy consumption for sequential and parallel genetic algorithms.The Journal of Supercomputing75, 10 (01 Oct 2019), 6194–6219. doi:10.1007/s11227- 019-02843-4

work page doi:10.1007/s11227- 2019
[2]

Amr Abdelhafez, Gabriel Luque, and Enrique Alba. 2020. Parallel execution combinatorics with metaheuristics: Comparative study.Swarm and Evolutionary Computation55 (2020), 100692

work page 2020
[3]

E Alba, G Luque, and J.M Troya. 2004. Parallel LAN/WAN heuristics for opti- mization.Parallel Comput.30, 5 (2004), 611–628. doi:10.1016/j.parco.2003.12.007 Parallel and nature-inspired computational paradigms and applications

work page doi:10.1016/j.parco.2003.12.007 2004
[4]

Muralidhar Andoorveedu, Zhanda Zhu, Bojian Zheng, and Gennady Pekhimenko

work page
[5]

InAdvances in Neural Information Processing Systems, S

Tempo: Accelerating Transformer-Based Model Training through Mem- ory Footprint Reduction. InAdvances in Neural Information Processing Systems, S. Koyejo, S. Mohamed, A. Agarwal, D. Belgrave, K. Cho, and A. Oh (Eds.), Vol. 35. Curran Associates, Inc., 12267–12282. https://proceedings.neurips.cc/paper_files/ paper/2022/file/4fc81f4cd2715d995018e0799262176b...

work page 2022
[6]

Bartoldson, Bhavya Kailkhura, and Davis Blalock

Brian R. Bartoldson, Bhavya Kailkhura, and Davis Blalock. 2023. Compute- Efficient Deep Learning: Algorithmic Trends and Opportunities.Journal of Machine Learning Research24, 122 (2023), 1–77. http://jmlr.org/papers/v24/22- 1208.html

work page 2023
[7]

Verónica Bolón-Canedo, Laura Morán-Fernández, Brais Cancela, and Amparo Alonso-Betanzos. 2024. A review of green artificial intelligence: Towards a more sustainable future.Neurocomputing599 (2024), 128096. doi:10.1016/j.neucom. 2024.128096

work page doi:10.1016/j.neucom 2024
[8]

Edmund K Burke, Michel Gendreau, Matthew Hyde, Graham Kendall, Gabriela Ochoa, Ender Özcan, and Rong Qu. 2013. Hyper-heuristics: A survey of the state of the art.Journal of the Operational Research Society64, 12 (2013), 1695–1724. doi:10.1057/jors.2013.71

work page doi:10.1057/jors.2013.71 2013
[9]

Jagat Sesh Challa, Aarti, Navneet Goyal, and Poonam Goyal. 2026. Time-sensitive data analytics: A survey of anytime techniques, applications and challenges. Computer Science Review59 (2026), 100850. doi:10.1016/j.cosrev.2025.100850

work page doi:10.1016/j.cosrev.2025.100850 2026
[10]

Carlos Cotta and Jesús Martínez-Cruz. 2024. Energy Consumption Analysis of Batch Runs of Evolutionary Algorithms. InProceedings of the Genetic and Evolutionary Computation Conference Companion(Melbourne, VIC, Australia) (GECCO ’24 Companion). Association for Computing Machinery, New York, NY, USA, 87––88. doi:10.1145/3638530.3664093

work page doi:10.1145/3638530.3664093 2024
[11]

2024.mlco2/codecarbon: v2.4.1

Benoit Courty, Victor Schmidt, Goyal-Kamal, MarionCoutarel, Boris Feld, Jérémy Lecourt, LiamConnell, SabAmine, inimaz, supatomic, Mathilde Léval, Luis Blanche, Alexis Cruveiller, ouminasara, Franklin Zhao, Aditya Joshi, Alexis Bogroff, Amine Saboni, Hugues de Lavoreille, Niko Laskaris, Edoardo Abati, Douglas Blank, Ziyao Wang, Armin Catovic, alencon, Mich...

work page doi:10.5281/zenodo.11171501 2024
[12]

Hanebutte, Rahul Khanna, and Christian Le

Howard David, Eugene Gorbatov, Ulf R. Hanebutte, Rahul Khanna, and Christian Le. 2010. RAPL: Memory power estimation and capping. In2010 International Symposium on Low-Power Electronics and Design. 189–194. doi:10.1145/1840845. 1840883

work page doi:10.1145/1840845 2010
[13]

Rafet Durgut, Mehmet Emin Aydin, and Ibrahim Atli. 2021. Adaptive operator selection with reinforcement learning.Information Sciences581 (2021), 773–790. doi:10.1016/j.ins.2021.10.025

work page doi:10.1016/j.ins.2021.10.025 2021
[14]

Josefa Díaz-Álvarez, Pedro A Castillo, Francisco Fernández de Vega, Francisco Chávez, and Jorge Alvarado. 2022. Population size influence on the energy consumption of genetic programming.Meas. and Control55, 1-2 (2022), 102–115. doi:10.1177/00202940211064471

work page doi:10.1177/00202940211064471 2022
[15]

Juan José Escobar, Julio Ortega, Antonio Francisco Díaz, Jesús González, and Miguel Damas. 2019. Energy-aware load balancing of parallel evolutionary algorithms with heavy fitness functions in heterogeneous CPU-GPU architec- tures.Concurrency and Computation: Practice and Experience31, 6 (2019), e4688. arXiv:https://onlinelibrary.wiley.com/doi/pdf/10.1002...

work page doi:10.1002/cpe.4688 2019
[16]

Francisco Fernández de Vega, Josefa Díaz, Juan Ángel García, Francisco Chávez, and Jorge Alvarado. 2020. Looking for Energy Efficient Genetic Algorithms. In Artificial Evolution. Springer, 96–109

work page 2020
[17]

Álvaro Fialho, Marc Schoenauer, and Michele Sebag. 2010. Toward comparison- based adaptive operator selection. InProceedings of the 12th Annual Conference on Genetic and Evolutionary Computation (GECCO ’10). ACM, 767–774. doi:10. 1145/1830483.1830619

work page arXiv 2010
[18]

Álvaro Fialho, Luis Da Costa, Marc Schoenauer, and Michèle Sebag. 2010. Analyz- ing bandit-based adaptive operator selection mechanisms.Annals of Mathematics and Artificial Intelligence60, 1–2 (Sept. 2010), 25–64. doi:10.1007/s10472-010- 9213-y

work page doi:10.1007/s10472-010- 2010
[19]

AE Gamal, L Hemachandra, Itzhak Shperling, and V Wei. 1987. Using simulated annealing to design good codes.IEEE Transactions on information theory33, 1 (1987), 116–123

work page 1987
[20]

Tomohiro Harada, Enrique Alba, and Gabriel Luque. 2024. Energy and Quality of Surrogate-Assisted Search Algorithms: a First Analysis. In2024 IEEE Congress on Evolutionary Computation (CEC). 1–8. doi:10.1109/CEC60901.2024.10611758

work page internal anchor Pith review Pith/arXiv arXiv doi:10.1109/cec60901.2024.10611758 2024
[21]

Mohammad Newaj Jamil and Ah-Lian Kor. 2022. Analyzing energy consumption of nature-inspired optimization algorithms.Green Technology, Resilience, and Sustainability2, 1 (27 Jan 2022), 1. doi:10.1007/s44173-021-00001-9

work page doi:10.1007/s44173-021-00001-9 2022
[22]

2002 , month =

Stuart A Kauffman. 1993.The Origins of Order: Self-Organization and Selection in Evolution. Oxford University Press. doi:10.1093/oso/9780195079517.001.0001

work page doi:10.1093/oso/9780195079517.001.0001 1993
[23]

Ji Li, Quan Zhou, Huw Williams, Hongming Xu, and Changqing Du. 2022. Cyber- Physical Data Fusion in Surrogate-Assisted Strength Pareto Evolutionary Al- gorithm for PHEV Energy Management Optimization.IEEE Transactions on Industrial Informatics18, 6 (2022), 4107–4117. doi:10.1109/TII.2021.3121287

work page doi:10.1109/tii.2021.3121287 2022
[24]

Ke Li, Álvaro Fialho, Sam Kwong, and Qingfu Zhang. 2014. Adaptive Operator Selection With Bandits for a Multiobjective Evolutionary Algorithm Based on Decomposition.IEEE Transactions on Evolutionary Computation18, 1 (2014), 114–130. doi:10.1109/TEVC.2013.2239648

work page doi:10.1109/tevc.2013.2239648 2014
[25]

Hou-I Liu, Marco Galindo, Hongxia Xie, Lai-Kuan Wong, Hong-Han Shuai, Yung- Hui Li, and Wen-Huang Cheng. 2024. Lightweight Deep Learning for Resource- Constrained Environments: A Survey.ACM Comput. Surv.56, 10, Article 267 (June 2024), 42 pages. doi:10.1145/3657282

work page doi:10.1145/3657282 2024
[26]

Florian Meier and Hayata Yamasaki. 2025. Energy-Consumption Advantage of Quantum Computation.PRX Energy4 (May 2025), 023008. Issue 2. doi:10.1103/ PRXEnergy.4.023008

work page 2025
[27]

Gaurav Menghani. 2023. Efficient Deep Learning: A Survey on Making Deep Learning Models Smaller, Faster, and Better.ACM Comput. Surv.55, 12, Article 259 (March 2023), 37 pages. doi:10.1145/3578938

work page doi:10.1145/3578938 2023
[28]

Merelo-Guervós, Mario García-Valdez, and Pedro A

Juan J. Merelo-Guervós, Mario García-Valdez, and Pedro A. Castillo. 2024. Green Evolutionary Algorithms and JavaScript: A Study on Different Software and Hardware Architectures. InSoftware Technologies, Hans-Georg Fill, Francisco José Domínguez Mayo, Marten van Sinderen, and Leszek A. Maciaszek (Eds.). Springer Nature Switzerland, Cham, 1–18

work page 2024
[29]

J. J. Moreno, G. Ortega, E. Filatovas, J. A. Martínez, and E. M. Garzón. 2016. Improving the Energy Efficiency of Evolutionary Multi-objective Algorithms. In Algorithms and Architectures for Parallel Processing, Jesus Carretero, Javier Garcia- Blas, Victor Gergel, Vladimir Voevodin, Iosif Meyerov, Juan A. Rico-Gallego, Juan C. Díaz-Martín, Pedro Alonso, J...

work page 2016
[30]

Rajeev Muralidhar, Renata Borovica-Gajic, and Rajkumar Buyya. 2022. Energy Efficient Computing Systems: Architectures, Abstractions and Modeling to Tech- niques and Standards.ACM Comput. Surv.54, 11s, Article 236 (Sept. 2022), 37 pages. doi:10.1145/3511094

work page doi:10.1145/3511094 2022
[31]

Adel Noureddine, Romain Rouvoy, and Lionel Seinturier. 2015. Monitoring energy hotspots in software.Automated Software Engineering22, 3 (2015), 291–

work page 2015
[32]

doi:10.1007/s10515-014-0171-1

work page doi:10.1007/s10515-014-0171-1
[33]

Martin Pelikan. 2008. Analysis of estimation of distribution algorithms and genetic algorithms on NK landscapes. InProceedings of the 10th Annual Con- ference on Genetic and Evolutionary Computation(Atlanta, GA, USA)(GECCO ’08). Association for Computing Machinery, New York, NY, USA, 1033–1040. doi:10.1145/1389095.1389287

work page doi:10.1145/1389095.1389287 2008
[34]

David Pisinger. 2005. Where are the hard knapsack problems?Computers & Operations Research32, 9 (2005), 2271–2284. doi:10.1016/j.cor.2004.03.002

work page doi:10.1016/j.cor.2004.03.002 2005
[35]

Spirals Research Group (University of Lille and Inria). 2019. pyRAPL Docu- mentation (Version 0.2.0). https://pyrapl.readthedocs.io/en/latest/. Accessed: 2026-01-14

work page 2019
[36]

Abdulaziz Tabbakh, Lisan Al Amin, Mahbubul Islam, G. M. Iqbal Mahmud, Im- ranul Kabir Chowdhury, and Md Saddam Hossain Mukta. 2024. Towards sustain- able AI: a comprehensive framework for Green AI.Discover Sustainability5, 1 (Nov. 2024). doi:10.1007/s43621-024-00641-4

work page doi:10.1007/s43621-024-00641-4 2024
[37]

Jihene Tmamna, Emna Ben Ayed, Rahma Fourati, Mandar Gogate, Tughrul Arslan, Amir Hussain, and Mounir Ben Ayed. 2024. Pruning Deep Neural Networks for Green Energy-Efficient Models: A Survey.Cognitive Computation16, 6 (July 2024), 2931–2952. doi:10.1007/s12559-024-10313-0

work page doi:10.1007/s12559-024-10313-0 2024
[38]

Nguyen Van Thieu and Seyedali Mirjalili. 2023. MEALPY: An open-source library for latest meta-heuristic algorithms in Python.Journal of Systems Architecture 139 (2023), 102871. doi:10.1016/j.sysarc.2023.102871

work page doi:10.1016/j.sysarc.2023.102871 2023
[39]

Roberto Verdecchia, June Sallou, and Luís Cruz. 2023. A systematic review of Green AI.WIREs Data Mining and Knowl. Disc.13, 4 (2023), e1507. doi:10.1002/ widm.1507

work page 2023
[40]

Shlomo Zilberstein. 1996. Using Anytime Algorithms in Intelligent Systems.AI Magazine17, 3 (1996), 73–83. doi:10.1609/aimag.v17i3.1232

work page doi:10.1609/aimag.v17i3.1232 1996

[1] [1]

Amr Abdelhafez, Enrique Alba, and Gabriel Luque. 2019. A component-based study of energy consumption for sequential and parallel genetic algorithms.The Journal of Supercomputing75, 10 (01 Oct 2019), 6194–6219. doi:10.1007/s11227- 019-02843-4

work page doi:10.1007/s11227- 2019

[2] [2]

Amr Abdelhafez, Gabriel Luque, and Enrique Alba. 2020. Parallel execution combinatorics with metaheuristics: Comparative study.Swarm and Evolutionary Computation55 (2020), 100692

work page 2020

[3] [3]

E Alba, G Luque, and J.M Troya. 2004. Parallel LAN/WAN heuristics for opti- mization.Parallel Comput.30, 5 (2004), 611–628. doi:10.1016/j.parco.2003.12.007 Parallel and nature-inspired computational paradigms and applications

work page doi:10.1016/j.parco.2003.12.007 2004

[4] [4]

Muralidhar Andoorveedu, Zhanda Zhu, Bojian Zheng, and Gennady Pekhimenko

work page

[5] [5]

InAdvances in Neural Information Processing Systems, S

Tempo: Accelerating Transformer-Based Model Training through Mem- ory Footprint Reduction. InAdvances in Neural Information Processing Systems, S. Koyejo, S. Mohamed, A. Agarwal, D. Belgrave, K. Cho, and A. Oh (Eds.), Vol. 35. Curran Associates, Inc., 12267–12282. https://proceedings.neurips.cc/paper_files/ paper/2022/file/4fc81f4cd2715d995018e0799262176b...

work page 2022

[6] [6]

Bartoldson, Bhavya Kailkhura, and Davis Blalock

Brian R. Bartoldson, Bhavya Kailkhura, and Davis Blalock. 2023. Compute- Efficient Deep Learning: Algorithmic Trends and Opportunities.Journal of Machine Learning Research24, 122 (2023), 1–77. http://jmlr.org/papers/v24/22- 1208.html

work page 2023

[7] [7]

Verónica Bolón-Canedo, Laura Morán-Fernández, Brais Cancela, and Amparo Alonso-Betanzos. 2024. A review of green artificial intelligence: Towards a more sustainable future.Neurocomputing599 (2024), 128096. doi:10.1016/j.neucom. 2024.128096

work page doi:10.1016/j.neucom 2024

[8] [8]

Edmund K Burke, Michel Gendreau, Matthew Hyde, Graham Kendall, Gabriela Ochoa, Ender Özcan, and Rong Qu. 2013. Hyper-heuristics: A survey of the state of the art.Journal of the Operational Research Society64, 12 (2013), 1695–1724. doi:10.1057/jors.2013.71

work page doi:10.1057/jors.2013.71 2013

[9] [9]

Jagat Sesh Challa, Aarti, Navneet Goyal, and Poonam Goyal. 2026. Time-sensitive data analytics: A survey of anytime techniques, applications and challenges. Computer Science Review59 (2026), 100850. doi:10.1016/j.cosrev.2025.100850

work page doi:10.1016/j.cosrev.2025.100850 2026

[10] [10]

Carlos Cotta and Jesús Martínez-Cruz. 2024. Energy Consumption Analysis of Batch Runs of Evolutionary Algorithms. InProceedings of the Genetic and Evolutionary Computation Conference Companion(Melbourne, VIC, Australia) (GECCO ’24 Companion). Association for Computing Machinery, New York, NY, USA, 87––88. doi:10.1145/3638530.3664093

work page doi:10.1145/3638530.3664093 2024

[11] [11]

2024.mlco2/codecarbon: v2.4.1

Benoit Courty, Victor Schmidt, Goyal-Kamal, MarionCoutarel, Boris Feld, Jérémy Lecourt, LiamConnell, SabAmine, inimaz, supatomic, Mathilde Léval, Luis Blanche, Alexis Cruveiller, ouminasara, Franklin Zhao, Aditya Joshi, Alexis Bogroff, Amine Saboni, Hugues de Lavoreille, Niko Laskaris, Edoardo Abati, Douglas Blank, Ziyao Wang, Armin Catovic, alencon, Mich...

work page doi:10.5281/zenodo.11171501 2024

[12] [12]

Hanebutte, Rahul Khanna, and Christian Le

Howard David, Eugene Gorbatov, Ulf R. Hanebutte, Rahul Khanna, and Christian Le. 2010. RAPL: Memory power estimation and capping. In2010 International Symposium on Low-Power Electronics and Design. 189–194. doi:10.1145/1840845. 1840883

work page doi:10.1145/1840845 2010

[13] [13]

Rafet Durgut, Mehmet Emin Aydin, and Ibrahim Atli. 2021. Adaptive operator selection with reinforcement learning.Information Sciences581 (2021), 773–790. doi:10.1016/j.ins.2021.10.025

work page doi:10.1016/j.ins.2021.10.025 2021

[14] [14]

Josefa Díaz-Álvarez, Pedro A Castillo, Francisco Fernández de Vega, Francisco Chávez, and Jorge Alvarado. 2022. Population size influence on the energy consumption of genetic programming.Meas. and Control55, 1-2 (2022), 102–115. doi:10.1177/00202940211064471

work page doi:10.1177/00202940211064471 2022

[15] [15]

Juan José Escobar, Julio Ortega, Antonio Francisco Díaz, Jesús González, and Miguel Damas. 2019. Energy-aware load balancing of parallel evolutionary algorithms with heavy fitness functions in heterogeneous CPU-GPU architec- tures.Concurrency and Computation: Practice and Experience31, 6 (2019), e4688. arXiv:https://onlinelibrary.wiley.com/doi/pdf/10.1002...

work page doi:10.1002/cpe.4688 2019

[16] [16]

Francisco Fernández de Vega, Josefa Díaz, Juan Ángel García, Francisco Chávez, and Jorge Alvarado. 2020. Looking for Energy Efficient Genetic Algorithms. In Artificial Evolution. Springer, 96–109

work page 2020

[17] [17]

Álvaro Fialho, Marc Schoenauer, and Michele Sebag. 2010. Toward comparison- based adaptive operator selection. InProceedings of the 12th Annual Conference on Genetic and Evolutionary Computation (GECCO ’10). ACM, 767–774. doi:10. 1145/1830483.1830619

work page arXiv 2010

[18] [18]

Álvaro Fialho, Luis Da Costa, Marc Schoenauer, and Michèle Sebag. 2010. Analyz- ing bandit-based adaptive operator selection mechanisms.Annals of Mathematics and Artificial Intelligence60, 1–2 (Sept. 2010), 25–64. doi:10.1007/s10472-010- 9213-y

work page doi:10.1007/s10472-010- 2010

[19] [19]

AE Gamal, L Hemachandra, Itzhak Shperling, and V Wei. 1987. Using simulated annealing to design good codes.IEEE Transactions on information theory33, 1 (1987), 116–123

work page 1987

[20] [20]

Tomohiro Harada, Enrique Alba, and Gabriel Luque. 2024. Energy and Quality of Surrogate-Assisted Search Algorithms: a First Analysis. In2024 IEEE Congress on Evolutionary Computation (CEC). 1–8. doi:10.1109/CEC60901.2024.10611758

work page internal anchor Pith review Pith/arXiv arXiv doi:10.1109/cec60901.2024.10611758 2024

[21] [21]

Mohammad Newaj Jamil and Ah-Lian Kor. 2022. Analyzing energy consumption of nature-inspired optimization algorithms.Green Technology, Resilience, and Sustainability2, 1 (27 Jan 2022), 1. doi:10.1007/s44173-021-00001-9

work page doi:10.1007/s44173-021-00001-9 2022

[22] [22]

2002 , month =

Stuart A Kauffman. 1993.The Origins of Order: Self-Organization and Selection in Evolution. Oxford University Press. doi:10.1093/oso/9780195079517.001.0001

work page doi:10.1093/oso/9780195079517.001.0001 1993

[23] [23]

Ji Li, Quan Zhou, Huw Williams, Hongming Xu, and Changqing Du. 2022. Cyber- Physical Data Fusion in Surrogate-Assisted Strength Pareto Evolutionary Al- gorithm for PHEV Energy Management Optimization.IEEE Transactions on Industrial Informatics18, 6 (2022), 4107–4117. doi:10.1109/TII.2021.3121287

work page doi:10.1109/tii.2021.3121287 2022

[24] [24]

Ke Li, Álvaro Fialho, Sam Kwong, and Qingfu Zhang. 2014. Adaptive Operator Selection With Bandits for a Multiobjective Evolutionary Algorithm Based on Decomposition.IEEE Transactions on Evolutionary Computation18, 1 (2014), 114–130. doi:10.1109/TEVC.2013.2239648

work page doi:10.1109/tevc.2013.2239648 2014

[25] [25]

Hou-I Liu, Marco Galindo, Hongxia Xie, Lai-Kuan Wong, Hong-Han Shuai, Yung- Hui Li, and Wen-Huang Cheng. 2024. Lightweight Deep Learning for Resource- Constrained Environments: A Survey.ACM Comput. Surv.56, 10, Article 267 (June 2024), 42 pages. doi:10.1145/3657282

work page doi:10.1145/3657282 2024

[26] [26]

Florian Meier and Hayata Yamasaki. 2025. Energy-Consumption Advantage of Quantum Computation.PRX Energy4 (May 2025), 023008. Issue 2. doi:10.1103/ PRXEnergy.4.023008

work page 2025

[27] [27]

Gaurav Menghani. 2023. Efficient Deep Learning: A Survey on Making Deep Learning Models Smaller, Faster, and Better.ACM Comput. Surv.55, 12, Article 259 (March 2023), 37 pages. doi:10.1145/3578938

work page doi:10.1145/3578938 2023

[28] [28]

Merelo-Guervós, Mario García-Valdez, and Pedro A

Juan J. Merelo-Guervós, Mario García-Valdez, and Pedro A. Castillo. 2024. Green Evolutionary Algorithms and JavaScript: A Study on Different Software and Hardware Architectures. InSoftware Technologies, Hans-Georg Fill, Francisco José Domínguez Mayo, Marten van Sinderen, and Leszek A. Maciaszek (Eds.). Springer Nature Switzerland, Cham, 1–18

work page 2024

[29] [29]

J. J. Moreno, G. Ortega, E. Filatovas, J. A. Martínez, and E. M. Garzón. 2016. Improving the Energy Efficiency of Evolutionary Multi-objective Algorithms. In Algorithms and Architectures for Parallel Processing, Jesus Carretero, Javier Garcia- Blas, Victor Gergel, Vladimir Voevodin, Iosif Meyerov, Juan A. Rico-Gallego, Juan C. Díaz-Martín, Pedro Alonso, J...

work page 2016

[30] [30]

Rajeev Muralidhar, Renata Borovica-Gajic, and Rajkumar Buyya. 2022. Energy Efficient Computing Systems: Architectures, Abstractions and Modeling to Tech- niques and Standards.ACM Comput. Surv.54, 11s, Article 236 (Sept. 2022), 37 pages. doi:10.1145/3511094

work page doi:10.1145/3511094 2022

[31] [31]

Adel Noureddine, Romain Rouvoy, and Lionel Seinturier. 2015. Monitoring energy hotspots in software.Automated Software Engineering22, 3 (2015), 291–

work page 2015

[32] [32]

doi:10.1007/s10515-014-0171-1

work page doi:10.1007/s10515-014-0171-1

[33] [33]

Martin Pelikan. 2008. Analysis of estimation of distribution algorithms and genetic algorithms on NK landscapes. InProceedings of the 10th Annual Con- ference on Genetic and Evolutionary Computation(Atlanta, GA, USA)(GECCO ’08). Association for Computing Machinery, New York, NY, USA, 1033–1040. doi:10.1145/1389095.1389287

work page doi:10.1145/1389095.1389287 2008

[34] [34]

David Pisinger. 2005. Where are the hard knapsack problems?Computers & Operations Research32, 9 (2005), 2271–2284. doi:10.1016/j.cor.2004.03.002

work page doi:10.1016/j.cor.2004.03.002 2005

[35] [35]

Spirals Research Group (University of Lille and Inria). 2019. pyRAPL Docu- mentation (Version 0.2.0). https://pyrapl.readthedocs.io/en/latest/. Accessed: 2026-01-14

work page 2019

[36] [36]

Abdulaziz Tabbakh, Lisan Al Amin, Mahbubul Islam, G. M. Iqbal Mahmud, Im- ranul Kabir Chowdhury, and Md Saddam Hossain Mukta. 2024. Towards sustain- able AI: a comprehensive framework for Green AI.Discover Sustainability5, 1 (Nov. 2024). doi:10.1007/s43621-024-00641-4

work page doi:10.1007/s43621-024-00641-4 2024

[37] [37]

Jihene Tmamna, Emna Ben Ayed, Rahma Fourati, Mandar Gogate, Tughrul Arslan, Amir Hussain, and Mounir Ben Ayed. 2024. Pruning Deep Neural Networks for Green Energy-Efficient Models: A Survey.Cognitive Computation16, 6 (July 2024), 2931–2952. doi:10.1007/s12559-024-10313-0

work page doi:10.1007/s12559-024-10313-0 2024

[38] [38]

Nguyen Van Thieu and Seyedali Mirjalili. 2023. MEALPY: An open-source library for latest meta-heuristic algorithms in Python.Journal of Systems Architecture 139 (2023), 102871. doi:10.1016/j.sysarc.2023.102871

work page doi:10.1016/j.sysarc.2023.102871 2023

[39] [39]

Roberto Verdecchia, June Sallou, and Luís Cruz. 2023. A systematic review of Green AI.WIREs Data Mining and Knowl. Disc.13, 4 (2023), e1507. doi:10.1002/ widm.1507

work page 2023

[40] [40]

Shlomo Zilberstein. 1996. Using Anytime Algorithms in Intelligent Systems.AI Magazine17, 3 (1996), 73–83. doi:10.1609/aimag.v17i3.1232

work page doi:10.1609/aimag.v17i3.1232 1996