Boyu Ma1,2,*, Jiaxiao Shi1,2,*, Yiming Ji1, and Zhengpu Wang1 1 State Key Laboratory of Robotics and Systems, Harbin Institute of Technology, China. 2 School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore. * Equal contribution.
explore
exploit
01 / Overview
ECO is a nature-inspired metaheuristic algorithm for complex nonlinear and non-convex global optimization. It models the population as an ecological system, where ecological interactions provide complementary search behaviours instead of relying on a single update rule.
Ecological inspiration
In an ecosystem, producers, consumers, decomposers, and the inorganic environment are connected by energy flow and material cycling. Producers supply organic matter, consumers transfer energy through predation, and decomposers return biological remains to the nutrient pool. ECO translates this coupled cycle into an iterative optimization process.
Fig. 1. Ecological relationships used as the inspiration for ECO.
From ecology to optimization
Each candidate solution is treated as an organism, and its fitness is inversely related to its energy. Better solutions are retained through survival of the fittest, while ecological interactions generate new candidates. In this way, energy flow guides useful information through the population and material cycling renews information that may otherwise become stagnant.
What ECO is designed to study
The paper first determines a stable internal configuration through parameter sensitivity analysis. ECO is then assessed on the CEC-2014, CEC-2017, and CEC-2020 numerical benchmark suites, followed by five constrained engineering design problems from CEC-2020-RW.
02 / Method
ECO models population evolution as an ecological cycle. Producers, consumers, and decomposers perform complementary updates, allowing the search to alternate between broad exploration and focused exploitation until the function-evaluation budget is exhausted.
Population initialization
The population is divided into producers, herbivores, carnivores, and omnivores. Their proportions satisfy PPro + PHer + PCar + POmn = 1, and individuals are randomly initialized within the constrained search space.
The first three group sizes are obtained from their prescribed proportions, while the omnivore group occupies the remaining population. This composition provides distinct ecological roles without introducing additional population-size parameters.
Producer strategy
Producers represent the foundation of the ecological system and absorb information recycled by decomposers. Their update strategy retains useful search information and refines promising regions, providing high-quality candidate solutions for the consumer groups.
Consumer strategy
Consumers are divided into herbivores, carnivores, and omnivores. Herbivores are guided by selected producers, carnivores by selected herbivores, and omnivores by a mixture of producers, herbivores, and carnivores.
Prey is selected by roulette-wheel sampling, so lower-fitness individuals are more likely to guide the update while multiple elite candidates remain available. These different predation paths diversify information exchange and reduce reliance on a single search direction.
Consumer-prey dynamics
The predation factor G determines the consumer-prey relationship. Values outside the local predation interval encourage consumers to leave the current target and explore a broader region, whereas values in the local interval promote exploitation around the selected prey.
As the iteration progresses, the random range of G contracts toward one. The mechanism therefore transitions from diverse early exploration to stable local refinement near high-quality solutions.
Fig. 2. Consumer-prey relationship used in ECO.Fig. 3. Iteration-dependent variation of the predation factor.
Decomposer strategy
After each ecological cycle, decomposers recycle population information through optimal, local-random, and global-random decomposition. Optimal decomposition samples near the current best solution to strengthen exploitation.
Local-random decomposition searches around the current individual with a radius determined by its distance from the best solution, while global-random decomposition uses a random walk to generate distant search directions. Their probabilities are controlled by popt and ploc.
ECO workflow
At every iteration, producers, consumers, and decomposers are updated in sequence. New candidates are evaluated, the best information is retained, and the ecological cycle is repeated until the available function evaluations are exhausted.
Fig. 4. Main workflow of the Ecological Cycle Optimizer.
03 / Experiments
The experimental study is organized from internal parameter selection to numerical benchmarking and engineering validation. All numerical tests follow the settings of the corresponding benchmark technical reports, and repeated runs are assessed by solution quality and statistical ranking.
Population composition and decomposition probabilities are investigated separately on 23 classic optimization functions. The population proportions are restricted to balanced ecological configurations, and the candidate settings are ranked from repeated optimization runs.
The selected default configuration is PPro = 0.2, PHer = 0.3, PCar = 0.3, POmn = 0.2, with popt = 0.6 and ploc = 0.6. It is adopted in the subsequent experiments.
Fig. 5. Population proportion sensitivity analysis.Fig. 6. Decomposition probability sensitivity analysis.
Screening of state-of-the-art algorithms
ECO is first evaluated against a pool of 30 metaheuristic algorithms on CEC-2014 and CEC-2017. Algorithms are ranked on each function by smaller Ave, followed by Min and Std, and their global performance is summarized using the Friedman mean rank.
ECO ranks first in this 30-algorithm screening. The five most competitive alternatives, ARO, CFOA, CSA, WSO, and INFO, are then selected for the more detailed CEC-2020 evaluation.
CEC-2020 statistical comparison
The six algorithms are compared on CEC-2020 at D = 10, 30, 50, and 100. The suite includes shifted, rotated, hybrid, and composition functions, which test robustness on nonseparable and multimodal landscapes.
The box plots show the distribution of final fitness values, while the radar charts report the function-wise ranks. ECO maintains narrow result distributions and the lowest Friedman mean rank across the four dimensions, indicating consistent solution quality as the dimension increases.
Fig. 7. Friedman mean ranks on the CEC-2020 test suite.Fig. 8. Fitness-value distributions on representative CEC-2020 functions.Fig. 9. Function-wise rank profiles across CEC-2020 dimensions.
Convergence behaviour
The convergence curves compare the average best fitness against the number of function evaluations. ECO typically performs broad early exploration, followed by adaptive refinement and stronger late-stage exploitation, which helps it retain competitive convergence on functions with different landscape structures.
Fig. 10. Convergence comparison on representative CEC-2020 functions.
Qualitative search analysis
The qualitative results visualize objective landscapes, search histories, best and average fitness, solution trajectories, and the exploration--exploitation balance. They illustrate how ECO combines population diversity in the early search with focused refinement near promising regions in later iterations.
Fig. 11. Qualitative analysis of ECO search behaviour.
Engineering validation
Five representative constrained design problems from CEC-2020-RW are used to evaluate practical applicability: speed reducer design, tension/compression spring design, welded beam design, three-bar truss design, and gear train design.
These problems include coupled variables, engineering constraints, and different objective landscapes. ECO attains the best overall rank among the evaluated algorithms, complementing the numerical tests with application-oriented validation.
This page acknowledges the contributions behind ECO and provides practical ways to support and reuse the project.
Author contributions
Boyu Ma and Jiaxiao Shi contributed equally to this work. Boyu Ma contributed to the conceptualization, methodology, and development of the ECO algorithm.
Jiaxiao Shi contributed to software implementation, experimental design, data analysis, visualization, and manuscript preparation. Yiming Ji contributed to benchmark preparation, result verification, and experimental evaluation.
Zhengpu Wang contributed to supervision, technical review, and guidance on the research direction. All authors reviewed the results and approved the final presentation of the project.
Open research
The source code, benchmark settings, figures, and supporting materials are provided to make ECO easier to inspect and reproduce. We welcome feedback, extensions, and independent comparisons using the same evaluation protocol.
If ECO is useful for your research, please consider giving the ECO-Optimizer repository a star ★. A star helps other researchers discover the implementation and supports the continued maintenance of the project.
BibTeX
@article{2026eco,
title = {Ecological Cycle Optimizer: A novel nature-inspired metaheuristic algorithm for non-convex global optimization},
author = {Boyu Ma and Jiaxiao Shi and Yiming Ji and Zhengpu Wang},
journal = {arXiv preprint arXiv:2508.20458},
year = {2026}
}
Contact
For questions about ECO, its implementation, or research collaboration, please contact Boyu Ma or Jiaxiao Shi.
