A Learning-Based Cooperative Coevolution Framework for Heterogeneous Large-Scale Global Optimization

Wenjie Qiu; Zixin Wang; Hongyu Fang; Zeyuan Ma; Yue-Jiao Gong

cs.NEMar 30, 2026

A Learning-Based Cooperative Coevolution Framework for Heterogeneous Large-Scale Global Optimization

Authors: Wenjie Qiu, Zixin Wang, Hongyu Fang, Zeyuan Ma, Yue-Jiao Gong

Organizations: South China University of Technology, Guangzhou, Guangdong, China

Abstract

Cooperative Coevolution (CC) effectively addresses Large-Scale Global Optimization (LSGO) via decomposition but struggles with the emerging class of Heterogeneous LSGO (H-LSGO) problems arising from real-world applications, where subproblems exhibit diverse dimensions and distinct landscapes. The prevailing CC paradigm, relying on a fixed low-dimensional optimizer, often fails to navigate this heterogeneity. To address this limitation, we propose the Learning-Based Heterogeneous Cooperative Coevolution Framework (LH-CC). By formulating the optimization process as a Markov Decision Process, LH-CC employs a meta-agent to adaptively select the most suitable optimizer for each subproblem. We also introduce a flexible benchmark suite to generate diverse H-LSGO problem instances. Extensive experiments on 3000-dimensional problems with complex coupling relationships demonstrate that LH-CC achieves superior solution quality and computational efficiency compared to state-of-the-art baselines. Furthermore, the framework exhibits robust generalization across varying problem instances, optimization horizons, and optimizers. Our findings reveal that dynamic optimizer selection is a pivotal strategy for solving complex H-LSGO problems.

Figures & tables

Figure 1. Motivation: Shifts in problem paradigms drive corresponding shifts in optimization paradigms.

Feature	Index	Formula	Explan
$\mathcal{S}_{\text{problem}}$	1	$(D_{k}/500)^{0.4}$	The relative size of the subproblem dimension $D_{k}$ .
	2	$\mathcal{I}(\left\|\left\{i\mid\sum_{j=1}^{D}\Theta[i,j]=1\right\}\right\|=D)$	The separability indicator, derived from the DSM $\Theta$ , where the dependency of variables is reflected.
	3	$\left\|\bigcup_{i=1}^{\|S\|}\bigcup_{j\neq i}^{\|S\|}(\Omega_{i}\cap\Omega_{j})\right\|/D$	The ratio of shared variables among all subcomponent pairs ( $\Omega_{i}\cap\Omega_{j}$ ) to the number of variables $D$ .
$\mathcal{S}_{\text{pop}}$	1	$d=\frac{1}{N(N-1)}\!\sum_{i\neq j}\!\\|x_{i}-x_{j}\\|$	The average pairwise distance among all individuals in the population.
	2	$d_{\text{top}}-d$	The difference between the average pairwise distance $d_{\mathrm{top}}$ of the top (10%) individuals and $d$ .
	3	$\frac{1}{NS}\sum_{s=1}^{S}\sum_{i=1}^{N}\mathcal{I}\bigl(\|c_{i}-c_{i}^{s}\|<\epsilon\bigr)$	The proportion of sampled individual costs $c_{i}^{s}$ that are close to the original cost $c_{i}$ in a tolerance $\epsilon$ .

Table 1. State Features in LH-CC

Figure 3. The generation pipeline for diverse problem instances within the Auto-H-LSGO.

Problem	LH-CC-based	CC-based		NDAs
Problem	LH-CC-X	OEDG-CMAES	OEDG-MMES - CMAES	SEP-CMAES	MMES
$\text{Ackley}_{1}$	2.16E+05	2.24E+05(+)	2.20E+05(+)	2.21E+05(+)	2.20E+05(+)
$\text{Ackley}_{1}$	$\pm$ 1.55E+03	$\pm$ 2.30E+03	$\pm$ 1.79E+03	$\pm$ 1.52E+02	$\pm$ 1.58E+03
$\text{Ackley}_{3}$	2.17E+05	2.19E+05(+)	2.19E+05(+)	2.23E+05(+)	2.20E+05(+)
$\text{Ackley}_{3}$	$\pm$ 4.63E+02	$\pm$ 1.68E+03	$\pm$ 1.22E+03	$\pm$ 1.93E+02	$\pm$ 9.40E+02
$\text{Ackley}_{5}$	2.19E+05	2.26E+05(+)	2.23E+05(+)	2.24E+05(+)	2.21E+05(+)

Table 2. Comparing LH-CC with Comparison Algorithms on Auto-H-LSGO at 3E6 FEs

Problem Type	LH-CC-based	CC-based		NDAs
Problem Type	LH-CC-X	OEDG-CMAES	OEDG-MMES - CMAES	SEP-CMAES	MMES
1	1095.51s	13191.61s	957.43s	796.19s	580.14s
2	1138.62s	14575.32s	1051.2s	787.46s	586.47s

Table 3. Comparison of Optimization Efficiency between LH-CC and Comparative Algorithms

Figure 4. Comparative Optimization Performance of LH-CC-G on Representative H-LSGO Problems

Figure 5. Ablation Study on the Action Space

Global Optimization

Global optimization seeks the best solution across an entire search space, including nonconvex problems with many local optima.

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Oct 27, 2026J/K move · Enter open · S save

WCC: A Learning-Based Framework for Deciding When to Apply Cooperative Coevolution in Large-Scale Optimization

Wenjie Qiu, Hepei Li, Jianfeng Wang, Jun Zhang+1

School of Computer Science and Engineering, South China University of Technology, Guangzhou 510006, China · Taiyuan University of Technology, Taiyuan 030024, China · Nankai University, Tianjin 300350, China, and also with Hanyang University ERICA, Ansan 15588, South Korea

Global Optimization Evolutionary Optimization Algorithm Selection Learning to Optimize

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Cooperative Coevolution (CC) and Non-Decomposition Algorithms (NDAs) are two primary approaches for large-scale global optimization (LSGO). Although both have achieved success, they exhibit markedly different performance across problem types and each faces approach-specific limitations, leaving the question of "when to use CC" unresolved. We address this gap with WCC, a novel learning-based framework that dynamically decides when to deploy CC in LSGO. WCC employs a streamlined design for efficient adaptive learning. We formulate the decision as a Markov decision process, designing a targeted feature set, a robust reward, and a tailored network architecture to provide the agent with rich information about the problem state and optimization progress. Our auto-regressive policy enables WCC to perform fine-grained, dynamic switching between CC and NDAs while conditionally allocating the computational budget without expert specifications. WCC shows strong competitiveness and superior generalization across problems, optimization horizons, and baseline optimizers. It realizes a "train-once and reuse" paradigm under a low budget, significantly curbing LSGO cost. Additionally, in-depth analyses yield insights not captured by existing theory, offering practical guidance on when and how to effectively deploy CC.

Abstract

Global Optimization

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