多环境选择策略引导的约束多目标进化优化算法

左明成; 薛源; 巩敦卫; 薛天洋

doi:10.12263/DZXB.20260026

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多环境选择策略引导的约束多目标进化优化算法

学术论文 | 更新时间：2026-10-16

- 多环境选择策略引导的约束多目标进化优化算法
- A Constrained Multi-Objective Evolutionary Algorithm Guided by Multi-Environment Selection Strategies
- 电子学报 2026年54卷第6期页码：2819-2836
- 作者机构：
  
  1.中国矿业大学计算机科学与技术学院/人工智能学院，江苏徐州 221116
  2.青岛科技大学微电子学院，山东青岛 266061
- 作者简介：
  
  左明成男，1992年9月出生于山东省烟台市。现为中国矿业大学计算机学院/人工智能学院副教授。主要研究方向为人工智能驱动的智能优化。E-mail: mingcheng.zuo@cumt.edu.cn
  薛源男，1998年6月出生于江苏省徐州市。现为中国矿业大学计算机学院/人工智能学院硕士研究生。主要研究方向为约束多目标进化优化。E-mail: ts23810019p31@cumt.edu.cn
  巩敦卫男，1970年3月出生于江苏省徐州市。现为青岛科技大学微电子学院二级教授、院长。主要研究方向为智能优化理论与应用。E-mail: dwgong@vip.163.com
  薛天洋男，2003年6月出生于河北省邢台市。现为中国矿业大学计算机学院/人工智能学院硕士研究生。主要研究方向为多PVT模拟集成电路优化。E-mail: ts24810017p31@cumt.edu.cn
- 基金信息：
  
  国家自然科学基金(62303465;62133015);山东省自然科学基金(ZR2023ZD06)
- DOI：10.12263/DZXB.20260026
  中图分类号： TN710.2;TP182
- 收稿：2026-04-13，
  
  录用：2026-05-05，
  
  纸质出版：2026-06-25
- 稿件说明：
移动端阅览
左明成, 薛源, 巩敦卫, 等. 多环境选择策略引导的约束多目标进化优化算法[J]. 电子学报, 2026, 54(06): 2819-2836.

ZUO Mingcheng, XUE Yuan, GONG Dunwei, et al. A Constrained Multi-Objective Evolutionary Algorithm Guided by Multi-Environment Selection Strategies[J]. Acta Electronica Sinica, 2026, 54(06): 2819-2836.
左明成, 薛源, 巩敦卫, 等. 多环境选择策略引导的约束多目标进化优化算法[J]. 电子学报, 2026, 54(06): 2819-2836. DOI：10.12263/DZXB.20260026

ZUO Mingcheng, XUE Yuan, GONG Dunwei, et al. A Constrained Multi-Objective Evolutionary Algorithm Guided by Multi-Environment Selection Strategies[J]. Acta Electronica Sinica, 2026, 54(06): 2819-2836. DOI：10.12263/DZXB.20260026

摘要

约束多目标优化问题（Constrained Multi-objective Optimization Problems，CMOPs）广泛存在于实际工程与科学领域，这类问题通常同时包含多个相互冲突的优化目标与复杂多样的约束条件。在约束多目标进化算法（Constrained Multi-Objective Evolutionary Algorithms，CMOEAs）中，环境选择策略（Environmental Selection Strategy，ESS）的设计与集成至关重要，它直接决定了算法能否在可行性（满足约束条件的程度）、收敛性（逼近帕累托前沿的速度）和多样性（解集的分布均匀性）三者之间取得有效平衡。然而，现有方法多依赖静态或预定义的策略调度机制，难以根据种群在进化过程中的实时状态自适应调整选择压力，导致在应对复杂约束、非连续可行域及昂贵目标评估等实际场景时，算法往往表现出明显的局限性：一方面，在进化初期种群完全不可行的情况下，缺乏足够的驱动力引导搜索快速进入可行域；另一方面，在找到可行解之后，难以动态地在收敛加速与多样性维持之间进行合理权衡，容易出现早熟收敛或多样性丧失，甚至在某些极端约束条件下长期无法找到任何可行解。这些问题严重限制了CMOEAs的整体性能与鲁棒性。鉴于此，本文提出一种基于强化学习（Reinforcement Learning，RL）的多环境选择策略集成方法，增强约束多目标进化算法的自主决策与动态适应能力。该方法首先根据种群在决策空间与目标空间的分布特征，从可行性、收敛性和多样性三个维度刻画进化状态：利用

-可行解比例反映种群满足约束的整体水平，利用归一化质心位移表征收敛趋势，利用

-可行解方差在种群总方差中的占比评估多样性。进而，受物理学中相互作用力原理的启发，本文设计了三种各具侧重且内在耦合的环境选择策略：第一种策略着重强化可行性保持，通过引入约束违背度排名构建排斥力模型，优先筛选可行解；第二种策略聚焦收敛加速，采用目标函数排名引导种群向帕累托前沿逼近；第三种策略则致力于多样性维持，仅依据个体间的空间距离产生排斥力，避免种群过度聚集。这三种策略相互耦合，即使某一次策略选择出现偏差也不会导致算法性能急剧恶化，从而为强化学习提供了稳定的决策基础。最后，通过强化学习构建种群状态与环境选择策略之间的映射模型。在三个基准测试集（LIR-CMOP、DASCMOP、DOC）与模拟集成电路优化设计问题上的实验表明，本文方法在大多数测试问题上显著优于六种先进的约束多目标进化算法，尤其在可行域狭窄、约束复杂、帕累托前沿不连续的困难场景下表现出更强的鲁棒性与适应性，能够以更少的函数评价次数获得更高质量的解集，从而充分验证了其在处理实际复杂约束多目标优化问题中的有效性、可扩展性与工程应用价值。

Abstract

Constrained multi-objective optimization problems (CMOPs) are widely prevalent in practical engineering and scientific fields. Such problems typically involve multiple conflicting optimization objectives and a variety of complex constraints.

In constrained multi-objective evolutionary algorithms (CMOEAs)

the design and integration of the environmental selection strategy (ESS) are crucial

as it directly determines whether the algorithm can achieve an effective balance among feasibility (degree of constraint satisfaction)

convergence (speed of approaching the Pareto front)

and diversity (uniformity of solution set distribution). However

existing methods mostly rely on static or predefined strategy scheduling mechanisms

making it difficult to adaptively adjust selection pressure according to the real-time state of the population during evolution. Consequently

when dealing with practical scenarios such as complex constraints

discontinuous feasible regions

and expensive objective evaluations

these algorithms exhibit significant limitations. On one hand

when the population is entirely infeasible in the early stages of evolution

there is insufficient driving force to guide the search quickly into the feasible region. On the other hand

after feasible solutions are found

it becomes challenging to dynamically achieve a reasonable trade-off between convergence acceleration and diversity maintenance

often leading to premature convergence or loss of diversity. In some extreme constraint conditions

the algorithm may even fail to find any feasible solution for a long time. These issues severely constrain the overall performance and robustness of CMOEAs. In view of this

this paper proposes a multi-environmental selection strategy integration method based on reinforcement learning (RL) to enhance the autonomous decision-making and dynamic adaptability of constrained multi-objective evolutionary algorithms. The proposed method first characterizes the evolutionary state from three dimensions (feasibility

convergence

and diversity) based on the distribution characteristics of the population in both decision space and objective space. The

-feasible solution ratio is used to reflect the overall level of constraint satisfaction of the

population; the normalized centroid displacement is used to indicate the convergence trend; and the proportion of the variance of

-feasible solutions in the total population variance is used to evaluate diversity. Then

inspired by the principle of interaction forces in physics

this paper designs three distinct yet inherently coupled environmental selection strategies. The first strategy focuses on enhancing feasibility preservation

constructing a repulsion force model by ranking constraint violation degrees to prioritize feasible solutions. The second strategy focuses on accelerating convergence

using objective function ranking to guide the population toward the Pareto front. The third strategy is dedicated to diversity maintenance

generating repulsion forces solely based on spatial distances among individuals to avoid excessive clustering. These three strategies are coupled with each other

such that even if a suboptimal strategy is selected at a certain step

it does not cause a sharp deterioration in algorithm performance

thereby providing a stable decision-making foundation for reinforcement learning. Finally

a mapping model between population states and environmental selection strategies is constructed through reinforcement learning. Experimental results on three benchmark test suites (LIR-CMOP

DASCMOP

DOC) and an analog integrated circuit optimization design problem show that the proposed method significantly outperforms six state-of-the-art constrained multi-objective evolutionary algorithms on most test problems. It exhibits stronger robustness and adaptability

particularly in challenging scenarios with narrow feasible regions

complex constraints

and discontinuous Pareto fronts. It obtains higher-quality solution sets with fewer function evaluations

thereby fully validating its effectiveness

scalability

and engineering application value in handling practical complex constrained multi-objective optimization problems.

关键词

Keywords

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