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浙江大学学报(工学版)
浙江大学学报(工学版)  2026, Vol. 60 Issue (12): 2755-2764    DOI: 10.3785/j.issn.1008-973X.2026.12.021
土木工程、交通工程     
基于多层次自适应协同算法的供电系统抗震韧性评估
刘晓航1(),秦卿1,*(),王凯歌2,黄军2,王长有2
1. 西安科技大学 建筑与土木工程学院，陕西 西安 710055
2. 西安建筑科技大学 土木工程学院，陕西 西安 710055
Seismic resilience assessment of power supply system based on multi-level adaptive cooperative algorithm
Xiaohang LIU1(),Qing QIN1,*(),Kaige WANG2,Jun HUANG2,Changyou WANG2
1. School of Civil and Architectural Engineering, Xi’an University of Science and Technology, Xi’an 710055, China
2. School of Civil Engineering, Xi’an University of Architecture and Technology, Xi’an 710055, China
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摘要：

为了量化评估并提升城市供电系统的抗震韧性与恢复效率，提出多目标优化的抗震韧性多维度评估与决策方法. 从技术、组织、社会3个维度构建性能函数与韧性指标，量化表征系统震后功能退化与恢复进程. 提出多层次自适应协同算法（MACA），采用图论分区启发式编码、层次化帕累托聚类与动态学习率，在保持解集多样性的同时提升收敛稳定性与全局寻优能力. 算法通过节点分区与修复队伍动态分配，实现修复群体间信息协同与经验迁移，获得综合最优修复方案. 算例结果表明，三维度框架能够有效量化震后性能并揭示各维度恢复差异；MACA优化方案相较随机修复，组织维度与社会维度的恢复力分别提升了5.2%和3.7%. 算法收敛率达到98.9%，解集方差较NSGA-Ⅱ降低了46.7%.
关键词： 多目标优化;  自适应协同优化算法;  供电系统;  抗震韧性;  三维度评估    
Abstract:

A multi-objective optimization–based multi-dimensional assessment and decision-making method for seismic resilience was proposed in order to quantitatively assess and enhance the seismic resilience and recovery efficiency of urban power supply system. Performance functions and resilience indicators were constructed from three dimensions—technical, organizational, and social—to quantitatively characterize the post-earthquake functional degradation and recovery process of the system. A multi-level adaptive cooperative algorithm (MACA) was introduced. Graph-theory-based partition heuristic encoding, hierarchical Pareto clustering, and dynamic learning rates were employed to improve convergence stability and global search capability while preserving solution diversity. Information synergy and experience transfer among repair groups were realized through node partitioning and dynamic allocation of repair crews, ultimately yielding a comprehensive optimal restoration plan. Case study results demonstrate that the three-dimensional framework can effectively quantify post-earthquake performance and reveal the differential recovery across dimensions. The MACA-optimized scheme improved organizational and social resilience by 5.2% and 3.7%, respectively compared with random restoration. The algorithm achieved a convergence rate of 98.9%, and the variance of the solution set was reduced by 46.7% compared with NSGA-Ⅱ.
Key words: multi-objective optimization    adaptive collaborative optimization algorithm    power supply system    seismic resilience    three-dimensional assessment
收稿日期: 2025-10-23 出版日期: 2026-10-21
CLC:  P 315  
基金资助: 陕西省科技厅资助项目（2025JC-YBQN 529）；陕西省教育厅专项科研计划资助项目（25JK0550）.
通讯作者: 秦卿     E-mail: liuxiaohang@xust.edu.cn;qinqing@xust.edu.cn
作者简介: 刘晓航（1995—），男，讲师，从事生命线系统抗震可靠性研究. orcid.org/0000-0001-7988-5507. E-mail：liuxiaohang@xust.edu.cn
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引用本文:

刘晓航,秦卿,王凯歌,黄军,王长有. 基于多层次自适应协同算法的供电系统抗震韧性评估[J]. 浙江大学学报(工学版), 2026, 60(12): 2755-2764.

Xiaohang LIU,Qing QIN,Kaige WANG,Jun HUANG,Changyou WANG. Seismic resilience assessment of power supply system based on multi-level adaptive cooperative algorithm. Journal of ZheJiang University (Engineering Science), 2026, 60(12): 2755-2764.

链接本文:

https://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2026.12.021    或    https://www.zjujournals.com/eng/CN/Y2026/V60/I12/2755

图 1  某一工况下供电系统三维度性能恢复进程的示意图
图 2  种群编码方式与模块调用的关系
输入：种群个体数量N
输出：分层的不同支配层{Fi}，i表示个体的支配层级
1: for j = 1: N
2: fitness_xj = fitness_function(xj); %计算个体xj适应度
3: dominance_level(j) = 0; % 初始化支配层级
4: for g = 1: N
5: fitness_xg = fitness_function(xg); % 计算个体xg适应度
6: if all(fitness_xj <= fitness_xg) && any (fitness_xj < fitness_xg)
7: dominance_level(j) = dominance_level(j)+1; % 更新支配层
8: end
9: end
10: $ {\eta }_{j} $= $ \eta_ {\max} $exp (?a·dominance_level(j)); % 根据层级调整
学习强度
11: xj_new = xj + ηj(x_best ? xj) + σ·randn(); % 协同学习更新
12: end
表 1  
图 3  三维度下不同节点的节点重要度占比
图 4  算例拓扑及相对重要性权重
图 5  基于随机修复方案的三维度恢复对比
图 6  韧性指标计算结果的对比
图 7  基于多目标优化调度模型的三维度韧性评估对比
图 8  不同算法的收敛率与稳定性对比
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