城市低空立体物流网络双种群协同优化方法

doi:10.7527/S1000-6893.2024.31477

Abstract

Abstract:

Urban Unmanned Aerial Vehicle （UAV） logistics is a significant application for the low-altitude economy， and the Urban Air Logistics （UAL） network is a critical infrastructure for achieving efficient drone delivery. This paper comprehensively considers critical urban factors such as noise constraints， economic costs， and ground safety risks to investigate optimization methodologies for urban air logistics networks. We propose a novel multiobjective mixed-integer programming model that simultaneously minimizes operational costs and ground safety risks while strictly under noise constraints. A dual-population coevolutionary optimization algorithm is developed， which enables knowledge transfer through individual interactions between populations， effectively enhancing the optimization capability of the algorithm in irregular solution spaces. Computational experiments show that the proposed algorithm outperforms existing methods with performance improving by over 20% on average. The designed multi-layered network achieves a balanced optimum in terms of cost， ground safety risk， and noise.

Key words: urban air logistics, network design, ground safety risk, UAV noise, multiobjective optimization, coevolutionary

CLC Number:

Chunxiao ZHANG, Tong GUO, Yumeng LI. Dual-population coevolutionary optimization for multi-layer urban air logistics network[J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(11): 531477.

Figures/Tables 23

Fig.1

Table 1

Problem sets and model parameter definitions

类型	符号	含义
集合	$N$	由起降节点构成的集合， $N = {i \| i = 1,2, …, N}$
	$N s$	噪声敏感点集合， $N s = {s \| s = 1,2, …, N s}$
	$H$	飞行高度层集合， $H = {h \| h = h 1, h 2, h 3}$
参数	$w i j$	起降节点 $i$ 到起降节点 $j$ 的需求
	$W$	所有起降点间的总运输需求
	$d i j h$	从起降点 $i$ 到起降点 $j$ 在 $h$ 高度的飞行距离
	$c i j h$	从起降点 $i$ 到起降点 $j$ 在 $h$ 层的单位流量飞行成本
	$r i j h$	从起降点 $i$ 到起降点 $j$ 在 $h$ 层的一次飞行安全风险
	$L i j s h$	从起降点 $i$ 到起降点 $j$ 在 $h$ 层的一次飞行对地面 $s$ 点造成的噪声暴露声级
	$F k$	将起降点 $k$ 设置为枢纽点的建设成本
	$g k l h$	激活枢纽点 $k$ 和 $l$ 间 $h$ 层的连接所需建设成本
	$p i k h$	激活非枢纽点 $i$ 和枢纽点 $k$ 间 $h$ 高度层的连接所需建设成本
	$q i j h$	激活非枢纽点 $i$ 和非枢纽点 $j$ 间 $h$ 高度层的连接所需建设成本
	$α$	枢纽成本系数
	$D$	无人机航程，以最大飞行距离定义

Table 1

Fig.2

Fig.3

Table 2

Decision variables for proposed model

变量	含义
$x k ∈ {0,1}$	在起降节点 $k$ 建立枢纽
$z k l ∈ {0,1}, k < l$	在枢纽节点 $k$ 和枢纽节点 $l$ 之间有连边
$z k l h ∈ {0,1}, k < l$	枢纽节点 $k$ 和枢纽节点 $l$ 间在 $h$ 层有连边
$T k i j ∈ {0,1}$	从枢纽 $k$ 出发的生成树经过枢纽连边i-j
$a i k h ∈ {0,1}$	非枢纽节点 $i$ 和枢纽节点 $k$ 间在 $h$ 层有连边
$f i j k l h ∈ [0, w i j]$	OD对 $(i, j)$ 的需求经过 $h$ 层的枢纽连边k-l
$a i j k h ∈ {0,1}$	OD对 $(i, j)$ 的需求经过 $h$ 层的接入连边i-k
$b i j l h ∈ {0,1}$	OD对 $(i, j)$ 的需求经过 $h$ 层的分发连边l-j
$s i j h ∈ {0,1}, i < j$	非枢纽节点 $i$ 和非枢纽节点 $j$ 在 $h$ 层有连边
$l i j h ∈ [0, W], i < j$	辅助变量，连边 $(i, j, h)$ 流经的所有需求流量

Table 2

Fig.4

Fig.5

Fig.6

Fig.7

Fig.8

Table 3

Fig.9

Fig.10

Fig.11

Table 4

Settings of tested algorithms

设置	CCMO-AOS	SSLAM-P	SSLM-P	MSwap-P
种群规模	200	200	200	150
$C 0$	1.0
SW长度	200
交叉概率		0.8	0.8	0.85
变异概率		点： $1 N H$ ，边：0.01	点： $1 N H$ ，边：0.01	0.3
个体选择		二元锦标赛	二元锦标赛	轮盘赌
交叉算子		单点	单点	多点
变异		SLAM	SLM	交换

Table 4

Table 5

Table 6

Fig.12

Fig.13

Table 7

Table 8

Comparison of solutions of different instances

解		节点
解		10	20	25	30	40
成本最小	成本/10⁷	6.340 7	4.543 8	3.921 4	3.233 3	2.997 1
	风险/10⁴	4.788 0	4.163 4	5.042 6	4.584 6	5.475 6
	$H N H$	5	7	8	7	9
	$N L H$	4	6	7	6	9
	$N L H S$	5	13	17	23	32
风险最小	成本/10⁷	10.327	7.257 3	9.888 4	5.218 5	10.360
	风险/10⁴	2.984 4	3.153 7	2.700 5	2.819 2	2.632 2
	$H N H$	9	11	17	11	22
	$N L H$	10	12	25	13	66
	$N L H S$	2	13	15	29	43
距离最小	成本/10⁷	7.386 2	6.863 4	6.422 9	3.765 3	9.001 5
	风险/10⁴	3.633 0	3.189 0	3.126 8	3.813 6	2.645 6
	$H N H$	6	10	13	8	20
	$N L H$	5	10	17	7	46
	$N L H S$	4	16	22	28	49

Table 8

Fig.14

Fig.15

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节点	指标	CCMO-AOS	SSLAM-P	SSLM-P	MSwap-P
10	平均值	0.921 1	0.751 5	0.555 4	0.408 9
	标准差	0.016 5	0.016 1	0.279 0	0.334 0
20	平均值	1.119 0	0.895 8	0.826 8	0.859 1
	标准差	0.025 9	0.030 1	0.010 3	0.014 9
25	平均值	1.094 2	0.934 3	0.898 7	0.933 1
	标准差	0.014 7	0.028 1	0.021 3	0.016 2
30	平均值	1.145 8	0.960 1	0.886 2	0.936 4
	标准差	0.028 7	0.041 5	0.014 8	0.040 9
40	平均值	1.151 3	1.001 4	0.932 3	0.955 9
	标准差	0.019 3	0.053 1	0.029 7	0.019 4

节点	指标	CCMO-AOS	SSLAM-P	SSLM-P	MSwap-P
10	平均值	0.020 3	0.179 8	0.344 8	0.516 9
	标准差	0.027 4	0.033 4	0.336 9	0.408 6
20	平均值	0.031 8	0.203 0	0.235 2	0.213 9
	标准差	0.014 9	0.011 5	0.003 6	0.018 3
25	平均值	0.028 4	0.133 0	0.164 1	0.139 4
	标准差	0.012 3	0.016 3	0.015 1	0.011 1
30	平均值	0.025 3	0.184 7	0.238 9	0.208 8
	标准差	0.023 7	0.029 1	0.010 9	0.029 9
40	平均值	0.028 5	0.114 8	0.163 1	0.146 1
	标准差	0.010 0	0.039 9	0.024 6	0.011 1

节点	指标	CCMO-AOS	CCMO-MN	CCMO-SN	AOS-P
10	平均值	0.930 9	0.928 8	0.930 3	0.783 1
	标准差	0.017 3	0.022 2	0.020 4	0.000 4
20	平均值	1.109 6	1.096 9	1.068 0	0.916 0
	标准差	0.026 1	0.023 3	0.018 9	0.015 0
25	平均值	1.071 6	1.079 2	1.074 1	1.005 0
	标准差	0.014 9	0.026 9	0.006 0	0.014 5
30	平均值	1.091 3	1.104 2	1.048 6	1.002 1
	标准差	0.036 4	0.039 8	0.068 0	0.074 8
40	平均值	1.139 2	1.104 6	1.070 8	1.082 6
	标准差	0.021 6	0.030 8	0.034 4	0.030 2

Dual-population coevolutionary optimization for multi-layer urban air logistics network

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算子	交叉算子	变异算子
1	单点交叉（前/后）	无
2	单点交叉（前/后）	SLAM
3	多点交叉（前/后）	无
4	多点交叉（前/后）	SLAM
5	无	SLAM
6	无	无

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