Multi-objective Joint Optimization of Resource Allocation and Task Scheduling for Accompanying Repair

doi:10.12382/bgxb.2023.0337

Abstract

Abstract:

The modern war has a fast pace and covers a wide area, which puts forward higher requirements for the accompanying repair support mode. Integrate the process of resource allocation and task scheduling in a complex battlefield to give full play to the effectiveness of accompanying repair system has become the urgent demand and development direction of equipment maintenance support. Comprehensively considering the factors of multi-center, open, multi-repair state, time window, non-traversal, capacity limitation and so on, an idea of replenishing goods at any time is put forward for the first time, which combines the regional risk coefficient with the current cost of the maintenance teams. A more perfect mathematical model is established to maximize the maintenance benefit and minimize the risk cost. For the above problems, the multi-objective artificial bee colony (MOABC) algorithm is improved, a multi-objective artificial bee colony algorithm for memorizing multiple honey sources per bee is proposed. The proposed algorithm shows good performance in terms of solution quality and convergence speed. Then, aiming at the problem that a small number of extreme values affect the mean, the use of coverage rate indicator is improved and displayed in the way of frequency. Finally, the scientificness of the model and algorithm is verified through the simulation experiments and the evaluation of multiple indicators, and the joint optimization of resource allocation and task scheduling for accompanying repair is realized. The study shows that the above model and algorithm are able to provide the appropriate assistant decision-making for accompanying repair support.

Key words: equipment maintenance support, accompanying repair, resource allocation, task scheduling, multi-objective optimization

CLC Number:

LIU Shengyu, QI Xiaogang, LIU Lifang. Multi-objective Joint Optimization of Resource Allocation and Task Scheduling for Accompanying Repair[J]. Acta Armamentarii, 2024, 45(7): 2442-2450.

Figures/Tables 9

Table 1 Symbol description

符号	说明
R	维修组集合
r∈R	维修组
v_r	r的行驶速度
c_ve	r的固有成本
I	地点集合
i,j∈I	i为需求点,j为维修中心
(x_i,y_i)	i的位置
s_ij	i、j间的路径长度
d_ij	i、j间的路径危险系数
d_ii	i的危险系数
k	需求点可修复状态
c_ik	维修i到k所需物资成本
c_r	r的当前成本
δ_ik	维修i到k的重要度
η_ik	维修i到k考虑时间窗约束的重要度
A_i	i时间窗约束下的重要度惩罚系数
[ $T i l o w$ , $T i u p$ ]	i最佳维修时段,即时间窗
T^pause	维修截止时刻
τ_ri∈{0,1}	若r维修i则τ_ri等于1,否则等于0
ξ_rij∈{0,1}	若r从i到j则ξ_rij等于1,否则等于0
$T g r i$	r到i的时刻
t_ik	维修i到k的耗时
$T f r i$	r离开i的时刻
T^pause- $T f r i$ ,(τ_ri=1)	i的二次作战时长
benefit_r	r创造的维修效益
risk_r	r承担的风险成本

Table 1 Symbol description

符号	说明
R	维修组集合
r∈R	维修组
v_r	r的行驶速度
c_ve	r的固有成本
I	地点集合
i,j∈I	i为需求点,j为维修中心
(x_i,y_i)	i的位置
s_ij	i、j间的路径长度
d_ij	i、j间的路径危险系数
d_ii	i的危险系数
k	需求点可修复状态
c_ik	维修i到k所需物资成本
c_r	r的当前成本
δ_ik	维修i到k的重要度
η_ik	维修i到k考虑时间窗约束的重要度
A_i	i时间窗约束下的重要度惩罚系数
[ $T i l o w$ , $T i u p$ ]	i最佳维修时段,即时间窗
T^pause	维修截止时刻
τ_ri∈{0,1}	若r维修i则τ_ri等于1,否则等于0
ξ_rij∈{0,1}	若r从i到j则ξ_rij等于1,否则等于0
$T g r i$	r到i的时刻
t_ik	维修i到k的耗时
$T f r i$	r离开i的时刻
T^pause- $T f r i$ ,(τ_ri=1)	i的二次作战时长
benefit_r	r创造的维修效益
risk_r	r承担的风险成本

Fig.1 Transition maintenance process of maintenance team

Fig.2 Algorithm decoding diagram

Table 2 Frequency of indicator C

Case 1	Case 2	Case 3	Case 4	Case 5
$1.00 1.00 0.09 0.00 0.18 0.00 0.00 0.82 0.00 0.91 1.00 1.00$	$1.00 1.00 0.18 0.00 0.00 0.00 0.00 1.00 0.00 0.82 1.00 1.00$	$0.91 0.91 0.09 0.09 0.18 0.00 0.09 0.82 0.00 0.91 1.00 1.00$	$1.00 1.00 0.18 0.00 0.36 0.00 0.00 0.64 0.00 0.82 1.00 1.00$	$1.00 0.91 0.18 0.00 0.00 0.00 0.09 1.00 0.00 0.82 1.00 1.00$
Case 6	Case 7	Case 8	Case 9	Case 10
$1.00 1.00 0.09 0.00 0.18 0.00 0.00 0.82 0.00 0.91 1.00 1.00$	$1.00 1.00 0.27 0.00 0.09 0.00 0.00 0.91 0.00 0.73 1.00 1.00$	$1.00 1.00 0.18 0.00 0.73 0.00 0.00 0.27 0.00 0.82 1.00 1.00$	$1.00 1.00 0.27 0.00 0.00 0.00 0.00 1.00 0.00 0.73 1.00 1.00$	$1.00 1.00 0.18 0.00 0.36 0.00 0.00 0.64 0.00 0.82 1.00 1.00$

Table 2 Frequency of indicator C

Case 1	Case 2	Case 3	Case 4	Case 5
$1.00 1.00 0.09 0.00 0.18 0.00 0.00 0.82 0.00 0.91 1.00 1.00$	$1.00 1.00 0.18 0.00 0.00 0.00 0.00 1.00 0.00 0.82 1.00 1.00$	$0.91 0.91 0.09 0.09 0.18 0.00 0.09 0.82 0.00 0.91 1.00 1.00$	$1.00 1.00 0.18 0.00 0.36 0.00 0.00 0.64 0.00 0.82 1.00 1.00$	$1.00 0.91 0.18 0.00 0.00 0.00 0.09 1.00 0.00 0.82 1.00 1.00$
Case 6	Case 7	Case 8	Case 9	Case 10
$1.00 1.00 0.09 0.00 0.18 0.00 0.00 0.82 0.00 0.91 1.00 1.00$	$1.00 1.00 0.27 0.00 0.09 0.00 0.00 0.91 0.00 0.73 1.00 1.00$	$1.00 1.00 0.18 0.00 0.73 0.00 0.00 0.27 0.00 0.82 1.00 1.00$	$1.00 1.00 0.27 0.00 0.00 0.00 0.00 1.00 0.00 0.73 1.00 1.00$	$1.00 1.00 0.18 0.00 0.36 0.00 0.00 0.64 0.00 0.82 1.00 1.00$

Table 3 Mean value of indicator S

算法	Case 1	Case 2	Case 3	Case 4	Case 5	Case 6	Case 7	Case 8	Case 9	Case 10
NSGA-Ⅱ	0.49	0.34	0.43	0.87	1.07	0.78	0.41	0.26	1.07	0.16
MOPSO	11.32	10.85	9.11	7.94	15.48	6.54	9.57	7.28	10.10	8.32
MOABC	9.15	11.36	11.44	7.94	12.24	7.58	17.62	8.75	10.60	11.46
MOABC-MMHS	0.00	0.00	0.01	0.12	0.12	0.00	0.00	0.03	0.03	0.05

Table 4 Mean value of indicator M*3

算法	Case 1	Case 2	Case 3	Case 4	Case 5	Case 6	Case 7	Case 8	Case 9	Case 10
NSGA-Ⅱ	16.87	13.87	14.35	15.61	15.47	17.42	17.40	17.11	15.87	16.57
MOPSO	15.95	15.48	14.39	14.53	16.18	16.16	16.31	17.67	17.49	16.13
MOABC	14.41	13.08	12.45	13.07	12.00	14.01	14.86	14.60	13.91	14.27
MOABC-MMHS	17.42	13.26	14.87	15.78	15.88	17.47	17.63	17.64	16.62	16.53

Table 5 Mean value of indicator area (×105)

算法	Case 1	Case 2	Case 3	Case 4	Case 5	Case 6	Case 7	Case 8	Case 9	Case 10
NSGA-Ⅱ	3.77	3.78	3.77	3.82	3.88	3.80	3.77	3.82	3.70	3.78
MOPSO	3.50	3.50	3.54	3.55	3.57	3.54	3.47	3.61	3.53	3.60
MOABC	3.46	3.60	3.53	3.59	3.56	3.46	3.52	3.48	3.50	3.54
MOABC-MMHS	3.83	3.81	3.96	3.95	3.93	3.91	3.80	3.88	3.90	3.84

Fig.3 Box plots of multiple indicators

Fig.4 Algorithms convergence speed and solution sets distribution

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