Multi-objective test optimization selection based on NSGA-Ⅱ under unreliable test conditions
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摘要:
针对测试不可靠因素严重影响测试优化选择结果以及现有方法不能很好解决多目标测试优化选择等问题，提出基于第二代非支配排序遗传算法(NSGA-Ⅱ)的多目标测试优化选择的方法。首先，描述了测试不可靠条件下多目标优化选择问题的数学模型；其次，在该数学模型下，将系统给出的故障检测率和隔离率作为约束条件，将测试代价、漏检率和虚警率作为优化目标，建立了多目标优化问题；然后，提出带有精英保留策略的NSGA-Ⅱ对多目标问题进行优化选择，利用NSGA-Ⅱ能够得到一组Pareto最优解，可根据实际需求选择最优的测试组合；最后，针对某装备进行实例分析，得到3组最优解，可以满足不同需求下的最优选择，验证了所提数学模型与多目标优化算法的可行性与有效性。
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关键词:
- 测试优化选择 /
- 测试性设计 /
- 多目标测试 /
- 不可靠测试 /
- 第二代非支配排序遗传算法(NSGA-Ⅱ)
Abstract:Since test optimization selection plays a vital role in the test design of various equipment systems, in the testability design of various types of equipment, test unreliable factors seriously affect the optimization of test selection. First, this paper describes the mathematical model of the multi-objective optimization selection problem under unreliable test conditions. Second, under this mathematical model, the test cost, missed detection rate, and false alarm rate are used as the optimization goals, and the fault detection rate and isolation rate are constraints. Thus, a multi-objective optimization problem was established. Third, the NSGA-Ⅱ algorithm, a fast Non-dominated multi-objective optimization Sorting Genetic Algorithm-Ⅱ with an elite retention strategy, was proposed to optimize the proposed multi-objective problem. Using the NSGA-Ⅱ algorithm, a set of Pareto optimal solutions are obtained, and the optimal test combination can be selected according to actual needs. Finally, an example analysis is performed on a certain equipment, three sets of optimal solutions are obtained, which can meet the optimal selection under different needs, and the feasibility and effectiveness of the mathematical model and multi-objective optimization algorithm are verified.
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Key words:
- test optimization selection /
- testability design /
- multi-objective test /
- unreliable test /
- NSGA-Ⅱ
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图 5 双目标优化问题下的Pareto等级及拥挤度示意图
Figure 5. Conceptual diagram of Pareto level and congestion degree under bi-objective optimization problem
表 1 系统故障与测试相关布尔逻辑矩阵
Table 1. System failure and test related Boolean logic matrix
F T t1 t2 t3 t4 t5 t6 t7 t8 t9 t10 t11 t12 t13 t14 t15 t16 t17 t18 t19 t20 f1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 f2 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 f3 1 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 f4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 f5 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 f6 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 f7 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 f8 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 f9 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 f10 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 f11 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 f12 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 f13 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 f14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 f15 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 0 f16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 注：f16为系统正常状态。 
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表 2 系统故障概率
Table 2. System failure probability
% 模式 f1 f2 f3 f4 f5 f6 f7 f8 f9 f10 f11 f12 f13 f14 f15 f16 概率 0.1 0.1 0.1 1 1 1 1 0.2 0.1 1 1 0.25 0.15 1 1 91.1
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表 3 可用测试成本
Table 3. Available test cost
测试 t1 t2 t3 t4 t5 t6 t7 t8 t9 t10 成本 60 66 120 60 52 90 50 60 20 36 测试 t11 t12 t13 t14 t15 t16 t17 t18 t19 t20 成本 7 18 36 80 30 60 45 9 20 30
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表 4 检测概率
Table 4. Detection probability
% F T t1 t2 t3 t4 t5 t6 t7 t8 t9 t10 f1 95.18 92.65 94.72 92.32 95.32 94.26 92.22 93.97 96.12 95.75 f2 89.33 0 93.7 97.32 86.91 88.98 89.68 87.93 85.83 98.59 f3 96.74 0 0 87.42 0 0 0 0 0 0 f4 92.95 91.23 96.13 98.72 85.16 91.57 91.06 90.32 93.44 98.86 f5 90.19 0 98.4 88.8 97.51 85.91 88.16 95.97 85.7 96.04 f6 0 0 88.53 87.79 98.84 93.12 94.53 90.82 91.14 f7 94.84 0 0 97.26 89.18 93.16 95.65 91.46 89.27 91.98 f8 0 0 0 0 0 90.93 92.42 92.95 97.24 88 f9 0 0 0 0 0 0 0 0 0 94.01 f10 0 0 0 0 0 0 0 0 0 0 f11 0 0 0 0 0 0 0 0 0 0 f12 0 0 0 0 0 0 0 0 0 0 f13 0 0 0 0 0 0 0 0 0 0 f14 0 0 0 0 0 0 0 0 0 0 f15 0 0. 0 0 0 0 0 0 85.21 0 f16 0 0 0 0 0 0 0 0 0 0 F T t11 t12 t13 t14 t15 t16 t17 t18 t19 t20 f1 89.48 87.98 85.61 93.22 91.7 95.02 91.42 91.02 90.91 0 f2 98.44 96.75 85.38 85.81 92.77 93.97 97.18 97.46 0 96.98 f3 0 0 89.38 90.15 86.69 87.67 98.08 95.29 0 0 f4 95.17 93.8 85.18 93.84 91.31 96.81 88.7 94.62 0 0 f5 90.77 86.87 90.38 95.05 95.02 97.12 87.24 89.85 0 0 f6 95.42 87.9 94.56 94.7 97.5 87.39 97.22 87.32 0 0 f7 88.75 93.5 86.3 86.18 88.82 98.92 88.33 87.18 0 0 f8 91.16 93.82 85.49 91.36 88.57 91.16 94.04 87.68 0 0 f9 98.07 90.19 93.57 91.19 97.12 89.76 98.54 0 0 0 f10 94.57 93.05 93.52 89.95 88.25 97.12 94.31 0 0 0 f11 0 91.32 85.22 87.15 96.27 90.11 97.19 0 0 0 f12 0 0 85.23 94.46 97.72 90.51 85.14 0 0 0 f13 0 0 0 94.79 88.25 93.28 86.92 0 0 0 f14 0 0 0 0 88.35 86.68 0 0 0 0 f15 0 0 87.66 95.19 85.7 97.52 96.46 0 0 0 f16 0 0 0 0 0 0 0 0 0 0
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表 5 虚警概率
Table 5. False alarm probability
% F T t1 t2 t3 t4 t5 t6 t7 t8 t9 t10 f1 0 0 0 0 0 0 0 0 0 0 f2 0 0.1 0 0 0 0 0 0 0 0 f3 0 0.17 0.18 0 0.14 0.18 0.11 0.2 0.17 0.11 f4 0 0 0 0 0 0 0 0 0 0 f5 0 0.17 0 0 0 0 0 0 0 0 f6 0.15 0.2 0.19 0 0 0 0 0 0 0 f7 0 0.16 0.18 0 0 0 0 0 0 0 f8 0.18 0.14 0.14 0.15 0.17 0 0 0 0 0 f9 0.15 0.12 0.16 0.19 0.18 0.15 0.17 0.11 0.2 0 f10 0.15 0.16 0.17 0.13 0.14 0.12 0.14 0.14 0.18 0.19 f11 0.15 0.17 0.12 0.17 0.14 0.17 0.11 0.15 0.17 0.19 f12 0.14 0.14 0.19 0.14 0.16 0.2 0.16 0.13 0.14 0.16 f13 0.19 0.1 0.16 0.16 0.16 0.18 0.18 0.16 0.16 0.13 f14 0.1 0.14 0.16 0.17 0.17 0.17 0.17 0.1 0.18 0.19 f15 0.13 0.18 0.12 0.14 0.15 0.15 0.2 0.16 0 0.15 f16 0 0 0 0 0 0 0 0 0 0 F T t11 t12 t13 t14 t15 t16 t17 t18 t19 t20 f1 0 0 0 0 0 0 0 0 0 0.0018 f2 0 0 0 0 0 0 0 0 0.13 0 f3 0.17 0.19 0 0 0 0 0 0 0.16 0.2 f4 0 0 0 0 0 0 0 0 0.15 0.16 f5 0 0 0 0 0 0 0 0 0.11 0.1 f6 0 0 0 0 0 0 0 0 0.11 0.18 f7 0 0 0 0 0 0 0 0 0.13 0.16 f8 0 0 0 0 0 0 0 0 0.14 0.17 f9 0 0 0 0 0 0 0 0.11 0.15 0.11 f10 0 0 0 0 0 0 0 0.19 0.19 0.14 f11 0.14 0 0 0 0 0 0 0.18 0.16 0.14 f12 0.2 0.13 0 0 0 0 0 0.18 0.13 0.12 f13 0.11 0.17 0.15 0 0 0 0 0.18 0.15 0.18 f14 0.16 0.11 0.14 0.16 0 0 0.16 0.17 0.16 0.18 f15 0.13 0.14 0 0 0 0 0 0.12 0.12 0.15 f16 0 0 0 0 0 0 0 0 0 0
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表 6 NSGA-Ⅱ参数设置
Table 6. NSGA-Ⅱ parameter setting
参数 数值 目标函数个数 3 决策变量个数 20 迭代次数 200 种群数量 500 拥挤度比较算子 0.5 交叉概率 0.9 变异概率 0.05 交叉算子 20 变异算子 20
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表 7 几组典型的优化组合
Table 7. Several typical optimization combinations
情况 测试组合 成本 漏检率/% 虚警率/% 成本最优组合 {1，1，1，0，0，0，0，0，1，1，1，1，0，0，1，0，1，0，1，1} 452 1.22 1.24 漏检率与虚警率最优组合 {1，1，1，0，0，1，0，0，1，1，1，1，1，0，1，0，0，0，1，1} 567 0.12 0.27 综合优化组合 {1，1，1，1，0，0，0，0，1，1，1，1，1，0，0，1，0，0，1，1} 533 0.88 0.82
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