# 基于约束一致策略的人工蜂群算法Artificial Bee Colony Algorithm Based on Constrained Consistent Strategy

DOI: 10.12677/CSA.2020.1011215, PDF, HTML, XML, 下载: 79  浏览: 162

Abstract: Over the last few decades, evolutionary algorithms have been widely used to solve complex optimization problems. However, when using evolutionary algorithms to solve constraint optimization problems, best results are often not obtained, because they cannot directly reduce the degree of constraint violation. In order to obtain the better optimal solution of the objective function and reduce the impact of constraint violation on the optimal solution, this paper integrates the global op-timization advantages of the artificial bee colony algorithm (ABC) and the stable computing characteristics of the constraint consensus strategy (CC) into a new hybrid heuristic algorithm—the constraint consensus strategy based artificial bee colony algorithm (ABCCC). During the evolutionary search, the constraint consensus strategy is quite effective for rapidly reducing constraint violations. Through a set of test functions and a comparison between PSOCC and DECC, it is proved that ABCCC has certain ability to deal with constraint optimization problems. Experimental results show that the algorithm has good performance in optimizing quality and convergence speed.

1. 引言

$\begin{array}{l}\mathrm{min}\text{ }\text{ }\text{ }\text{ }\text{ }f\left(x\right)\\ s.t.\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }{g}_{j}\left(x\right)\le 0\text{ },\text{\hspace{0.17em}}\text{\hspace{0.17em}}j=1,2,\cdots ,q\\ \text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }{h}_{j}\left(x\right)=0\text{ },\text{\hspace{0.17em}}\text{\hspace{0.17em}}j=q+1,\cdots ,m\\ \text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }{l}_{i}\le {x}_{i}\le {u}_{i}\text{ },\text{\hspace{0.17em}}i=1,2,\cdots ,n\end{array}$ (1)

2. 约束一致策略

$fv=v\text{ }d\nabla c\left(x\right)/{‖\nabla c\left(x\right)‖}^{2}$ (2)

Table 1. Pseudocode of constraint consensus strategy

3. 人工蜂群算法

Table 2. Pseudocode of ABC algorithm

${x}_{i,j}={x}_{j}^{\mathrm{min}}+rand\left(0,1\right)\left({x}_{j}^{\mathrm{max}}-{x}_{j}^{\mathrm{min}}\right)$ (3)

${v}_{i,j}={x}_{i,j}+\varphi \left({x}_{i,j}-{x}_{k,j}\right)$ (4)

k是不同于i的随机蜜源，j是随机选择的维度。f是在[−1, 1]范围内的一个均匀分布的随机数，决定了扰动程度。通过改变x上的一个维度来确定新的蜜源v，如果这个操作产生的这个维度的值超过了预定边界，就把其设置为边界值。

${P}_{i}=\frac{fitnes{s}_{i}}{\underset{j=1}{\overset{SN}{\sum }}fitnes{s}_{j}}$ (5)

$fi{t}_{i}=\left\{\begin{array}{l}1/\left(1+{f}_{i}\right)\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }{f}_{i}\ge 0\\ 1+abs\left({f}_{i}\right)\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }otherwise\end{array}$ (6)

${x}_{i}^{t+1}=\left\{\begin{array}{l}{x}_{j}^{\mathrm{min}}+rand\left(0,1\right)\left({x}_{j}^{\mathrm{max}}-{x}_{j}^{\mathrm{min}}\right)\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{\text{trial}}_{i}\ge \mathrm{lim}\text{it}\\ {x}_{i}^{t}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{ }\text{ }{\text{trial}}_{i}\text{< limit}\end{array}$ (7)

4. 基于约束一致策略的人工蜂群算法

Figure 1. Flow chart of the ABCCC algorithm

${x}_{i,d}={L}_{d}+rand\left(0,1\right)\left({U}_{d}-{L}_{d}\right)$ (8)

${{x}^{\prime }}_{i,d}={x}_{i,d}+{x}_{cc,d}$ (9)

$|{h}_{j}\left(x\right)|-\epsilon \le 0$ (10)

Table 3. Pseudocode of ABCCC

5. 实验结果与分析

5.1. 测试函数集与参数设置

5.2. 实验结果

Table 4. Comparison results of ABCCC, DECC and PSOCC

C01 C02 C03 C04 C05 C06 C07C08 C09 C10

Figure 2. Convergence curves of each test functions

C01 C02 C03 C 04 C05 C 06 C07 C 08 C09 C 10

Figure 3. Box chart comparison results of each test functions

5.3. SPP值对ABCCC的影响

Table 5. The influence of SSP on results

Figure 4. Convergence curve of ABCCC under different SPP values (C02)

5.4. ABCCC与其他算法的比较结果

Table 6. Comparison results of ABCCC、CLSHADE and UDE

Table 7. Comparison results of ABCCC, CABCCC and GABCCC

6. 结论

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