带有个体淘汰的强制进化随机游走算法优化质量交换网络

doi:10.19596/j.cnki.1001-246x.8576

摘要/Abstract

摘要：

针对强制进化随机游走算法(RWCE)在优化质量交换网络进程中, 存在部分个体在竞争中长期处于劣势状态以及个体结构高度相似的现象, 提出带有个体淘汰的RWCE算法优化质量交换网络。即在一定的周期内, 通过对种群中个体优化状态的实时监控, 首先对个体的网络结构进行标准化处理, 以此识别出结构中相似的质量交换器, 再根据其数目评价个体的结构相似度, 将种群中的个体划分为若干个集团, 并以年度总费用作为评价个体优化性能的指标, 淘汰种群中的劣势和相似个体, 以此加强种群间个体的信息交流, 提升个体优化活力和种群多样性, 同时有效增强算法优化质量交换网络的全局搜索能力。将该方法应用于2个质量交换网络实例中, 优化结果均优于文献最优结果, 说明该方法能改变结构的进化方向, 激励种群间个体的差异性进化和保持个体的优化活力, 且有效提升算法的全局寻优性能。

关键词: 质量交换网络, 节点非结构模型, 强制进化随机游走算法, 传质, 同步优化

Abstract:

In the process of optimizing the mass exchange network by random walk algorithm with compulsive evolution, some individuals are in a long-term disadvantaged state in the competition and the individual structure is highly similar. RWCE algorithm with individual elimination is proposed to optimize the mass exchange network. That is, in a certain period, through the real-time monitoring of the optimal state of the individuals in the population, the network structure of the individual is first standardized, so as to identify the similar quality exchangers in the structure, and then evaluate the structural similarity of the individual according to its number. Divide the individuals in the population into several groups, and use the total annual cost as an indicator to evaluate the individual optimization performance, and eliminate the disadvantaged and similar individuals in the population. Strengthen the information exchange of individuals between populations, improve individual optimization vitality and population diversity, and effectively enhance the global search ability of the algorithm to optimize the mass exchange network. Applying this method to two examples of mass exchange networks, the optimization results are better than the best results in the literature, indicating that the method can change the evolution direction of the structure, stimulate the differential evolution of individuals between populations and maintain the optimization vitality of individuals, and effectively improve the global optimization performance of the algorithm.

Key words: mass exchange network, nodes-based nonstructural model, random walk algorithm with compulsive evolution, mass transfer, simultaneous optimization

马秀宝, 崔国民, 周志强, 肖媛, 徐玥, 杨其国. 带有个体淘汰的强制进化随机游走算法优化质量交换网络[J]. 计算物理, 2023, 40(3): 376-388.

Xiubao MA, Guomin CUI, Zhiqiang ZHOU, Yuan XIAO, Yue XU, Qiguo YANG. Optimizing Mass Exchange Network Using RWCE Algorithm with Individual Elimination[J]. Chinese Journal of Computational Physics, 2023, 40(3): 376-388.

图/表 16

图1 优化模型示意图

Fig.1 Schematic diagram of optimization model

图2 拉直处理后的模型结构

Fig.2 Model structure diagram after straightening

图3 基础RWCE算法优化流程图

Fig.3 Optimization flow chart of basic RWCE algorithm

图4 TAC变化曲线

Fig.4 Graph of TAC change

图5 相似质量交换器示意图

Fig.5 Schematic of a similar mass exchanger

图6 网络结构标准化处理的流程图

Fig.6 Flow chart of network structure standardization processing

图7 网络结构标准化处理示意图 (a)随机生成的网络结构；(b)分流组位置调整后的结构；(c)标准化的网络结构

Fig.7 Schematic diagram of network structure standardization processing (a) randomly generated network structure; (b) adjusted structure of the split group position; (c) standardized network structure

图8 方法执行流程图

Fig.8 Flowchart of method execution

图9 劣势个体TAC变化曲线

Fig.9 TAC change graph of disadvantaged individuals

图10 相似个体结构改变对比 (a)改变前的网络结构；(b)改变后的网络结构

Fig.10 Comparison of structural changes of similar individuals (a) the network structure before the change; (b) the network structure after the change

表1 算例1的流股数据

Table 1 Streams data in Case 1

富流股	G_i/(kg·s^-1)	Y_iⁱⁿ/(kg·kg^-1)	Y_i^out/(kg·kg^-1)	贫流股	L_j^c/(kg·s^-1)	X_jⁱⁿ/(kg·kg^-1)	X_j^out/(kg·kg^-1)	C_j^L/(＄·s·kg^-1·a^-1)
R₁	0.9	0.07	0.000 3	S₁	2.3	0.000 6	0.031	117 360
R₂	0.1	0.051	0.000 1	S₂	∞	0.000 2	0.003 5	176 040

图11 历史最优个体TAC变化曲线

Fig.11 Historical optimal individual TAC change curve

表2 算例1优化结果的对比

Table 2 Comparison results of Case 1

参考文献	L₁/(kg·s^-1)	L₂/(kg·s^-1)	No. of units	TAC/(＄·a^-1)
Ref. [25]	2.205	0.236 62	6	469 968
Ref. [24]	2.23	0.46	4	433 730
Ref. [17]	2.192	0.37	4	413 450
Ref. [18]	2.190 9	0.369 2	4	413 160
Ref. [23]	2.192	0.357	4	411 166
Ref. [11]	2.189 3	0.383 7	6	410 971
Ref. [27]	2.189 54	0.381 24	6	410 565
Fig. 10(b)	2.196 22	0.319 6	4	409 603

表3 算例2的流股数据

Table 3 Streams data in Case 2

富流股	G_i/(kg·s^-1)	Y_iⁱⁿ/(kg·kg^-1)	Y_i^out/(kg·kg^-1)	贫流股	L_j^c/(kg·s^-1)	X_jⁱⁿ/(kg·kg^-1)	X_j^out/(kg·kg^-1)	C_j^L/(＄·s·kg^-1·a^-1)
R₁	3.3	0.05	0.001 5	S₁	10	0.001 3	0.025	58 680
R₂	0.6	0.07	0.003	S₂	10			417 060

R₃	1.4	0.02	0.003	再生流股	M₁^c/(kg·s^-1)	Z₁ⁱⁿ/(kg·kg^-1)	Z₁^out/(kg·kg^-1)	C₁^M/(＄·s·kg^-1·a^-1)
R₄	0.2	0.03	0.002	H₁	10	0	0.005	88 020

图12 算例2优化网络结构

Fig.12 Optimization network structure diagram of Case 2

表4 算例2优化结果的对比

Table 4 Comparison results of Case 2

参考文献	L₁/(kg·s^-1)	L₂/(kg·s^-1)	No. of units	TAC/(＄·a^-1)
Ref.[30]				720 000
Ref.[28]	9.6	0.319	8	706 000
Ref.[14]	9.602	0.349	7	694 000
Ref.[25]	9.594	0.373	8	693 976
Ref.[31]	9.576	0.442	8	689 300
Fig. 12	9.572 17	0.346 33	7	688 932

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