植物根系生长模拟与优化：根增长算法新方法

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"根系生长模型：植物根系数值函数优化和仿真的新方法" 这篇科研论文探讨了一种基于植物根系生长的优化模型，旨在利用生物学的灵感解决复杂系统的建模与计算问题，特别是针对高维度数值函数的优化。文章作者包括Hao Zhang、Yunlong Zhu和Hanning Chen，发表于2013年，被SoftComput杂志收录。文章首先介绍了研究背景和目标，即创建一个数学框架和架构来模拟植物根系在土壤中的生长模式。这种模拟考虑了土壤与根系生长间的相互作用，这是理解植物生态适应性和生长策略的关键因素。通过观察和分析根系生长的自然规律，研究者开发出了一种名为“根生长算法”（RGA）的新方法。 RGA是一种优化算法，它借鉴了植物根系在土壤中寻找养分和水分的动态过程。在算法设计中，根系的生长被视为一种搜索和优化过程，这与传统优化方法有所不同。通过仿真研究，RGA的性能得到了验证。这些仿真结果表明，该模型能够准确地反映出植物根系在土壤中的实际生长行为，同时，数值分析也证实了RGA在处理高维数值函数优化问题时展现出的强大能力。在高维度空间中进行优化是一个极具挑战性的任务，因为维度增加会导致“维度灾难”，使得传统的优化技术效率下降。RGA的优势在于其自然启发的机制，能够在复杂环境中有效地探索解决方案空间，这在一定程度上克服了高维度优化的难题。此外，该研究的创新性不仅在于提出了一种新的优化算法，还在于将生物学原理应用于工程问题的解决，这种跨学科的研究方法对于促进生物启发式算法的发展具有重要意义。它不仅有助于优化理论的进步，也为理解和模拟自然系统提供了新的工具，可能在未来被广泛应用于农业、环境科学、生态学以及工程优化等领域。 "根系生长模型：植物根系数值函数优化和仿真的新方法"这篇论文通过建立基于植物根系生长的优化模型，提出了RGA这一强大的优化工具，并通过仿真验证了其在高维度数值优化中的有效性。这一研究为生物学和计算科学的交叉领域开辟了新的研究方向，为解决复杂问题提供了新的思路。

524 H. Zhang et al.

SELECT THE ROOT TIP WITH

THE LARGEST FITNESS VALUE

AS THE FIRST ONE TO BRANCH

SELECT THE ROOT TIP WITH

THE LARGEST FITNESS VALUE

IN THE REMAINING ONES

STOP CRITERIA

CALCULATE

DISTANCE BETWEEN

THE ROOT TIPS

DETERMINE THE ROOT TIP

TO BRANCH

THE SELECTION

PROCESS ENDS

YES

GREATER THAN

THE THRESHOLD

LESS THAN THE

THRESHOLD

Fig. 1 The selection process of the root tips

from the old root tip in memory, the proposed model uses the

following expression:



+ (2 ×δ

− 1) j = k

j = k

(2)

where k ∈{1, 2,...,D} are randomly chosen indexes and

j ∈{1, 2,...,D}. pg

(i = 1, 2,...,S) are S new growing

points. δ

is a random number between [−1, 1].

3.4 Root hair growth

After new growing points are produced, root hairs begin to

grow from these growing points. Root hair growth depends

on its growth angle and growth length. The growth angle is

a vector for measuring the growth direction of root hair. The

growth angle of each root hair ϕ

(i = 1, 2,...,n) which is

produced randomly can be expressed as:

(φ

,φ

,...,φ

) = rand(D) (3)

(φ

,φ

,...,φ

)



+ φ

+···+φ

(4)

The growth length of each root hair is deﬁned as δ

(i =

1, 2,...,n) which is an important parameter in the root

growth model. Some strategies of tuning the parameter

can produce multiple versions of the root growth model.

After growing, a new root tip is produced by the following

expression:

= x

+ δ

(5)

In order to simulate the trophotropism of root system, some

rules are deﬁned as follows:

(1) If morphactin concentration (ﬁtness) of a new root tip is

better than old one in the same cycle t, the root tip will

continue to grow. A new root tip in the inner loop can be

expressed as:

= x

+ δ

(6)

But the number of iterations in the inner loop is a prede-

ﬁned value. While the number of iterations in the inner

loop equals a predeﬁned value, the inner loop stops.

(2) If morphactin concentration of a new root tip is worse

than old one in the same cycle t, the root tip will stop

growing and t = t +1. A new root tip can be expressed

as:

t+1

= x

t+1

+ δ

(7)

3.5 Root growth algorithm

The root growth model proposed is instantiated as RGA for

simulation of root system of plant and higher-dimensional

numerical function optimization. The threshold of the dis-

tance between root tips and the growth length of each root

hair are important parameters for RGA. The ﬂowchart of the

RGA is presented in Fig. 2. The pseudocode for the RGA is

listed in Table 2.

4 Simulation of root system of plant

4.1 Simulating root–soil interaction

As the ﬁrst stage of a comprehensive root growth model, the

objective of the study was to simulate the interactive rela-

tionships between changing soil environment and the root

growth. In the simulation, Ackley function is used as soil

environment in computer. Ackley function is presented in

Sect. 4.1 and the setting of the parameters is the same as one

in Sect. 4.2. Figures 3 and 4 shows the simulation result of

root–soil interaction. The color changes in the simulation of

soil indicate the uneven distribution of nutrients in the soil.

The root system is represented by points and a point rep-

resents a root tip. It is simulated successfully that the roots

of plant grow towards the directions with the higher con-

centration of nutrients. It is also illustrated that RGA can

obtain optimal solution for numerical function optimization

in Figs. 3 and 4.

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