大型群组粒子优化器的个人最优位置引导策略

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本文档主要探讨了针对大规模优化问题的一种改进型粒子群优化算法——带有个人最佳位置引导的群组粒子群优化（Grouping Particle Swarm Optimizer with Personal-Best-Position, GPSP）。粒子群优化（Particle Swarm Optimization, PSO）作为一种广泛应用且研究广泛的搜索算法，在许多领域都得到了广泛的关注和实现。然而，标准的PSO在保持种群多样性方面存在不足，这可能导致算法过早收敛或陷入局部最优解。为了克服这一问题，作者提出了一种创新策略，即在PSO的基础上融入个人最佳位置的概念。个人最佳位置（Personal-Best-Position, PBP）指的是每个粒子在其迭代过程中找到的最优解，它有助于个体探索更广阔的搜索空间，从而提高种群的整体性能。在GPSP中，群体被划分为若干子群，每个子群内部的粒子相互竞争，同时它们还会参考各自的最佳个人解（PBP）来更新自己的位置，这样既能保持个体间的竞争，又能够利用全局最优信息。作者们详细描述了GPSP的设计与实施步骤，包括初始化、速度更新公式、位置更新以及群体结构的维护等关键环节。通过引入个人最佳位置的动态调整和群体之间的协同作用，GPSP旨在提高优化过程中的全局搜索能力，防止过早收敛，并减少局部最优的可能性。实验部分展示了GPSP在各种复杂优化问题上的优越性能，特别是在大规模和高维度优化任务中，其结果表明这种新型算法具有更好的适应性和稳定性。此外，该研究还涉及到算法的可扩展性、收敛速度分析以及与传统PSO和其他优化算法的比较，以验证GPSP的有效性和改进效果。最后，论文提供了论文引用信息，包括DOI和期刊发表信息，以便读者进一步查阅和研究。总结来说，这篇论文提供了一个重要的工具，即GPSP，为解决大规模优化问题提供了新的策略和方法，有助于提高PSO在实际应用中的性能和效率。对于那些关注优化算法改进和高性能计算的科研人员和工程师而言，这篇工作具有很高的实用价值和理论参考价值。

1545-5963 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TCBB.2017.2701367, IEEE/ACM

Transactions on Computational Biology and Bioinformatics

II. PRELIMINARIES

A. Canonical Particle Swarm Optimization

As a famous swarm intelligence algorithm, PSO was ﬁrst

proposed by Kennedy and Eberhart in 1995 [22]. This algorith-

m was initially inspired from the behaviors of birds ﬂocking to

build a dynamic model that can be employed in optimization.

In PSO, each particle has two variables that are position and

velocity respectively. Over the course of optimization, particles

update their positions and velocities based on the updating

equations shown in (1):

(t + 1) = ωV

(t) + c

(t)(pbest

(t) − X

(t))

+ c

(t)(gbest(t) − X

(t))

(t + 1) = X

(t) + V

(t + 1)

(1)

where t is the iteration (generation) number, V

(t) and X

(t)

represent the velocity and position of the i

particle at gener-

ation t respectively; ω is termed inertia weight, c

and c

are

the acceleration coefﬁcients, R

(t) and R

(t) are two vectors

randomly generated within [0, 1]

and d is the dimension of

the problem; pbest i(t) is the personal historical best position

of the i

particle and g

best

(t) is the current best particle found

so far. Kennedy has referred c

(t)(pbest

(t) − X

(t)) and

(t)(gbest

(t) − X

(t)) as the cognitive component and

social component, respectively [22].

According to (1), each particle will learn from its own

historical best position p

best

, so p

best

guides the direction for

individual particle. Besides, all particles will learn from g

best

so g

best

plays the role to guide the whole swarm. If g

best

is a

local optima, it is hard for the whole swarm to get rid of it.

In current years, many researches are conducted to weaken

the inﬂuence of g

best

to the whole swarm. In [17], the author

proposed a variant of PSO, where particles will learn from

best

only. However, in the algorithm the parameter setting,

which heavily affects algorithms’ performance, is on the

basis of empirical experiments. In [18], the authors divided

the whole swarm into pairs and employed a competitive

mechanism in pair comparison. The loser particle will learn

from the winner one. However, since in one generation only

half of particles, say loser particles, are involved in update,

while the winner particles do not update, so the whole swarm

has a low efﬁciency in convergence. In this paper, we propose

a novel particle swarm optimizer by employing grouping

strategy with p

best

guidance. We split the whole swarm into

several groups. In each group, the worse particles will learn

from the group best one. In addition, every particle has a

probability to learn from p

best

of other particles. In this

way, both convergence and diversity maintenance can be

considered simultaneously.

B. Measures of Population Diversity

There are mainly two ways to measure population diversity.

The ﬁrst one is distance-based measurement (DBM) which

calculates the Euclidian distances among individuals. There

are several different forms of DBMs, such as the mean spatial

distance among all individuals, the mean distance between

individuals and the center position of the swarm, the maximum

distance between individuals, etc [23], [24], [25]. Normally, a

large distance means an abundant population diversity, while

a small distance implies a poor population diversity.

The second way is frequency-based measurement (FBM). In

FBM, the frequency of representative individuals is counted to

evaluate the population diversity [26], [27]. In [28], mean gene

frequency is employed to determine the population diversity.

Besides, entropy measurement is another way belonging to

FBM, since entropy uses the probability of appearance of

genes/ﬁtness. A detail investigation of FBM for swarm in-

telligence can be found in [29], [30].

In [31], Wineberg and Oppacher draw the conclusion that,

although the two measurements have different forms, both of

them use the distance-based idea between all possible pairs

of chromosomes and organisms in a swarm. For FBM, it is

usually to count the frequency of each individuals. Especially

for continuous problems, it rarely appears two same individu-

als. Hence, the we do not use FBM to measure the population

diversity in this paper, but only use DBM. According to [30],

many types of DBM are proposed. In this paper, we employ

the sum of variance of each dimension as the measurement.

The diversity D for a swarm is given in (2).

D =

j=1

(2)

where D is the diversity of a swarm, n is the dimension and

i=1

− ¯x

]

(3)

¯x

i=1

(4)

and x

is the j

dimension of the i

particle, m is the

population size.

III. GROUPING PARTICLE SWARM OPTIMIZER WITH P

best

GUIDANCE (GPSO-PG)

A. Design of GPSO-PG

To weaken the effects of one solution, such as g

best

, to

PSO’s performance, we design a novel variant of PSO, termed

Grouping Particle Swarm Optimization with P

best

Guidance

(GPSO-PG). The motivation is to reduce the effects of any

individual particle to the whole swarm. First, at the beginning

of each generation, we divide the whole swarm into several

groups in a random way. The size of each group is equal.

In each group, we compare the particles and select a local

best particle called a winner for the rest particles. Besides, all

loser particles will be involved in the velocity update by the

equations shown in (5). In (5), we employ the set of p

best

provided by all particles, but not g

best

, to guide the swarm’s

direction.

(t + 1) = ωV

(t) + c

(t)(X

(t) − X

(t))

+ c

(t)(pbest

(t) − X

(t))

(t + 1) = X

(t) + V

(t + 1)

(5)

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