短长期记忆的邻居学习粒子群优化器处理动态优化问题

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"这篇研究论文提出了一种新颖的粒子群优化算法，用于解决动态优化问题。该算法在粒子群优化的速率更新过程中引入了基于邻居的学习策略，旨在增强粒子的探索和开发能力。通过结合短期记忆和长期记忆，算法提高了在动态环境中适应变化的能力。关键词包括：基于邻居的学习、粒子群优化、最差替换、短期记忆、长期记忆以及动态优化问题。" 本文主要探讨的是针对动态优化问题的一种改进版粒子群优化算法（Particle Swarm Optimization, PSO）。在传统的PSO中，每个粒子根据其当前位置和全局最优位置来更新速度和位置。然而，在动态环境中，目标函数或约束条件可能会随时间变化，这要求优化算法能够快速适应这些变化。论文作者Leilei Cao、Lihong Xu和Erik D. Goodman提出了一个结合短期记忆和长期记忆的邻域学习策略。这种策略增强了粒子在搜索空间中的探索性，同时保证了对全局最优解的高效追踪。具体来说，算法在更新粒子速度时考虑了邻近粒子的信息，这有助于粒子从局部最优中跳出，增加全局搜索的可能性。 "基于邻居的学习"是指粒子不仅考虑自身的最优历史位置，还考虑其邻居的历史最优位置。这种机制鼓励群体内的信息交流，增强了群体的整体性能。而“最差替换”策略则意味着当粒子的记忆达到一定长度时，会用新发现的更优解替换旧的较差解，从而保持记忆中的信息质量。短期记忆关注最近的优化历程，帮助粒子快速响应环境变化；长期记忆则保留更早的信息，可以防止算法过早收敛，避免丢失可能的重要解。这种结合两者的记忆机制使得粒子在处理动态问题时既能迅速适应变化，又能保持对全局最优的敏感性。此外，该研究论文还可能涵盖了算法的实现细节、性能评估方法、与其他优化算法的比较，以及在实际动态优化问题上的应用案例。通过这些分析，作者可能展示了所提算法在处理复杂和多变环境中的优势，证明了其在动态优化领域的有效性。这篇研究论文为解决动态优化问题提供了一种创新的粒子群优化方法，通过引入邻域学习和双重记忆机制，提升了算法在动态环境下的适应性和优化效率。这对于工程、经济、生物等多个领域的动态优化问题具有重要的理论和实践意义。

L. Cao et al. / Information Sciences 453 (2018) 463–485 467

also incorporate a multi-population and a memory scheme into the proposed modiﬁed particle swarm optimization to ad-

dress dynamic optimization problems.

3. The Proposed algorithm

3.1. Neighbor-based learning strategy

As a global search technique, an algorithm must have both exploration and exploitation abilities to solve even static

optimization problems. The classical PSO has an excellent exploitation ability but it is a little weak at exploration for some

optimization problems [10] . In contrast, DE makes full use of other individuals’ information to explore more of the search

space. Motivated by the core principle of DE, we incorporate the inﬂuence of a stochastic particle’s position into the velocity

update of PSO [10] . Therefore, each learning particle (which we also call the target particle) learns from positions of two

members from the swarm, in which all other members are deﬁned as neighbors of that learning particle. One member is

a stochastically selected neighbor and the other is the global best particle (means the particle with the best ﬁtness) in the

swarm. For particle i in the swarm, let k be the index of another (different) randomly chosen particle among its neighbors,

Then the d

velocity component (1 ≤ d ≤ no. of dimensions) of particle i is updated as follows:



∗ v

+ F ∗



− x



+ c ∗ rand3

∗



gbest

− x



, if rand 4

< p

, ot her wise

(3)

where F is a scaling factor borrowed from DE, rand3

and rand4

are two uniformly random numbers between 0 and 1

which are generated independently. The meanings of ω and c are as in PSO. p is a learning probability, which means that

only if this probability is met, then the d

velocity component learns from these two positions. Otherwise, the d

velocity

component retains its previous value. x

gbest

is the d

component of the current global best particle’s position. x

is the

component of the position of target particle i . x

is the d

component of the positon of the selected another particle.

Similarly to conventional PSO, the particle’s velocity in each dimension is restricted to its range.

The learning probability enables some components of the previous velocity of the target particle to be corresponding

components of its new velocity. This probability-based learning strategy inherits some components from the target parti-

cle’s previous velocity as a memory, which prevent the target particle from completely being attracted by a strong global

best particle or a randomly selected particle with a quite good ﬁtness. Compared to the classic PSO, learning from neighbors

enhances the exploration of particles. In the classic PSO, each particle’s velocity update utilizes only the information of its

historical best position and that of the global best particle to alter its current velocity. Therefore the search direction is

limited, which reduces the diversity of the swarm. But learning from different stochastic neighbors provides more informa-

tion for the target particle in order to search a more widely distributed solution region. More details will be showed in the

Section 3.6 .

In the original DE operator, F is a ﬁxed value which is suggested to be set in: F ∈ [0.5, 1]. Choosing a suitable parameter

value usually depends on the speciﬁc problem class, which might ordinarily require repeated runs to identify. Instead, a

self-adaptive method is proposed here to control this scaling factor [5] as follows:

(

)



min

(

max

− F

min

)

∗ ϕ if r

< τ

(

g − 1

)

ot her wise

(4)

where F ( g ) is the value for the g

generation, F

min

is the minimum value of F, F

max

is the maximum value of F , ϕ and r

are

two uniformly random numbers between 0 and 1, but they are generated independently. τ is the probability of adjusting F .

If this probability is not met, F retains its value from the previous generation. In the following experiment section, we will

show the strength of this self-adaptive method.

3.2. Swarm update

For particle i , its previous position is added to the updated velocity to form a new position U

= x

+ v

(5)

In the classical PSO, the particle always moves to the new position whether or not it is better than the old. Its personal

historical best position and the global best position are always updated. In the classical DE, a greedy strategy is employed

in the selection operator—the target individual is replaced if its offspring is better, otherwise, the old target individual

is retained. The greedy strategy can make the population evolve, but it often may not be the best approach for global

optimization. Viewed from the whole population, although the new individual may not be better than its parent, it may be

better than others in the population. In this proposed algorithm, we present a novel strategy to update the swarm. Since

each particle has the same chance to be selected to inﬂuence the other particles, a particle with particularly poor ﬁtness

may affect the performance of the whole swarm. In the extreme, the performance of the whole swarm might be strongly

inﬂuenced by the particle with the worst ﬁtness. Accordingly, the worst particle in the swarm should be given priority to

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短长期记忆的邻居学习粒子群优化器处理动态优化问题

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