=Paper=
{{Paper
|id=Vol-3777/short13
|storemode=property
|title=Handling Outliers in Swarm Algorithms: a Review
|pdfUrl=https://ceur-ws.org/Vol-3777/short13.pdf
|volume=Vol-3777
|authors=Dmytro Uzlov,Yehor Havryliuk,Ivan Hushchyn,Volodymyr Strukov,Sergiy Yakovlev
|dblpUrl=https://dblp.org/rec/conf/profitai/UzlovHHSY24
}}
==Handling Outliers in Swarm Algorithms: a Review==
https://ceur-ws.org/Vol-3777/short13.pdf
Handling outliers in swarm algorithms: a review
Dmytro Uzlov1, Yehor Havryliuk1, Ivan Hushchyn1, Volodymyr Strukov1, and Sergiy
Yakovlev1
1
V.N. Karazin Kharkiv National University. 4 Svobody, Sq., Kharkiv, 61022, Ukraine
Abstract
Swarm optimization algorithms, inspired by the collective behavior of biological swarms, are a promising
tool for solving the problem of optimizing complex systems where traditional methods are often ineffective.
However, the problem of outliers can significantly affect the process of finding an optimal solution.
Therefore, the study of methods for detecting and processing outliers in swarm algorithms, such as the
particle swarm optimization (PSO), is an urgent task that has significant potential to improve the efficiency
and reliability of these algorithms in various practical applications, such as drone control systems, financial
systems, environmental control and modeling systems. The article deals with the problem of outliers in
swarm optimization algorithms such as PSO. An overview of existing approaches to managing outliers,
including adaptive methods, methods using swarm topologies, hybrid algorithms, and others, is provided.
The advantages and disadvantages of each approach are analyzed. Particular attention is paid to new
promising areas, such as the combination of neural networks and reinforcement learning, to develop more
efficient and adaptive swarm algorithms. The article is aimed at researchers and practitioners in the field
of optimization who are interested in improving the efficiency and reliability of swarm algorithms.
Keywords
Swarm algorithms, particle swarm optimization, deep learning. handling outliers.1
1. Introduction
Swarm optimization algorithms, inspired by biological swarms, are crucial for solving complex
problems in fields like engineering, economics, and medicine. Despite their power, these algorithms
often suffer from early convergence, where particles get stuck in local optima due to outliers. This
article reviews methods for detecting and managing outliers in swarm systems on the example of
PSO, analyzing adaptive methods, swarm topologies, and hybrid algorithms. It also explores
emerging solutions like neural networks and reinforcement learning hybridization, which could
enhance swarm algorithms' ability to avoid local optima and find global solutions.
2. Problem statement and state of the arts
In [1], the authors emphasize that an "outlier is strange data values that stand out from datasets".
From this definition, outliers in swarm systems can be represented as particles in the swarm that do
not follow the expected swarm behavior, such as particles that move much faster or slower than
other particles in the swarm. Such particles have all the characteristics inherent in the standard
definition of an outlier: they can deviate significantly from the swarm trajectory, interfere with other
particles, and prevent them from moving toward the optimal solution. This leads to slower swarm
convergence or suboptimal results.
The issue of outliers in swarm algorithms is underexplored but crucial, as optimizing them could
greatly enhance swarm convergence, benefiting many modern applications. Swarm systems, such as
drone control systems, are widely used in a variety of areas, including transportation systems [2],
ProfIT AI 2024: 4th International Workshop of IT-professionals on Artificial Intelligence (ProfIT AI 2024), September 25–27,
2024, Cambridge, MA, USA
dmytro.uzlov@karazin.ua (D. Uzlov); gavrilyk2903@gmail.com (Y. Havryliuk); gushchin.iv@gmail.com (I.Hushchyn);
struk_vm@ukr.net (V. Strukov); svsyak7@gmail.com (S. Yakovlev)
0000-0003-3308-424X (D. Uzlov); 0000-0002-4392-2000 (Y. Havryliuk); 0000-0002-1917-716X (I. Hushchyn); 0000-0003-
4722-3159 (V. Strukov); 0000-0003-1707-843X (S. Yakovlev)
© 2024 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
Wor
Pr
ks
hop
oceedi
ngs
ht
I
tp:
//
ceur
-
SSN1613-
ws
.or
0073
g
CEUR Workshop Proceedings (CEUR-WS.org)
CEUR
ceur-ws.org
Workshop ISSN 1613-0073
Proceedings
search and rescue operations [3], and other industries. In such systems, rogue drones can not only
slow down the convergence of the swarm, but also lead to a loss of control over individual drones,
which can cause safety hazards and involve damage to property or people.
In financial systems where swarm systems such as PSO are used to optimize investment
portfolios, outliers can cause unpredictable fluctuations in portfolio value [4]. These fluctuations can
negatively affect the stability and predictability of investments, creating additional risks for financial
markets.
Outliers can have severe consequences in control systems [5], leading to unpredictable behavior
and potential damage. In environmental models, they can cause inaccurate predictions. There is no
universal solution for handling outliers in swarm systems, as hyperparameters in swarm algorithms
greatly impact their efficiency and stability. Tailoring strategies to specific problems and exploring
alternative outlier control methods are key research priorities. Developing effective detection and
management techniques for outliers in swarm systems is crucial and requires innovative approaches.
3. State of the arts
The outlier problem, though well-known in statistics, is especially crucial in swarm algorithms.
Viewing swarm particles as data points frames the outlier issue as a statistical anomaly detection
problem, where outliers signal an imbalance in exploration and exploitation. Traditional methods,
like removing outliers [6], aren't always viable, especially in applications like drone systems where
losing a unit isn't acceptable. Thus, exploring alternative outlier management strategies is essential.
Recent studies have proposed a wide range of variations of the PSO algorithm aimed at solving
various problems and improving the basic algorithm. These variations include adaptive approaches,
where hyperparameters dynamically change during the optimization process, considering the
current state of the swarm and the characteristics of the problem. Researchers also consider methods
that utilize swarm topologies (in a standard PSO, one of the topologies shown in Figure 1 is often
used) [7], which affect the information exchange between particles, allowing for more efficient
exploration of the solution space and avoiding early convergence. In addition, hybrid algorithms
combining PSO with other optimization methods, such as genetic algorithms or bee swarm methods,
are actively being investigated to combine the advantages of different approaches [7, 8].
Figure 1: Standard swarm topologies: (a) Global-Best, (b) Ring, (c) Wheel, (d) Pyramid, (e) Von
Neumann
The research papers [7, 8] provide an overview of such modern variations of PSO, their processing
principles and purpose. Further analysis of these variations, presented in this paper, will allow to
deeper understand their advantages and disadvantages, as well as to determine the optimal vector
for future research on the outlier problem not only in PSO, but also in the domain of swarm
algorithms in general, and finding a solution that will increase the efficiency and reliability of swarm
algorithms in various practical problems.
4. Managing outliers in swarm algorithms
4.1. Outliers causes
Outliers in swarm systems, as in any other systems where they occur, are stochastic in nature. It is
proposed to study outliers in swarm systems on the example of one of the most common and simplest
implementations of swarm intelligence algorithms for function optimization – PSO [9]. Determining
PSO hyperparameters involves dealing with outlier particles that deviate from the swarm's general
trend, making PSO ideal for studying outliers in swarm algorithms.
Among the main reasons for the occurrence of outliers in PSO algorithms are the following:
1. Initialization: some particles may start moving with initial values of position and velocity
that are far from optimal
2. Particle divergence: particles explore the search space and may deviate from the swarm
3. Stochasticity: the algorithm is inherently random, potentially leading to some particles
having significantly different positions or velocities than the rest of the swarm
4. Inappropriate hyperparameters: the behavior of PSO is strongly influenced by the choice of
its hyperparameters
The initial position and velocity of particles in the simplest implementation are determined
according to a uniform distribution in the search area. They also affect the speed of finding the
optimal solution by a swarm. There are effective methods for solving this problem [10, 11].
Such causes of outliers as particle divergence, stochasticity, and inappropriate hyperparameters
are related to the choice of parameters such as inertia weights and acceleration coefficients [9] - they
affect the degree of exploration and exploitation of particles, thereby changing the behavior of
agents. The choice of such parameters is usually a separate task when implementing PSO to optimize
the objective function. For a static end state, it is possible to select such parameters. When the
objective function changes dynamically, this approach becomes suboptimal, because each change in
the objective function can potentially lead to unexpected results due to the static choice of initial
parameters. To solve the problem of optimizing swarm outliers, as well as to overcome the need to
find a compromise between the exploratory and exploitative behavior of a particle, many variations
of PSO, were developed. For example, one of them is adaptive PSO.
Adaptive PSO (APSO) [12] has better search efficiency than the standard PSO, can perform a
global search over the entire search space with a higher convergence rate, and can automatically
control inertia weights, acceleration factors, and other algorithmic parameters at runtime, thereby
improving search efficiency and performance simultaneously. In addition, this algorithm can
influence a single swarm particle with the global best found value to "force" it out of the likely local
optimum.
But as any other variation mentioned in this article, APSO has its own set of limitations and
potential problems. Some of the most common problems include [12]:
• Over-adaptation
• Complexity
• Convergence
• Performance
Although APSO is widely utilized among PSO variants, it may not represent the most optimal
approach for all application scenarios.
4.2. An overview of existing PSO variations
APSO is by far the most common modification of the standard algorithm, being more flexible and
more versatile, but it does not solve all problems and creates new disadvantages. We will consider
other modifications of PSO further.
Scientists Meetu Jain, Vibha Saihjpal Narinder Singh, Satya Bir Singh noted the following
variations of the PSO algorithm in their work, each aimed at solving the specific standard PSO
limitation [8]:
1. Fuzzy adaptive PSO algorithm – improves PSO optimization capabilities
2. Homogeneous particle swarm optimizer (HPSO) – modified version for solving multi-
objective optimization problems
3. Hybrid PSO with ranking, selection and mean square error criterion (STPSO) – combines
PSO with statistical methods to solve stochastic optimization problems
4. Evolutionary modified PSO –improves search efficiency
5. Improved PSO algorithm (IPSO) – improves the search efficiency
6. Fully informed particles in PSO –improves performance
The authors of another paper [7], in addition to a general review of the PSO algorithm and its
principles, provide a brief overview of the most recent PSO review documents, as well as a list of
recent publications with PSO variations and their limitations. The main PSO variants the article
focuses include the following:
1. Cooperative PSO – solving the outliers’ problem through particle cooperation
2. Multi-swarm PSO – improves exploration avoiding local optima convergence
3. Hybrid PSO – improves performance in dynamic object layout problems
4. Binary PSO – can optimize both continuous and discrete functions
The article also provides an additional list of other PSO variations that are less popular or less
efficient. These variations of PSO are usually aimed at eliminating a specific drawback of the
standard algorithm, for example, the possibility of hitting a local optimum. But each of them also has
its own drawbacks. For example, adding new parameters to the algorithm increases the complexity
of the initial model setup and generally complicates the system with more hyperparameters, and, in
addition, requires additional computational costs [7].
The PSO variations in [7, 8] show ongoing evolution and improvement for solving diverse
optimization problems, but their multitude suggests that each may offer a less universal solution for
specific problem types.
4.3. Comparative analysis of the PSO modifications
The analysis of recent publications on the topic [7, 8] shows that many researchers' efforts are
focused on the development and improvement of the PSO algorithm. As a result of intensive
scientific activity, a wide range of modifications and hybridizations of the basic PSO algorithm have
been proposed, each of which has its own strengths and weaknesses. Based on the analysis of [7, 8],
the authors of this article present a qualitative comparison of PSO variations (Table 1).
While these PSO variations offer improvements over the standard PSO, there is limited evidence
of their effectiveness in real-world applications. Current literature indicates that no PSO variant is
universally optimal or improves PSO without introducing new constraints. Thus, selecting a specific
algorithm requires careful consideration of the problem's specifics, convergence speed, and solution
accuracy, necessitating further research and experimentation.
Table 1
Qualitative comparison of different PSO modifications
Name Description Limitations
Standard PSO Simple and resource efficient. Particles can get stuck in local
optima.
Adaptive PSO Balances exploration and Increased complexity due to
exploitation by dynamically dynamic inertial weight, which
adjusting the inertial weight, requires additional tuning
improving convergence speed compared to fixed-parameter
and solution quality. PSO options.
Cooperative PSO (CPSO) Aimed at solving the problem Particles can get stuck in local
of outliers through the optima.
cooperation of the particles.
Not suitable for tasks where
Gaussian PSO (GPSO) It only requires specifying the setting specific parameters is
number of particles before use. critical for optimal
performance.
Improves convergence Increased computational
Concurrent PSO (CONPSO) performance compared to the complexity due to parallel
original PSO. operations.
It can optimize both Not always as effective as
Binary PSO (BPSO) continuous and discrete specialized
specific types
algorithms for
of tasks (e.g.,
functions. continuous vs. discrete).
It is not always as effective in
Bare-Bones PSO Eliminates the speed formula, complex, multidimensional
making it simpler. search spaces where speed
control is important.
Particles are influenced by all Increased computational costs
Fully Informed PSO (FIPS) neighbors, not just the best due to the consideration of
one. information from all neighbors.
Designed for classification
Binary PSO for Classification tasks, showing promising Not suitable for other types of
results compared to machine optimization problems.
learning methods.
Uses a fuzzy system to adapt Increased
the
complexity due to
fuzziness of the system,
Fuzzy Adaptive PSO (FAPSO) the inertia weight, improving requiring additional
convergence. customization and expertise.
Specially designed to recognize Limited applicability to other
Guided PSO (GPSO) facial emotions, it
demonstrates promising problem
emotion
areas other than facial
detection.
accuracy.
Includes human learning Requires careful adjustment of
Self-Regulating PSO (SRPSO) strategies to improve
exploration and exploitation self-regulation mechanisms for
optimal performance.
processes.
Solves the problems of slow Tends to generalize poorly to
convergence and limitations of other problem areas or
Improved PSO (IPSO) the basic PSO when planning demonstrate stable
the trajectory of a mobile performance in different
robot. scenarios.
Designed to solve the Knapsack Increased complexity due to
Genotype Phenotype Modified problem, offering improved genotype-phenotype mapping,
Binary PSO (GPMBPSO) performance compared to which may require additional
BPSO. computing resources.
It is not always suitable for
Modified Binary PSO (MBPSO) Outperforms
algorithm.
the original BPSO other types of optimization
problems and requires
adaptation to a specific task.
Combines PSO with other Increased complexity due to its
algorithms (e.g., simulated hybrid
Hybrid PSO (HPSO) annealing) to improve multiple nature,algorithms
requiring
to be
performance in dynamic object configured.
layout problems.
Hybridizes PSO with statistical Increased complexity due to its
STPSO (Stochastic PSO) methods to solve stochastic hybrid multiple
nature,
algorithms
requiring
to be
optimization problems. configured.
While these PSO variations offer improvements over the standard PSO, there is limited evidence
of their effectiveness in real-world applications. Current literature indicates that no PSO variant is
universally optimal or improves PSO without introducing new constraints. Thus, selecting a specific
algorithm requires careful consideration of the problem's specifics, convergence speed, and solution
accuracy, necessitating further research and experimentation.
Having examined this, the authors believe that it is advisable to consider other ways to improve
the PSO algorithm, other than the above approaches. One of these alternatives is to integrate PSO
with neural networks (NN), which will allow to use the advantages of both approaches. PSO can be
used to optimize the NN architecture, find optimal values of weights and thresholds, or find optimal
hyperparameters. In turn, NNs can be used to model complex nonlinear dependencies and improve
PSO's ability to find solutions.
In addition, combining PSO with NNs can be especially useful in problems where many
parameters need to be considered or where the objective function is complex and multimodal. In
such cases, NNs can help PSO avoid local optima and find more accurate solutions (resolving outliers’
problem as well).
The use of hybrid approaches that combine PSO with NN may grant new opportunities for solving
complex optimization problems and improving the efficiency of existing solutions. To confirm this
hypothesis, additional research and experiments are needed to assess the potential of this approach
and determine its advantages and disadvantages.
5. Deep learning models used over PSO
Modifying and hybridizing PSO isn't the only way to improve it. Paper [8] reviews how integrating
collective intelligence, like self-organization and swarm intelligence, can enhance deep learning. The
authors explore using these principles to address deep learning challenges, such as combining
cellular automata with neural networks for image processing and rethinking reinforcement learning
with self-organizing agents. The authors identify four main areas of deep learning that have begun
to incorporate the ideas of collective intelligence:
1. Image processing
2. Deep Reinforcement Learning (DRL)
3. Multi-agent learning
4. Meta learning
Based on these studies, it can be assumed that the introduction of a reinforcement learning model
for outlier’s optimization in PSO has prerequisites for future research to overcome the limitations of
other algorithm modifications. For instance, it can be predicted that one of the potential advantages
of integrating reinforcement learning with PSO is that the introduction of neural network models
into swarm operation will solve the problem of overfitting. Reinforcement learning algorithms are
designed to learn optimal policies that generalize well to new environments [13], so it is reasonable
to consider such integration as conducive to an effective process of adaptation to various
optimization problems.
Let us consider an example of a possible potential application of the hybrid PSO-DRL approach.
The GPT models, such as ChatGPT by OpenAI, which have become a modern breakthrough in the
field of artificial intelligence, use deep neural networks with many parameters, which makes their
training and tuning a complex and resource-intensive process [14]. Using PSO to optimize the GPT
model architecture can help find the optimal number of layers, neurons in each layer, and types of
connections between them. This will reduce the number of model parameters, speed up its training,
and improve its ability to generate text.
In addition, PSO can be used to optimize hyperparameters like learning rate, data set size, and
regularization, balancing training speed and model accuracy. DRL can help model complex
relationships between parameters and performance, enhancing PSO's efficiency in finding optimal
solutions. Some studies, like [15], have explored combining these methods, showing that the
introduced parameter adaptation method based on reinforcement learning (RLAM) improves PSO's
convergence rate and outperforms other variants. However, RLAM increases computational
complexity, complicates implementation, and risks overfitting. Despite these challenges, combining
PSO and DRL could effectively optimize GPT models, improving performance, reducing resource
use, and speeding up development. It is also promising to combine the modified PSO algorithm with
reinforcement learning models. Such integration has the prerequisites for further improving the
convergence property of the modified algorithm. Optimal policies in reinforcement learning
algorithms are obtained by maximizing the reward signal, which can be used to control the search
process in an adaptive algorithm [16].
However, in the context of such integration, it is also worth noting potential limitations:
1. Additional complexity of initialization
2. Setting additional hyperparameters
3. Over-fitting of the RL model
In addition, determining the best strategy for integrating the reinforcement learning algorithm
with PSO for a particular optimization problem, as well as finding another possible method for
combining the two algorithms that could reduce the number of algorithm limitations while
improving the performance of the standard PSO, requires additional research. The implementation
of this approach, as well as experimental confirmation or refutation of its advantages and
disadvantages, is the subject of the author's future research.
6. Conclusions
Outliers in particle swarm optimization are a major challenge, influenced by factors like velocity,
position, and acceleration coefficients. Addressing their causes can improve convergence speed,
accuracy, stability, and reliability in complex search spaces. This article examines the causes,
concepts, and solutions to outlier issues in swarm optimization on the example of PSO, focusing on
methods that enhance convergence and reduce outliers, including adaptive methods, swarm
topologies, and hybrid algorithms.
For example, the adaptive particle swarm method balances exploration and fast convergence but
is more complex than standard PSO. Cooperative PSO aids particle cooperation but can get stuck in
local optima, while binary PSO handles both continuous and discrete parameters but may be less
efficient than specialized algorithms. It has been determined that none of the existing variations of
PSO is a universal solution; each comes with its own limitations.
It has been proposed to use of hybrid approaches combining PSO with neural networks and
reinforcement learning, which will grant new opportunities for solving complex optimization
problems and improving the efficiency of existing solutions. In contrast to algorithmic solutions, the
use of neural networks in combination with the particle swarm method (or its variations) would be
appropriate to obtain a positive practical result when applied to drone control systems or financial
systems for which other variations of algorithms are not optimal for one reason or another.
Further research will be aimed at studying and experimentally confirming or refuting the
advantages and disadvantages of the proposed approach, as well as developing a new method for
effective detection and management of outliers in swarm systems on the example of PSO.
References
[1] Misinem, A. A. Bakar, A. R. Hamdan, M. Z. A. Nazri. "A rough set outlier detection based on
particle swarm optimization", 10th international conference on intelligent systems design and
applications, Cairo, Egypt, 2010. pp. 1021-1025. doi: 10.1109/ISDA.2010.5687054.
[2] F. Schiano, P. M. Kornatowski, L. Cencetti, D. Floreano. "Reconfigurable drone system for
transportation of parcels with variable mass and size." IEEE Robotics and Automation Letters,
vol. 7, no. 4, pp. 12150-12157. Oct. 2022. doi: 10.1109/LRA.2022.3208716.
[3] A. A. Nathan, J. Rakesh, I. Kurmi, O. Bimber. "Drone swarm strategy for the detection and
tracking of occluded targets in complex environments." Communications Engineering, vol. 2,
55, 2023. doi: 10.1038/s44172-023-00104-0.
[4] S. G. Reid, K. M. Malan, A. P. Engelbrecht. "Carry trade portfolio optimization using particle
swarm optimization." 2014 IEEE Congress on Evolutionary Computation (CEC). Beijing, China,
pp. 3051-3058. 2014. doi: 10.1109/CEC.2014.6900497.
[5] J. Hamidi. "Control system design using particle swarm optimization (PSO)." International
Journal of Soft Computing and Engineering: Blue Eyes Intelligence Engineering & Sciences
Publication, vol. 1, issue 6, pp. 2231-2307. 2012. URL: https://www.ijsce.org/wp-
content/uploads/papers/v1i6/F0280111611.pdf.
[6] T.W. Gress, J. Denvir, J.I. Shapiro. "Effect of removing outliers on statistical inference:
implications to interpretation of experimental data in medical research." Marshall Journal of
Medicine, vol. 4, issue 2.9. 2018. doi: 10.18590/mjm.
[7] T. M. Shami, A. A. El-Saleh, M. Alswaitti, Q. Al-Tashi, M. A. Summakieh, S. Mirjalili. "Particle
swarm optimization: A comprehensive survey." IEEE Access, vol. 10, pp. 10031-10061. 2022. doi:
10.1109/ACCESS.2022.3142859.
[8] M. Jain, V. Saihjpal, N. Singh, S.B. Singh. "An overview of variants and advancements of PSO
algorithm." Appl. Sci. vol. 12, no. 17: 8392. 2022. doi: 10.3390/app12178392.
[9] J. Kennedy, R. Eberhart. "Particle swarm optimization." Proceedings of IEEE International
Conference on Neural Networks, vol. IV. pp. 1942–1948. 1995. doi:10.1109/ICNN.1995.488968.
[10] X. Hu, R. Shonkwiler, M. Spruill. "Random Restarts in Global Optimization." Georgia Tech
Library. Georgia Institute of Technology: School of Mathematics. 2009. URL:
http://hdl.handle.net/1853/31310.
[11] M. Barad. "Design of Experiments (DOE) — A Valuable Multi-Purpose Methodology." Applied
Mathematics, vol. 5, no 14, pp. 2120-2129. 2014. doi: 10.4236/am.2014.514206.
[12] Z-H. Zhan, J. Zhang, Y. Li, H.S-H. Chung. "Adaptive Particle Swarm Optimization." IEEE
Transactions on Systems, Man, and Cybernetics, vol. 39 (6), pp. 1362-1381.
doi:10.1109/TSMCB.2009.2015956.
[13] J. Shuford. "Deep Reinforcement Learning: Unleashing the Power of AI in Decision-Making."
Journal of Artificial Intelligence General Science JAIGS, vol. 1, issue 1. 2024. URL:
https://www.researchgate.net/publication/378335647_ARTICLE_INFO_Deep_Reinforcement_L
earning_Unleashing_the_Power_of_AI_in_Decision-Making
[14] A. Birhane, A. Kasirzadeh, D. Leslie. "Science in the age of large language models." Nature
Reviews Physics, vol. 5, pp. 277–280. doi: 10.1038/s42254-023-00581-4.
[15] S. Yin, M. Jin, H. Lu. "Reinforcement-learning-based parameter adaptation method for particle
swarm optimization." Complex Intell. Syst, vol. 9, pp. 5585–5609. 2023. doi: 10.1007/s40747-023-
01012-8.
[16] L. P. Kaelbling, M. L. Littman, A. W. Moore. "Reinforcement Learning: A Survey." Journal of
Artificial Intelligence Research, vol. 4. pp. 237–285. 1996. doi: 10.1613/jair.301.