A Survey on Particle Swarm Optimization Algorithms for Multimodal Function Optimization
---
paper_title: Adaptively choosing niching parameters in a PSO

paper_content:

Niching techniques play an important role in evolutionary algorithms. Existing niching methods often require user-specified parameters, limiting their usefulness. This paper proposes a niching method for Particle Swarm Optimisation (PSO) where population statistics are used to adaptively determine the niching parameters during a run. The proposed niching method is compared to another niching based PSO, SPSO. Our results show that the proposed adaptive niching PSO can solve difficult multimodal functions more reliably and with fewer evaluations.
---
paper_title: Particle swarm optimization for multimodal functions: a clustering approach

paper_content:

The particle swarm optimization (PSO) algorithm is designed to find a single optimal solution and needs some modifications to be able to locate multiple optima on a multimodal function. In parallel with evolutionary computation algorithms, these modifications can be grouped in the framework of niching. In this work, we present a new approach to niching in PSO based on clustering particles to identify niches. The neighborhood structure, on which particles rely for communication, is exploited together with the niche information to locate multiple optima in parallel. Our approach was implemented in the k-means-based PSO (kPSO), which employs the standard k-means clustering algorithm, improved with a mechanism to adaptively identify the number of clusters. kPSO proved to be a competitive solution when compared with other existing algorithms, since it showed better performance on a benchmark set of multimodal functions.
---
paper_title: Genetic drift in sharing methods

paper_content:

Adding a sharing method to a genetic algorithm promotes the formation and maintenance of stable subpopulations. The paper explores the limits of sharing by deriving closed-form expressions for the expected time to disappearance of a subpopulation. The time to disappearance is shown to be an exponential function of population size, with relative subpopulation fitnesses determining the base of the exponential. However, disappearance time decreases rapidly as the number of subpopulations increases. Both theoretical and experimental illustrations are given of genetic drift in sharing. >
---
paper_title: Multimodal function optimization based on particle swarm optimization

paper_content:

In this paper, a new algorithm for the multimodal function optimization is proposed, based on the particle swarm optimization (PSO). A new method, named the multigrouped particle swarm optimization (MGPSO), keeps basic concepts of the PSO, and, thus, shows a more straightforward convergence compared to conventional hybrid type approaches. Moreover, the MGPSO has a unique advantage in that one can search N superior peaks of a multimodal function when the number of groups is N. The usefulness of the proposed algorithm was verified by the application to various case studies, including a practical electromagnetic optimization problem
---
paper_title: An Improved Particle Swarm Optimization Algorithm Mimicking Territorial Dispute Between Groups for Multimodal Function Optimization Problems

paper_content:

In the present paper, an improved particle swarm optimization (PSO) algorithm for multimodal function optimization is proposed. The new algorithm, named auto-tuning multigrouped PSO (AT-MGPSO) algorithm mimics natural phenomena in ecosystem such as territorial dispute between different group members and immigration of weak groups, resulting in automatic determination of the size of each group's territory and robust convergence. The usefulness of the proposed algorithm is verified by the application to a specially designed test function and a practical electromagnetic optimization problem.
---
paper_title: Multi-Species Particle Swarm Optimizer for Multimodal Function Optimization

paper_content:

This paper introduces a modified particle swarm optimizer (PSO) called the Multi-Species Particle Swarm Optimizer (MSPSO) for locating all the global minima of multi-modal functions. MSPSO extend the original PSO by dividing the particle swarm spatially into a multiple cluster called a species in a multi-dimensional search space. Each species explores a different area of the search space and tries to find out the global or local optima of that area. We test our MSPSO for several multi-modal functions with multiple global optima. Our MSPSO can successfully locate all the global optima of all the test functions, and in particular, can locate all 18 global optima of the two-dimensional Shubert function. We also examined how the performance of MSPSO depends on various algorithm parameters.
---
paper_title: Niching Without Niching Parameters: Particle Swarm Optimization Using a Ring Topology

paper_content:

Niching is an important technique for multimodal optimization. Most existing niching methods require specification of certain niching parameters in order to perform well. These niching parameters, often used to inform a niching algorithm how far apart between two closest optima or the number of optima in the search space, are typically difficult to set as they are problem dependent. This paper describes a simple yet effective niching algorithm, a particle swarm optimization (PSO) algorithm using a ring neighborhood topology, which does not require any niching parameters. A PSO algorithm using the ring topology can operate as a niching algorithm by using individual particles' local memories to form a stable network retaining the best positions found so far, while these particles explore the search space more broadly. Given a reasonably large population uniformly distributed in the search space, PSO algorithms using the ring topology are able to form stable niches across different local neighborhoods, eventually locating multiple global/local optima. The complexity of these niching algorithms is only O(N), where N is the population size. Experimental results suggest that PSO algorithms using the ring topology are able to provide superior and more consistent performance over some existing PSO niching algorithms that require niching parameters.
---
paper_title: Adaptively Choosing Neighbourhood Bests Using Species in a Particle Swarm Optimizer for Multimodal Function Optimization

paper_content:

This paper proposes an improved particle swarm optimizer using the notion of species to determine its neighbourhood best values, for solving multimodal optimization problems. In the proposed species- based PSO (SPSO), the swarm population is divided into species sub- populations based on their similarity. Each species is grouped around a dominating particle called the species seed. At each iteration step, species seeds are identified from the entire population and then adopted as neig- hbourhood bests for these individual species groups separately. Species are formed adaptively at each step based on the feedback obtained from the multimodal fitness landscape. Over successive iterations, species are able to simultaneously optimize towards multiple optima, regardless of if they are global or local optima. Our experiments demonstrated that SPSO is very effective in dealing with multimodal optimization functions with lower dimensions.
---
paper_title: Enhancing the robustness of a speciation-based PSO

paper_content:

Speciation encourages an evolutionary algorithm to locate multiple solutions in multimodal environments. Speciation algorithms often require a user to specify a parameter to de fi ne the species radius, which can be a major drawback since this knowledge may not be available a priori. This paper proposes a technique using a time-based convergence measure to overcome this problem. The proposed method is used to enhance the performance of a speciation-based PSO (SPSO) and has been shown to be robust over a wide range of values for this user-speci fy ed parameter.
---
paper_title: PSO with sharing for multimodal function optimization

paper_content:

The particle swarm optimizer (PSO) has exhibited good performance on unimodal problem. But on multimodal problem it tends to suffer from premature convergence. In this paper, we propose a modification of the base PSO named fitness sharing particle swarm optimizer (FSPSO) to solve such problem. Through using fitness sharing technique, FSPSO can maintain diversity and avoid convergence to local solution successfully. Experiment indicates that FSPSO is an effective strategy on multimodal problem.
---
paper_title: A Species Conserving Genetic Algorithm for Multimodal Function Optimization

paper_content:

This paper introduces a new technique called species conservation for evolving parallel subpopulations. The technique is based on the concept of dividing the population into several species according to their similarity. Each of these species is built around a dominating individual called the species seed. Species seeds found in the current generation are saved (conserved) by moving them into the next generation. Our technique has proved to be very effective in finding multiple solutions of multimodal optimization problems. We demonstrate this by applying it to a set of test problems, including some problems known to be deceptive to genetic algorithms.
---
paper_title: Genetic drift in sharing methods

paper_content:

Adding a sharing method to a genetic algorithm promotes the formation and maintenance of stable subpopulations. The paper explores the limits of sharing by deriving closed-form expressions for the expected time to disappearance of a subpopulation. The time to disappearance is shown to be an exponential function of population size, with relative subpopulation fitnesses determining the base of the exponential. However, disappearance time decreases rapidly as the number of subpopulations increases. Both theoretical and experimental illustrations are given of genetic drift in sharing. >
---
paper_title: A multimodal particle swarm optimizer based on fitness Euclidean-distance ratio

paper_content:

One of the most critical issues that remains to be fully addressed in existing multimodal evolutionary algorithms is the difficulty in pre-specifying parameters used for estimating how far apart optima are. These parameters are typically represented as some sorts of niching parameters in existing EAs. Without prior knowledge of a problem, it is almost impossible to determine appropriate values for such niching parameters. This paper proposes a PSO for multimodal optimization that removes the need of these niching parameters. Our results show that the proposed algorithm, Fitness Euclidean-distance Ratio based PSO (FER-PSO) is able to reliably locate multiple global optima on the search landscape over some widely used multimodal optimization test functions, given that the population size is sufficiently large.
---
paper_title: Multimodal function optimization based on particle swarm optimization

paper_content:

In this paper, a new algorithm for the multimodal function optimization is proposed, based on the particle swarm optimization (PSO). A new method, named the multigrouped particle swarm optimization (MGPSO), keeps basic concepts of the PSO, and, thus, shows a more straightforward convergence compared to conventional hybrid type approaches. Moreover, the MGPSO has a unique advantage in that one can search N superior peaks of a multimodal function when the number of groups is N. The usefulness of the proposed algorithm was verified by the application to various case studies, including a practical electromagnetic optimization problem
---
paper_title: Dynamic Niche Clustering: a fuzzy variable radius niching technique for multimodal optimisation in GAs

paper_content:

This paper describes the recent developments and improvements made to the variable radius niching technique called Dynamic Niche Clustering (DNC). DNC is fitness sharing based technique that employs a separate population of overlapping fuzzy niches with independent radii which operate in the decoded parameter space, and are maintained alongside the normal GA population. We describe a speedup process that can be applied to the initial generation which greatly reduces the complexity of the initial stages. A split operator is also introduced that is designed to counteract the excessive growth of niches, and it is shown that this improves the overall robustness of the technique. Finally, the effect of local elitism is documented and compared to the performance of the basic DNC technique on a selection of 2D test functions. The paper is concluded with a view to future work to be undertaken on the technique.
---
paper_title: A Sequential Niche Technique for Multimodal Function Optimization

paper_content:

A technique is described that allows unimodal function optimization methods to be extended to locate all optima of multimodal problems efficiently. We describe an algorithm based on a traditional genetic algorithm (GA). This technique involves iterating the GA but uses knowledge gained during one iteration to avoid re-searching, on subsequent iterations, regions of problem space where solutions have already been found. This gain is achieved by applying a fitness derating function to the raw fitness function, so that fitness values are depressed in the regions of the problem space where solutions have already been found. Consequently, the likelihood of discovering a new solution on each iteration is dramatically increased. The technique may be used with various styles of GAs or with other optimization methods, such as simulated annealing. The effectiveness of the algorithm is demonstrated on a number of multimodal test functions. The technique is at least as fast as fitness sharing methods. It provides an acceleration of between 1 and l0p on a problem with p optima, depending on the value of p and the convergence time complexity.
---
paper_title: A novel algorithm for multimodal function optimization based on evolution strategy

paper_content:

In this paper, a novel algorithm for multimodal function optimization is proposed, based on the concept of evolution strategy. A new concept, named restricted evolution, shows more improved characteristics than conventional approaches that have been used for multimodal function optimization. The efficiency and usefulness of the proposed method will be verified by the application to various cases including practical optimization problems.
---
paper_title: Stereotyping: improving particle swarm performance with cluster analysis

paper_content:

Individuals in the particle swarm population were "stereotyped" by cluster analysis of their previous best positions. The cluster centers then were substituted for the individuals' and neighbors' best previous positions in the algorithm. The experiments, which were inspired by the social-psychological metaphor of social stereotyping, found that performance could be generally improved by substituting individuals', but not neighbors', cluster centers for their previous bests.
---
paper_title: An artificial immune network for multimodal function optimization

paper_content:

This paper presents the adaptation of an immune network model, originally proposed to perform information compression and data clustering, to solve multimodal function optimization problems. The algorithm is described theoretically and empirically compared with similar approaches from the literature. The main features of the algorithm include: automatic determination of the population size, combination of local with global search (exploitation plus exploration of the fitness landscape), defined convergence criterion, and capability of locating and maintaining stable local optima solutions.
---
paper_title: Multi-Species Particle Swarm Optimizer for Multimodal Function Optimization

paper_content:

This paper introduces a modified particle swarm optimizer (PSO) called the Multi-Species Particle Swarm Optimizer (MSPSO) for locating all the global minima of multi-modal functions. MSPSO extend the original PSO by dividing the particle swarm spatially into a multiple cluster called a species in a multi-dimensional search space. Each species explores a different area of the search space and tries to find out the global or local optima of that area. We test our MSPSO for several multi-modal functions with multiple global optima. Our MSPSO can successfully locate all the global optima of all the test functions, and in particular, can locate all 18 global optima of the two-dimensional Shubert function. We also examined how the performance of MSPSO depends on various algorithm parameters.
---
paper_title: On the computation of all global minimizers through particle swarm optimization

paper_content:

This paper presents approaches for effectively computing all global minimizers of an objective function. The approaches include transformations of the objective function through the recently proposed deflection and stretching techniques, as well as a repulsion source at each detected minimizer. The aforementioned techniques are incorporated in the context of the particle swarm optimization (PSO) method, resulting in an efficient algorithm which has the ability to avoid previously detected solutions and, thus, detect all global minimizers of a function. Experimental results on benchmark problems originating from the fields of global optimization, dynamical systems, and game theory, are reported, and conclusions are derived.
---
paper_title: Adaptively Choosing Neighbourhood Bests Using Species in a Particle Swarm Optimizer for Multimodal Function Optimization

paper_content:

This paper proposes an improved particle swarm optimizer using the notion of species to determine its neighbourhood best values, for solving multimodal optimization problems. In the proposed species- based PSO (SPSO), the swarm population is divided into species sub- populations based on their similarity. Each species is grouped around a dominating particle called the species seed. At each iteration step, species seeds are identified from the entire population and then adopted as neig- hbourhood bests for these individual species groups separately. Species are formed adaptively at each step based on the feedback obtained from the multimodal fitness landscape. Over successive iterations, species are able to simultaneously optimize towards multiple optima, regardless of if they are global or local optima. Our experiments demonstrated that SPSO is very effective in dealing with multimodal optimization functions with lower dimensions.
---
paper_title: Reproductive adaptive plans

paper_content:

This paper traces the experimental development of a new class of powerful and flexible adaptive plans, called reproductive plans. Adaptive plans are formally presented as search procedures for locating superior devices in an extremely large space. Reproductive adaptive plans operate by treating the search procedure as an evolutionary process of finding the best organism in a certain environment. Devices are represented as strings or chromosomes. At each “generation” or time step a population of devices is tested and each device is copied (rewarded) according to its performance. Then the copies “mate” using a number of genetic-like operators to produce a modified population of devices. In this particular study devices are pattern recognition programs although they could be any set of modifiable procedures. Much of the work is concerned with experimentally testing and improving the general reproductive plan to achieve fast and continuous adaptation.
---
paper_title: Multimodal optimization using crowding-based differential evolution

paper_content:

Multimodal optimization is an important area of active research within the evolutionary computation community. The ability of algorithms to discover and maintain multiple optima is of great importance - in particular when several global optima exist or when other high-quality solutions might be of interest. The differential evolution algorithm (DE) is extended with a crowding scheme making it capable of tracking and maintaining multiple optima. The introduced CrowdingDE algorithm is compared with a DE using the well-known sharing scheme that penalizes similar candidate solutions. In conclusion, the introduced CrowdingDE outperformed the sharing-based DE algorithm on fourteen commonly used benchmark problems.
---
paper_title: A clearing procedure as a niching method for genetic algorithms

paper_content:

The clearing procedure is a niching method inspired by the principle stated by J.H. Holland (1975) - that of sharing limited resources within subpopulations of individuals characterized by some similarities - but instead of evenly sharing the available resources among the individuals of a subpopulation, the clearing procedure supplies these resources only to the best individuals of each subpopulation. The clearing is naturally adapted to elitist strategies. This can significantly improve the performance of genetic algorithms (GAs) applied to multimodal optimization. Moreover, the clearing procedure allows a GA to efficiently reduce the genetic drift when used with an appropriate selection operator. Some experimental results are presented for a massively multimodal deceptive function optimization.
---
paper_title: Adaptively choosing niching parameters in a PSO

paper_content:

Niching techniques play an important role in evolutionary algorithms. Existing niching methods often require user-specified parameters, limiting their usefulness. This paper proposes a niching method for Particle Swarm Optimisation (PSO) where population statistics are used to adaptively determine the niching parameters during a run. The proposed niching method is compared to another niching based PSO, SPSO. Our results show that the proposed adaptive niching PSO can solve difficult multimodal functions more reliably and with fewer evaluations.
---
paper_title: Particle swarm optimization

paper_content:

A concept for the optimization of nonlinear functions using particle swarm methodology is introduced. The evolution of several paradigms is outlined, and an implementation of one of the paradigms is discussed. Benchmark testing of the paradigm is described, and applications, including nonlinear function optimization and neural network training, are proposed. The relationships between particle swarm optimization and both artificial life and genetic algorithms are described.
---
paper_title: Particle swarm optimization for multimodal functions: a clustering approach

paper_content:

The particle swarm optimization (PSO) algorithm is designed to find a single optimal solution and needs some modifications to be able to locate multiple optima on a multimodal function. In parallel with evolutionary computation algorithms, these modifications can be grouped in the framework of niching. In this work, we present a new approach to niching in PSO based on clustering particles to identify niches. The neighborhood structure, on which particles rely for communication, is exploited together with the niche information to locate multiple optima in parallel. Our approach was implemented in the k-means-based PSO (kPSO), which employs the standard k-means clustering algorithm, improved with a mechanism to adaptively identify the number of clusters. kPSO proved to be a competitive solution when compared with other existing algorithms, since it showed better performance on a benchmark set of multimodal functions.
---
paper_title: PSO with sharing for multimodal function optimization

paper_content:

The particle swarm optimizer (PSO) has exhibited good performance on unimodal problem. But on multimodal problem it tends to suffer from premature convergence. In this paper, we propose a modification of the base PSO named fitness sharing particle swarm optimizer (FSPSO) to solve such problem. Through using fitness sharing technique, FSPSO can maintain diversity and avoid convergence to local solution successfully. Experiment indicates that FSPSO is an effective strategy on multimodal problem.
---
paper_title: Genetic drift in sharing methods

paper_content:

Adding a sharing method to a genetic algorithm promotes the formation and maintenance of stable subpopulations. The paper explores the limits of sharing by deriving closed-form expressions for the expected time to disappearance of a subpopulation. The time to disappearance is shown to be an exponential function of population size, with relative subpopulation fitnesses determining the base of the exponential. However, disappearance time decreases rapidly as the number of subpopulations increases. Both theoretical and experimental illustrations are given of genetic drift in sharing. >
---
paper_title: A multimodal particle swarm optimizer based on fitness Euclidean-distance ratio

paper_content:

One of the most critical issues that remains to be fully addressed in existing multimodal evolutionary algorithms is the difficulty in pre-specifying parameters used for estimating how far apart optima are. These parameters are typically represented as some sorts of niching parameters in existing EAs. Without prior knowledge of a problem, it is almost impossible to determine appropriate values for such niching parameters. This paper proposes a PSO for multimodal optimization that removes the need of these niching parameters. Our results show that the proposed algorithm, Fitness Euclidean-distance Ratio based PSO (FER-PSO) is able to reliably locate multiple global optima on the search landscape over some widely used multimodal optimization test functions, given that the population size is sufficiently large.
---
paper_title: Multimodal function optimization based on particle swarm optimization

paper_content:

In this paper, a new algorithm for the multimodal function optimization is proposed, based on the particle swarm optimization (PSO). A new method, named the multigrouped particle swarm optimization (MGPSO), keeps basic concepts of the PSO, and, thus, shows a more straightforward convergence compared to conventional hybrid type approaches. Moreover, the MGPSO has a unique advantage in that one can search N superior peaks of a multimodal function when the number of groups is N. The usefulness of the proposed algorithm was verified by the application to various case studies, including a practical electromagnetic optimization problem
---
paper_title: An Improved Particle Swarm Optimization Algorithm Mimicking Territorial Dispute Between Groups for Multimodal Function Optimization Problems

paper_content:

In the present paper, an improved particle swarm optimization (PSO) algorithm for multimodal function optimization is proposed. The new algorithm, named auto-tuning multigrouped PSO (AT-MGPSO) algorithm mimics natural phenomena in ecosystem such as territorial dispute between different group members and immigration of weak groups, resulting in automatic determination of the size of each group's territory and robust convergence. The usefulness of the proposed algorithm is verified by the application to a specially designed test function and a practical electromagnetic optimization problem.
---
paper_title: Stereotyping: improving particle swarm performance with cluster analysis

paper_content:

Individuals in the particle swarm population were "stereotyped" by cluster analysis of their previous best positions. The cluster centers then were substituted for the individuals' and neighbors' best previous positions in the algorithm. The experiments, which were inspired by the social-psychological metaphor of social stereotyping, found that performance could be generally improved by substituting individuals', but not neighbors', cluster centers for their previous bests.
---
paper_title: Multi-Species Particle Swarm Optimizer for Multimodal Function Optimization

paper_content:

This paper introduces a modified particle swarm optimizer (PSO) called the Multi-Species Particle Swarm Optimizer (MSPSO) for locating all the global minima of multi-modal functions. MSPSO extend the original PSO by dividing the particle swarm spatially into a multiple cluster called a species in a multi-dimensional search space. Each species explores a different area of the search space and tries to find out the global or local optima of that area. We test our MSPSO for several multi-modal functions with multiple global optima. Our MSPSO can successfully locate all the global optima of all the test functions, and in particular, can locate all 18 global optima of the two-dimensional Shubert function. We also examined how the performance of MSPSO depends on various algorithm parameters.
---
paper_title: Niching Without Niching Parameters: Particle Swarm Optimization Using a Ring Topology

paper_content:

Niching is an important technique for multimodal optimization. Most existing niching methods require specification of certain niching parameters in order to perform well. These niching parameters, often used to inform a niching algorithm how far apart between two closest optima or the number of optima in the search space, are typically difficult to set as they are problem dependent. This paper describes a simple yet effective niching algorithm, a particle swarm optimization (PSO) algorithm using a ring neighborhood topology, which does not require any niching parameters. A PSO algorithm using the ring topology can operate as a niching algorithm by using individual particles' local memories to form a stable network retaining the best positions found so far, while these particles explore the search space more broadly. Given a reasonably large population uniformly distributed in the search space, PSO algorithms using the ring topology are able to form stable niches across different local neighborhoods, eventually locating multiple global/local optima. The complexity of these niching algorithms is only O(N), where N is the population size. Experimental results suggest that PSO algorithms using the ring topology are able to provide superior and more consistent performance over some existing PSO niching algorithms that require niching parameters.
---
paper_title: On the computation of all global minimizers through particle swarm optimization

paper_content:

This paper presents approaches for effectively computing all global minimizers of an objective function. The approaches include transformations of the objective function through the recently proposed deflection and stretching techniques, as well as a repulsion source at each detected minimizer. The aforementioned techniques are incorporated in the context of the particle swarm optimization (PSO) method, resulting in an efficient algorithm which has the ability to avoid previously detected solutions and, thus, detect all global minimizers of a function. Experimental results on benchmark problems originating from the fields of global optimization, dynamical systems, and game theory, are reported, and conclusions are derived.
---
paper_title: Adaptively Choosing Neighbourhood Bests Using Species in a Particle Swarm Optimizer for Multimodal Function Optimization

paper_content:

This paper proposes an improved particle swarm optimizer using the notion of species to determine its neighbourhood best values, for solving multimodal optimization problems. In the proposed species- based PSO (SPSO), the swarm population is divided into species sub- populations based on their similarity. Each species is grouped around a dominating particle called the species seed. At each iteration step, species seeds are identified from the entire population and then adopted as neig- hbourhood bests for these individual species groups separately. Species are formed adaptively at each step based on the feedback obtained from the multimodal fitness landscape. Over successive iterations, species are able to simultaneously optimize towards multiple optima, regardless of if they are global or local optima. Our experiments demonstrated that SPSO is very effective in dealing with multimodal optimization functions with lower dimensions.
---
paper_title: Reproductive adaptive plans

paper_content:

This paper traces the experimental development of a new class of powerful and flexible adaptive plans, called reproductive plans. Adaptive plans are formally presented as search procedures for locating superior devices in an extremely large space. Reproductive adaptive plans operate by treating the search procedure as an evolutionary process of finding the best organism in a certain environment. Devices are represented as strings or chromosomes. At each “generation” or time step a population of devices is tested and each device is copied (rewarded) according to its performance. Then the copies “mate” using a number of genetic-like operators to produce a modified population of devices. In this particular study devices are pattern recognition programs although they could be any set of modifiable procedures. Much of the work is concerned with experimentally testing and improving the general reproductive plan to achieve fast and continuous adaptation.
---
paper_title: Enhancing the robustness of a speciation-based PSO

paper_content:

Speciation encourages an evolutionary algorithm to locate multiple solutions in multimodal environments. Speciation algorithms often require a user to specify a parameter to de fi ne the species radius, which can be a major drawback since this knowledge may not be available a priori. This paper proposes a technique using a time-based convergence measure to overcome this problem. The proposed method is used to enhance the performance of a speciation-based PSO (SPSO) and has been shown to be robust over a wide range of values for this user-speci fy ed parameter.
---
paper_title: Evolutionary computation based cryptanalysis: A first study

paper_content:

In this contribution we apply the particle swarm optimization method, which originates from the field of evolutionary computation, to address an interesting problem introduced by the cryptanalysis of block-cipher cryptosystems. The results on the data encryption standard reduced to four rounds indicate that this is a promising approach. 2005 Elsevier Ltd. All rights reserved.
---
paper_title: Multimodal function optimization based on particle swarm optimization

paper_content:

In this paper, a new algorithm for the multimodal function optimization is proposed, based on the particle swarm optimization (PSO). A new method, named the multigrouped particle swarm optimization (MGPSO), keeps basic concepts of the PSO, and, thus, shows a more straightforward convergence compared to conventional hybrid type approaches. Moreover, the MGPSO has a unique advantage in that one can search N superior peaks of a multimodal function when the number of groups is N. The usefulness of the proposed algorithm was verified by the application to various case studies, including a practical electromagnetic optimization problem
---
paper_title: Niching Without Niching Parameters: Particle Swarm Optimization Using a Ring Topology

paper_content:

Niching is an important technique for multimodal optimization. Most existing niching methods require specification of certain niching parameters in order to perform well. These niching parameters, often used to inform a niching algorithm how far apart between two closest optima or the number of optima in the search space, are typically difficult to set as they are problem dependent. This paper describes a simple yet effective niching algorithm, a particle swarm optimization (PSO) algorithm using a ring neighborhood topology, which does not require any niching parameters. A PSO algorithm using the ring topology can operate as a niching algorithm by using individual particles' local memories to form a stable network retaining the best positions found so far, while these particles explore the search space more broadly. Given a reasonably large population uniformly distributed in the search space, PSO algorithms using the ring topology are able to form stable niches across different local neighborhoods, eventually locating multiple global/local optima. The complexity of these niching algorithms is only O(N), where N is the population size. Experimental results suggest that PSO algorithms using the ring topology are able to provide superior and more consistent performance over some existing PSO niching algorithms that require niching parameters.
---
paper_title: K-means Algorithm Based on Particle Swarm Optimization Algorithm for Anomaly Intrusion Detection

paper_content:

K-means as a clustering algorithm has been studied in intrusion detection. However, with the deficiency of global search ability it is not satisfactory. Particle swarm optimization (PSO) is one of the evolutionary computation techniques based on swarm intelligence, which has high global search ability. So K-means algorithm based on PSO (PSO-KM) is proposed in this paper. Experiment over network connection records from KDD CUP 1999 data set was implemented to evaluate the proposed method. A Bayesian classifier was trained to select some fields in the data set. The experimental results clearly showed the outstanding performance of the proposed method.
---

Title: A Survey on Particle Swarm Optimization Algorithms for Multimodal Function Optimization

Section 1: INTRODUCTION
Description 1: Explain the concept of Multimodal Function Optimization and the motivation behind using Evolutionary Algorithms, particularly Particle Swarm Optimization (PSO), for these problems.

Section 2: NICHING TECHNIQUES
Description 2: Describe the different niching techniques used to maintain diversity in populations, such as crowding methods, fitness sharing, and species conservation, and their application in solving multimodal function optimization problems.

Section 3: MULTIMODAL PARTICLE SWARM OPTIMIZATION
Description 3: Review the development of Particle Swarm Optimization algorithms tailored for multimodal function optimization, discussing various PSO-based methods and their performance under different conditions.

Section 4: APPLICATIONS TO MULTIMODAL FUNCTION OPTIMIZATION
Description 4: Discuss real-world applications of multimodal function optimization, including neural network training, engineering design, cryptography, and intrusion detection.

Section 5: CONCLUSIONS
Description 5: Summarize the current state of multimodal function optimization algorithms based on Evolutionary Algorithms, highlight the challenges, and suggest future research directions to improve the flexibility, efficiency, and applicability of these algorithms.