Particle swarm optimization with composite particles in dynamic environments

This article is placed here with the permission of IEEE - Copyright @ 2010 IEEEIn recent years, there has been a growing interest in the study of particle swarm optimization (PSO) in dynamic environments. This paper presents a new PSO model, called PSO with composite particles (PSO-CP), to address dynamic optimization problems. PSO-CP partitions the swarm into a set of composite particles based on their similarity using a "worst first" principle. Inspired by the composite particle phenomenon in physics, the elementary members in each composite particle interact via a velocity-anisotropic reflection scheme to integrate valuable information for effectively and rapidly finding the promising optima in the search space. Each composite particle maintains the diversity by a scattering operator. In addition, an integral movement strategy is introduced to promote the swarm diversity. Experiments on a typical dynamic test benchmark problem provide a guideline for setting the involved parameters and show that PSO-CP is efficient in comparison with several state-of-the-art PSO algorithms for dynamic optimization problems.This work was supported in part by the Key Program of the National Natural Science Foundation (NNSF) of China under Grant 70931001 and 70771021, the Science Fund for Creative Research Group of the NNSF of China under Grant 60821063 and 70721001, the Ph.D. Programs Foundation of the Ministry of education of China under Grant 200801450008, and by the Engineering and Physical Sciences Research Council of U.K. under Grant EP/E060722/1

A convergence and diversity guided leader selection strategy for many-objective particle swarm optimization

Recently, particle swarm optimizer (PSO) is extended to solve many-objective optimization problems (MaOPs) and becomes a hot research topic in the field of evolutionary computation. Particularly, the leader particle selection (LPS) and the search direction used in a velocity update strategy are two crucial factors in PSOs. However, the LPS strategies for most existing PSOs are not so efficient in high-dimensional objective space, mainly due to the lack of convergence pressure or loss of diversity. In order to address these two issues and improve the performance of PSO in high-dimensional objective space, this paper proposes a convergence and diversity guided leader selection strategy for PSO, denoted as CDLS, in which different leader particles are adaptively selected for each particle based on its corresponding situation of convergence and diversity. In this way, a good tradeoff between the convergence and diversity can be achieved by CDLS. To verify the effectiveness of CDLS, it is embedded into the PSO search process of three well-known PSOs. Furthermore, a new variant of PSO combining with the CDLS strategy, namely PSO/CDLS, is also presented. The experimental results validate the superiority of our proposed CDLS strategy and the effectiveness of PSO/CDLS, when solving numerous MaOPs with regular and irregular Pareto fronts (PFs)

Metaheuristic design of feedforward neural networks: a review of two decades of research

Over the past two decades, the feedforward neural network (FNN) optimization has been a key interest among the researchers and practitioners of multiple disciplines. The FNN optimization is often viewed from the various perspectives: the optimization of weights, network architecture, activation nodes, learning parameters, learning environment, etc. Researchers adopted such different viewpoints mainly to improve the FNN's generalization ability. The gradient-descent algorithm such as backpropagation has been widely applied to optimize the FNNs. Its success is evident from the FNN's application to numerous real-world problems. However, due to the limitations of the gradient-based optimization methods, the metaheuristic algorithms including the evolutionary algorithms, swarm intelligence, etc., are still being widely explored by the researchers aiming to obtain generalized FNN for a given problem. This article attempts to summarize a broad spectrum of FNN optimization methodologies including conventional and metaheuristic approaches. This article also tries to connect various research directions emerged out of the FNN optimization practices, such as evolving neural network (NN), cooperative coevolution NN, complex-valued NN, deep learning, extreme learning machine, quantum NN, etc. Additionally, it provides interesting research challenges for future research to cope-up with the present information processing era

A new hybrid PSO algorithm based on a stochastic Markov chain model

International audienceBased on the recent research concerning the PageRank Algorithm used in the famous search engine Google, a new Inverse-PageRank-Particle Swarm Optimizer (I-PR-PSO) is presented in order to improve the performances of classic PSO. The resulted algorithm uses a stochastic Markov chain model to define an intelligent topological structure of the swarm's population, in which the better particles have an important influence on the others. In the presented experiments, calculations on some benchmark functions classically used to test optimization methods are performed, and the results are compared to different versions of the standard PSO, that is using different topological structures of the population. The experimental results show that I-PR-PSO can converge quicker on the tested functions, and can find better results in the solution domain than its tested peers

Solving Robotic Trajectory Sequential Writing Problem via Learning Character’s Structural and Sequential Information

The writing sequence of numerals or letters often affects aesthetic aspects of the writing outcomes. As such, it remains a challenge for robotic calligraphy systems to perform, mimicking human writers’ implicit intention. This article presents a new robot calligraphy system that is able to learn writing sequences with limited sequential information, producing writing results compatible to human writers with good diversity. In particular, the system innovatively applies a gated recurrent unit (GRU) network to generate robotic writing actions with the support of a prelabeled trajectory sequence vector. Also, a new evaluation method is proposed that considers the shape, trajectory sequence, and structural information of the writing outcome, thereby helping ensure the writing quality. A swarm optimization algorithm is exploited to create an optimal set of parameters of the proposed system. The proposed approach is evaluated using Arabic numerals, and the experimental results demonstrate the competitive writing performance of the system against state-of-the-art approaches regarding multiple criteria (including FID, MAE, PSNR, SSIM, and PerLoss), as well as diversity performance concerning variance and entropy. Importantly, the proposed GRU-based robotic motion planning system, supported with swarm optimization can learn from a small dataset, while producing calligraphy writing with diverse and aesthetically pleasing outcomes

Hybrid meta-heuristic algorithm based parameter optimization for extreme learning machines classification

Most classification algorithms suffer from manual parameter tuning and it affects the training computational time and accuracy performance. Extreme Learning Machines (ELM) emerged as a fast training machine learning algorithm that eliminates parameter tuning by randomly assigning the input weights and biases, and analytically determining the output weights using Moore Penrose generalized inverse method. However, the randomness assignment, does not guarantee an optimal set of input weights and biases of the hidden neurons. This will lead to ELM instability and local minimum solution. ELM performance also is affected by the network structure especially the number of hidden nodes. Too many hidden neurons will increase the network structure complexity and computational time. While too few hidden neuron numbers will affect the ELM generalization ability and reduce the accuracy. In this study, a heuristic-based ELM (HELM) scheme was designed to secure an optimal ELM structure. The results of HELM were validated with five rule-based hidden neuron selection schemes. Then HELM performance was compared with Support Vector Machine (SVM), k-Nearest Neighbour (KNN), and Classification and Regression Tree (CART) to investigate its relative competitiveness. Secondly, to improve the stability of ELM, the Moth-Flame Optimization algorithm is hybridized with ELM as MFO-ELM. MFO generates moths and optimizes their positions in the search space with a logarithm spiral model to obtain the optimal values of input weights and biases. The optimal weights and biases from the search space were passed into the ELM input space. However, it did not completely solve the problem of been stuck in the local extremum since MFO could not ensure a good balance between the exploration and exploitation of the search space. Thirdly, a co-evolutionary hybrid algorithm of the Cross-Entropy Moth-Flame Optimization Extreme Learning Machines (CEMFO-ELM) scheme was proposed. The hybrid of CE and MFO metaheuristic algorithms ensured a balance of exploration and exploitation in the search space and reduced the possibility of been trapped in the local minima. The performances of these schemes were evaluated on some selected medical datasets from the University of California, Irvine (UCI) machine learning repository, and compared with standard ELM, PSO-ELM, and CSO-ELM. The hybrid MFO-ELM algorithm enhanced the selection of optimal weights and biases for ELM, therefore improved its classification accuracy in a range of 0.4914 - 6.0762%, and up to 8.9390% with the other comparative ELM optimized meta-heuristic algorithms. The convergence curves plot show that the proposed hybrid CEMFO meta-heuristic algorithm ensured a balance between the exploration and exploitation in the search space, thereby improved the stability up to 53.75%. The overall findings showed that the proposed CEMFO-ELM provided better generalization performance on the classification of medical datasets. Thus, CEMFO-ELM is a suitable tool to be used not only in solving medical classification problems but potentially be used in other real-world problems