Learning-Based Multi-Directional Adaptive PSO

Particle swarm optimisation (PSO) was developed by Kennedy and Eberhart in 1995 (Kennedy & Eberhart, 1995) inspired by the collective behaviour of natural birds or fish. PSO is a stochastic optimisation technique that uses a behaviour of population composed by many search points called particle. In spite of easy implementation in computer algorithms, it is well known as a powerful numerical optimizer. In the typical PSO algorithms, a set of particles searches the optimal solution in the problem space efficiently, by sharing the common attractor called global best. There are many modified versions of PSO by improving convergence property to a certain problem. While, a standard PSO is defined by Bratton and Kennedy (Bratton & Kennedy, 2007) to give a real standard for PSO studies. PSO seems as one of the evolutionary computations (ECs), and it has been shown that PSO is comparable to a genetic algorithm (Angeline, 1998). Thus, a lot of studies have demonstrated the effectiveness of PSO family in optimizing various continuous and discrete optimization problems. And a plenty of applications of PSO, such as the neural network training, PID controller tuning, electric system optimisation have been studied and achieved well results (Kennedy, 1997). However, PSO is often failed in searching the global optimal solution in the case of the objective function has a large number of dimensions. The reason of this phenomenon is not only existence of the local optimal solutions, the velocities of the particles sometimes lapsed into the degeneracy, so that the successive range is restricted in the sub-plain of the whole search hyper-plain. The sub-plane that is defined by finite number of particle velocities is a partial space in the whole search space. The issue of local optima in PSO has been studied and proposed several modifications on the basic particle driven equation (Parsopoulos et al., 2001; Hendtlass, 2005; Liang et al., 2006). There used a kind of adaptation technique or randomized method (e.g. mutation in evolutionary computations) to keep particles velocities or to accelerate them. Although such improvements work well and have ability to avoid fall in the local optima, the problem of early convergence by the degeneracy of some dimensions is still remaining, even if there are no local optima. Hence the PSO algorithm does not always work well for the high-dimensional function.

A velocity-based butterfly optimization algorithm for high-dimensional optimization and feature selection

Cloud computing and big data: Technologies and applications

The term "Artificial Human Optimization" was first created by the corresponding author of this paper in December 2016, when he published a paper titled "Entrepreneur : Artificial Human Optimization" in Transactions on Machine Learning and Artificial Intelligence (TMLAI) Volume 4, No 6 in December 2016. (December 2016). The Artificial Human Optimization Field is described as the collection of all optimization methods suggested based on Artificial Humans, according to a paper released in 2016. In the real world, we (Humans) are responsible for resolving issues. Artificial Humans imitate real Humans in the search space and solve optimization issues in the same way. The basic entities in the solution space of Particle Swarm Optimization (PSO) are Artificial Birds, whereas the basic entities in the search space of Artificial Human Optimization are Artificial Humans. Each Artificial Human is associated with a certain location in the solution space. The following are ten strategies for Artificial Human Optimization :“Human Bhagavad Gita Particle Swarm Optimization (HBGPSO)”, “Human Poverty Particle Swarm Optimization (HPPSO)”, “Human Dedication Particle Swarm Optimization (HuDePSO)”, “Human Selection Particle Swarm Optimization (HuSePSO)”, “Human Safety Particle Swarm Optimization (HuSaPSO)”, “Human Kindness Particle Swarm Optimization (HKPSO)”, “Human Relaxation Particle Swarm Optimization (HRPSO)”, “Multiple Strategy Human Particle Swarm Optimization (MSHPSO)”, “Human Thinking Particle Swarm Optimization (HTPSO)”, “Human Disease Particle Swarm Optimization (HDPSO)”. The results of applying ten Artificial Human Optimization methods to various benchmark functions are presented in this paper.&nbsp

Since chaos systems generally have the intrinsic properties of sensitivity to initial conditions, topological mixing and density of periodic orbits, they may tactfully use the chaotic ergodic orbits to achieve the global optimum or their better approximation to given cost functions with high probability. During the past decade, they have increasingly received much attention from academic community and industry society throughout the world. To improve the performance of particle swarm optimization (PSO), we herein propose a chaotic proportional integral derivative (PID) controlling PSO algorithm by the hybridization of chaotic logistic dynamics and hierarchical inertia weight. The hierarchical inertia weight coefficients are determined in accordance with the present fitness values of the local best positions so as to adaptively expand the particles’ search space. Moreover, the chaotic logistic map is not only used in the substitution of the two random parameters affecting the convergence behavior, but also used in the chaotic local search for the global best position so as to easily avoid the particles’ premature behaviors via the whole search space. Thereafter, the convergent analysis of chaotic PID controlling PSO is under deep investigation. Empirical simulation results demonstrate that compared with other several chaotic PSO algorithms like chaotic PSO with the logistic map, chaotic PSO with the tent map and chaotic catfish PSO with the logistic map, chaotic PID controlling PSO exhibits much better search efficiency and quality when solving the optimization problems. Additionally, the parameter estimation of a nonlinear dynamic system also further clarifies its superiority to chaotic catfish PSO, genetic algorithm (GA) and PSO.

Particle swarm optimization (PSO) is a powerful stochastic evolutionary algorithm that is used to find the global optimum solution in search space. However, PSO often easily fall into local minima because the particles could quickly converge to a position by the attraction of the best particles. Under this circumstance, all the particles could hardly be improved. This paper presents a hybrid PSO, namely LSPSO, to solve this problem by employing an adaptive local search operator. Experimental results on 8 well-known benchmark problems show that LSPSO achieves better results than the standard PSO, PSO with Gaussian mutation and PSO with Cauchy mutation on majority of test problems.

Particle swarm optimization (PSO) is a recently developed optimization method that has attracted interest of researchers in various areas. PSO has been shown to be effective in solving a variety of complex optimization problems. With properly chosen parameters, PSO can converge to local optima. However, conventional PSO does not have global convergence. Empirical evidences indicate that the PSO algorithm may fail to reach global optimal solutions for complex problems. We propose to combine the branch-and-bound framework with the particle swarm optimization algorithm. With this integrated approach, convergence to global optimal solutions is theoretically guaranteed. We have developed and implemented the BB-PSO algorithm that combines the efficiency of PSO and effectiveness of the branch-and-bound method. The BB-PSO method was tested with a set of standard benchmark optimization problems. Experimental results confirm that BB-PSO is effective in finding global optimal solutions to problems that may cause difficulties for the PSO algorithm.

Particle swarm optimization (PSO) is a stochastic population-based algorithm which was originally introduced by Kennedy and Eberhart [1]. This optimization algorithm is motivated by intelligent collective behavior of some animals such as flocks of birds or schools of fish. As in most of the metaheuristic optimization algorithms, in PSO, a population of individuals, known as particles, are evolved through successive iterations. The most important advantages of PSO, compared to other optimization strategies, are its easy implementation and few parameters requiring adjustment. Since the initial development of PSO by Kennedy and Eberhart, several variants of this algorithm have been proposed by researchers. The first modification was introducing an inertia weight parameter in the velocity update equation of the initial PSO-a PSO model which is now accepted as the global best PSO algorithm [2]. The goal of the inertia weight parameter is to balance the exploration and exploitation characteristics of PSO. Generally, large inertia weight values are expected to increase the velocity of the particles and improve the long-range exploration of the PSO algorithm, while low inertia values increase the short-range exploration. Due to the strong effect of the inertia weight on the performance of PSO, many researchers have investigated different inertia weight control approaches during the past decades, and many different strategies have been proposed. Various inertia weighting strategies can be categorized into three main classes (Figure 7.1): (1) constant or random, (2) time-varying, and (3) adaptive inertia weights. The first class contains strategies in which the value of the inertia weight is constant during the search or is determined randomly. In the second class, the inertia weight is defined as a function of time (iteration number), and hence these strategies are referred to as time-varying inertia weight strategies. These methods are not considered adaptive since they do not monitor the situation of the particles in the search space, and the value of the inertia weight in each iteration is known before the execution of the algorithm. The third class of the inertia weight strategies consists of those methods which use a feedback parameter to monitor the state of the algorithm and adjust the value of the inertia weight based on the feedback parameter's value. This chapter presents the major existing inertia weight control strategies in the above three categories and discusses examples of each category in detail. The remainder of this chapter is organized as follows. The next section gives a short review of the PSO algorithm, and the role ofthe inertia weight parameter in the velocity update equation. Sections 7.2-7.4 review the three groups of inertia weight strategies, constant or random, time-varying, and adaptive models. Section 7.5 reports some experimental evaluations of different inertia weight models. Finally, Section 7.6 concludes this chapter. A short description of the symbols frequently used in this chapter is shown in Table 7.1.

Sub-pixel displacement measurement in Digital Image Correlation (DIC) is an optimization problem in search of a point of the deformed image where has the maximum correlation coefficient value to the point of the reference image. Particle Swarm Optimization (PSO) is a novel swarm intelligence algorithm which has great prospect in multidimensional nonlinear optimization because of its advantages of high convergence rate, global search effectiveness, robustness and having few parameters. In this paper, PSO is first applied into DIC to get sub-pixel displacement fields with our aim of proving the feasibility of this method. Two displacements and four deformation gradients for a subset of DIC can all be taken into PSO, while we only take the first two displacements into calculation in consideration of rigid body translation. With set iterative time 20, an accuracy of 0.005 pixels has been achieved between two computer-simulated images by using basic PSO algorithm. In order to limit positions of particles within small areas and thus reduce iterative calculation, an improved integer pixel displacement search method called Grid Method is put forward for accurate integer pixel displacement measurement. Besides, through empirical study, Inverse Function Decreasing Inertia Weight has been proposed and other parameters of PSO have been discussed concerning DIC correlation coefficient function while we attempt to minimize the iterative calculation. We compare the proposed parameters with commonly used PSO parameters and find that PSO with the proposed parameters has much higher convergence rate. So Inverse Function Decreasing Inertia Weight and the set parameters are recommended for use in the PSO method of DIC.

With the development of science and technology, many optimization problems in real life have developed into high-dimensional optimization problems. The meta-heuristic optimization algorithm is regarded as an effective method to solve high-dimensional optimization problems. However, considering that traditional meta-heuristic optimization algorithms generally have problems such as low solution accuracy and slow convergence speed when solving high-dimensional optimization problems, an adaptive dual-population collaborative chicken swarm optimization (ADPCCSO) algorithm is proposed in this paper, which provides a new idea for solving high-dimensional optimization problems. First, in order to balance the algorithm’s search abilities in terms of breadth and depth, the value of parameter G is given by an adaptive dynamic adjustment method. Second, in this paper, a foraging-behavior-improvement strategy is utilized to improve the algorithm’s solution accuracy and depth-optimization ability. Third, the artificial fish swarm algorithm (AFSA) is introduced to construct a dual-population collaborative optimization strategy based on chicken swarms and artificial fish swarms, so as to improve the algorithm’s ability to jump out of local extrema. The simulation experiments on the 17 benchmark functions preliminarily show that the ADPCCSO algorithm is superior to some swarm-intelligence algorithms such as the artificial fish swarm algorithm (AFSA), the artificial bee colony (ABC) algorithm, and the particle swarm optimization (PSO) algorithm in terms of solution accuracy and convergence performance. In addition, the APDCCSO algorithm is also utilized in the parameter estimation problem of the Richards model to further verify its performance.

In constraint optimization problems set in continuous spaces, a feasible search space may consist of many disjoint regions and the global optimal solution might be within any of them. Thus, locating these feasible regions (as many as possible, ideally all of them) is of great importance. In this chapter, we introduce niching techniques that have been studied in connection with multimodal optimization for locating feasible regions, rather than for finding different local optima. One of the successful niching techniques was based on the particle swarm optimizer (PSO) with a specific topology, called nonoverlapping topology, where the swarm was divided into several nonoverlapping sub-swarms. Earlier studies have shown that PSO with such nonoverlapping topology, with a small number of particles in each sub-swarm, is quite effective in locating different local optima if the number of dimensions is small (up to 8). However, its performance drops rapidly when the number of dimensions grows. First, a new PSO, called mutation linear PSO, MLPSO, is proposed. This algorithm is effective in locating different local optima when the number of dimensions grows. MLPSO is applied to optimization problems with up to 50 dimensions, and its results in locating different local optima are compared with earlier algorithms. Second, we incorporate a constraint handling technique into MLPSO; this variant is called EMLPSO. We test different topologies of EMLPSO and evaluate them in terms of locating feasible regions when they are applied to constraint optimization problems with up to 30 dimensions. The results of this test show that the new method with nonoverlapping topology with small swarm size in each sub-swarm performs better in terms of locating different feasible regions in comparison to other topologies, such as the global best topology and the ring topology.

Particle Swarm Optimization (PSO) is an evolution-nary computation technique. Separate adjustment to inertia weight and learning factors in PSO undermines the integrity and intelligent characteristic in the evolutionary process of particle swarm to some extent, thus it is not suitable for solving most complicated optimization problems. On the basis of previous researches, the aim of this study was to improve the computational efficiency of PSO and avoid premature convergence for multimodal, higher dimensional complicated optimization problems by considering the mutual influences of inertia weight and learning factors on the updates of particle's veloci-ties. A great number of experiment data provided evidence that the nonlinear adjustment to inertia weight, cognitive learning factor and social learning factor within a certain interval is a good selection. Moreover, the simulation results on four typical functions show that the improved strategy of PSO proposed in the paper is available for solving multimodal and higher dimensional complicated optimization problems, and can accelerate convergence speed, improve optimization quality effectively in comparison to the algorithms of standard PSO and existing relevant improved PSO.

Fuzzy systems (FSs) have been extensively applied to automatic control, pattern recognition, and decision analysis. However, a common bottleneck is encountered in the derivation of fuzzy rules, which is often difficult, time consuming, and relies on expert knowledge. To automate the design of FSs, many metaheuristic learning algorithms have been proposed. One major optimization category uses Swarm Intelligence (SI) model (Kennedy et al., 2001). The SI technique studies collective behavior in decentralized systems. Its development was based on mimicking the social behavior of animals or insects in an effort to find the optima in the problem space. SI models are initialized with a population of random solutions. One well-known SI model is particle swarm optimization (PSO) (Kennedy & Eberhart, 1995). Many modified PSO models have been proposed and successfully applied to different optimization problems (Clerc & Kennedy, 2002; Bergh & Engelbrecht, 2004; Ratnaweera et al., 2004; Juang, 2004; Kennedy & Mendes, 2006; Parrott & Li, 2006; Chen & Li, 2007). FS design using PSO has also been proposed in several studies (Juang, 2004; Chatterjee et al., 2005; Juang et al., 2007; Araujo & Coelho, 2008; Sharma et al., 2009). Another well-known SI is ant colony optimization (ACO) (Dorigo & Stutzle, 2004). The ACO technique is inspired by real ant colony observations. It is a multi-agent approach that was originally proposed to solve difficult discrete combinatorial optimization problems, such as the traveling salesman problem (TSP) (Dorigo et al., 1996; Dorigo & Gambardella, 1997). In the original ACO meta-heuristic, artificial ant colonies cooperate to find good solutions for difficult discrete optimization problems. Different ACO models have been applied to FS design problems (Cassillas et al., 2000; Cassillas et al., 2005; Mucientes & Casillas; 2007; Juang & Lo, 2007; Juang et al., 2008; Juang & Lu; 2009). In (Cassillas et al.,2000; Mucientes & Casillas; 2007; Juang et al., 2008; Juang & Lu; 2009), the FS input space was partitioned in grid type with antecedent part parameters of an FS manually assigned in advance. In (Juang & Lo, 2007), the FS input space was flexibly partitioned using a fuzzy clustering-like algorithm in order to reduce the total number of rules. For all of these studies, the consequent part parameters were optimized in discrete space using ACO. Since only the consequent part parameters are optimized, and the optimization space is restricted to be discrete, the designed FSs are unsuitable for problems where high accuracy is a major concern. Source: Fuzzy Systems, Book edited by: Ahmad Taher Azar, ISBN 978-953-7619-92-3, pp. 216, February 2010, INTECH, Croatia, downloaded from SCIYO.COM

On the basis of the analyses of Ant Colony Optimization (ACO) and Particle Swarm Optimization (PSO), Continuous Ant- Particle Swarm Optimization (CA-PSO) applied in continuous function optimization is proposed. After the space partition is properly employed, ACO is applied to search the sensitive areas through the whole solution space. And then PSO is initialized according to ACO search results and applied to search the optimal solution in every area. After every iteration, swarm renovation is processed following Ant-Colony topological structure and transfer rules. As a result, the ants gradually assemble in the areas where optimal solution is mostly likely to be. With the number growth of particles in the sensitive areas, local PSO can search more meticulously until find the optimal solution. In conclusion, the CA-PSO can not only ensure the distributing diversity of the solution, but also avoid suboptimal solution when it is applied in the Multimodal function optimization.

Recently, the use of the particle swarm optimization (PSO) technique for the reconstruction of microwave images has received increasing interest from the optimization community due to its simplicity in implementation and its inexpensive computational overhead. However, the basic PSO algorithm is easily trapping into local minimum and may lead to the premature convergence. When a local optimal solution is reached with PSO, all particles gather around it, and escaping from this local optima becomes di-cult. To overcome the premature convergence of PSO, we propose a new hybrid algorithm of particle swarm optimization (PSO), simulated annealing (SA) and tabu search algorithm (TS) for solving the scattering inverse problem. The incorporation of tabu search (TS) and simulated annealing (SA) as local improvement approaches enable the hybrid algorithm to overleap local optima and intensify its search ability in local regions. Reconstructions of dielectric scatterers from experimental inverse- scattering data are flnally presented to demonstrate the accuracy and e-ciency of the hybrid technique.