Evolving Particle Swarm Optimization Implemented by a Genetic Algorithm

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 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.

In this paper, we present a comprehensive and in-depth investigation on the optimization of Proportional-Integral (PI) controller tuning for achieving stability and desired overshoot in the step response. The main objective of this study is to compare the effectiveness of Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) techniques in finding the optimal parameters for the PI controller. The PI controller is a widely used control algorithm that plays a crucial role in many industrial processes. Its tuning greatly affects the system's performance, particularly in terms of stability and overshoot. Therefore, finding the optimal tuning parameters is of utmost importance. To address this optimization problem, we propose the utilization of two popular metaheuristic algorithms, GA and PSO. These algorithms are known for their ability to efficiently search through large solution spaces and find near-optimal solutions. By applying these algorithms to the PI controller tuning problem, we aim to determine which technique yields better results in terms of stability and overshoot tuning. In our comparative study, we provide a detailed explanation of both GA and PSO algorithms, focusing on their working principles and mathematical formulations. We also describe how these algorithms can be applied to the PI controller tuning problem. Furthermore, we highlight the key differences between GA and PSO, shedding light on their strengths and weaknesses. To assess the performance of GA and PSO, we conduct several experiments using different benchmark functions and step response models. We measure the stability and overshoot metrics for various parameter settings obtained through GA and PSO. By thoroughly analyzing the obtained results, we draw meaningful conclusions regarding the effectiveness of each technique. Our findings demonstrate that both GA and PSO exhibit promising results in optimizing PI controller tuning. These observations provide valuable insights and guidelines for choosing the appropriate algorithm based on specific control requirements. In conclusion, this comparative study is thought to contribute to the field of control systems engineering by offering a comprehensive analysis of GA and PSO techniques in the context of PI controller tuning. By highlighting their strengths and weaknesses, it is aimed to provide researchers and practitioners with valuable information for making informed decisions when optimizing control parameters for stability and overshoot reduction purposes.

Optimisation of fixture layout is critical to reduce geometric and form error of the workpiece during the machining process. In this paper the optimal placement of fixture elements (locator and clamp locations) under dynamic conditions is investigated using evolutionary techniques. The application of the newly developed particle swarm optimisation (PSO) algorithm and widely used genetic algorithm (GA) is presented to minimise elastic deformation of the workpiece considering its dynamic response. To improve the performances of GA and PSO, an improved GA (IGA) obtained by basic GA (GA) with sharing and adaptive mutation and an improved PSO (IPSO) obtained by basic PSO (PSO) incorporated into adaptive mutation are developed. ANSYS parametric design language (APDL) of finite element analysis is employed to compute the objective function for a given fixture layout. Three layout optimisation cases derived from the high speed slot milling case are used to test the effectiveness of the GA, IGA, PSO and IPSO based approaches. The comparisons of computational results show that IPSO seems superior to GA, IGA and PSO approaches with respect to the trade-off between global optimisation capability and convergence speed for the presented type problems.

A dynamic adaptive particle swarm optimization and genetic algorithm is presented to solve constrained engineering optimization problems. A dynamic adaptive inertia factor is introduced in the basic particle swarm optimization algorithm to balance the convergence rate and global optima search ability by adaptively adjusting searching velocity during search process. Genetic algorithm–related operators including a selection operator with time-varying selection probability, crossover operator, and n-point random mutation operator are incorporated in the particle swarm optimization algorithm to further exploit optimal solutions generated by the particle swarm optimization algorithm. These operators are used to diversify the swarm and prevent premature convergence. Tests on nine constrained mechanical engineering design optimization problems with different kinds of objective functions, constraints, and design variables in nature demonstrate the superiority of the dynamic adaptive particle swarm optimization and genetic algorithm against several other meta-heuristic algorithms in terms of solution quality, robustness, and convergence rate in most cases.

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

A method for optimization designs of rolling fin-tube heat exchangers was put forward with Particle Swarm Optimization (PSO) and Genetic Algorithm (GA), respectively. The length of tube bundles, the row numbers of tubes, the width of heat exchanger core and fin pitch were used as the optimization variables. The allowable pressure drop and heat exchange requirements were considered as restrictive conditions. According to specific design requirements, the volume, weight or pressure drop may be chosen as the optimization objective function. In the same design parameters, ranges of the search variables and restrictive conditions, optimization results compared with GA, the minimum volume, weight and pressure drop PSO could decrease by 3.34%, 4.31% and 14.04%, respectively, and corresponding CPU time could be reduced by 32.39%, 40.23% and 33.45%, respectively. In the fields of optimization designs of heat exchanger, Particle Swarm Optimization is a promising optimization method.

Estimation of transformer parameters from nameplate data by imperialist competitive and gravitational search algorithms

The complexity of embedded system design increase as the technology keeps evolving from day to day. Hardware software partitioning has been a promising approach to solve this design problem of complexity in the embedded systems, by providing a solution that automatically decides the partitioning. A lot of research has been done to automate the partitioning which focusing on exact and heuristic algorithm. Then due to the slow performance of the exact algorithms, the study focus shift to heuristic algorithms such as Genetic Algorithm (GA) and Particle Swarm Optimization (PSO). In this research the performance of both PSO algorithm and GA are analyzed in the application of the partitioning. In order to get the best among these two algorithms, hybrid combination across the two algorithms is designed. The best cost and their average time to achieve it are compared among PSO, GA and hybrid design. As a result, the graph obtained from the hybrid GA-GA-PSO required a smaller number of iterations to reach best cost. Compared to previous work, GA-GA-PSO obtained a smooth as the successive PSO graph. In conclusion, a new idea of hybrid across PSO and GA has been introduced and it results into a better solution for Hardware Software Partitioning.

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.

Each university has different regulations in making lecture schedule according to the conditions of respective institution. In this study, regulation on lecture scheduling used the maximum limit of credits of lecturer in a day, in which if exceeds the maximum limit, then the schedule of course will be moved on another day. This study attempts to optimize the schedule preparation in each semester by considering the maximum limit of credits of a lecturer in a day. Lecture scheduling is a combination of space, time, and resources. It is categorized into combinatorial optimization group. There are two methods for solving the combinatorial optimization problems, i.e. exact and approximation method. The approximation method consists of two types, heuristics and metaheuristics. The algorithm metaheuristics categories include genetic algorithm (GA), particle swarm optimization (PSO), ant colony optimization (ACO), bee colony optimization (BCO), simulated annealing, and so on. This paper employed metaheuristics approach. Research on the preparation of lecture scheduling using ACO algorithm has been conducted and proven to be able to prepare the lecture scheduling. The ACO algorithm has numbers of parameters that in solving issues, one must manually set a number of parameters by using the Design of Experiments (DoE) tool, which takes time to solve the optimization problem. Hence, to solve the issue, an automated parameter optimization is required. PSO algorithm has fewer parameters compared to the ACO. Therefore, the purpose of this paper is a hybrid between PSO and ACO in preparing lecture scheduling.

Adequate is better: particle swarm optimization with limited-information

Genetic Algorithms (GA), Ant Colony Optimization (ACO), Particle Swarm Optimization (PSO) and Artificial Bee Colonies (ABC) are some vital nature inspired computing (NIC) techniques. These approaches have been used in early prophecy of various diseases. This article analyzes the efficacy of various NIC techniques in diagnosing diverse critical human disorders. It is observed that GA, ACO, PSO and ABC have been successfully used in early diagnosis of different diseases. As compared to ACO, PSO and ABC algorithms, GA has been extensively used in diagnosis of ecology, cardiology and endocrinologist. In addition, from the last six years of research, it has been observed that the accuracy accomplished using GA, ACO, PSO and ABC in the early diagnosis of cancer, diabetes and cardio problems lies between 73.5%-99.7%, 70%-99.2%, 80%-98% and 76.4% to 99.98% respectively. Furthermore, ACO, PSO and ABC are found to be best suited in diagnosing lung, prostate and breast cancer respectively. Moreover, the hybrid use of NIC techniques produces better results as compared to their individual use.

This paper presents an efficient and accurate way of solving radial distribution system reconfiguration (DSR), which plays an important role in distribution automation for realizing smart grids. It deploys different heuristic optimization approaches to resolve the desired optimum configuration and to efficiently reconfigure the connectivity of the distribution networks. The objective is to minimize the system power loss while the voltage in each bus is limited to some allowable range, and the topology of the system is kept radial. In this paper, a hybrid algorithm consisting of particle swarm optimization (PSO) and genetic algorithm (GA) is proposed. The first part of the hybrid approach is based on a modified PSO where the initial swarm of particles fit the radiality constraint and it introduces external randomness to velocities and locations with certain probabilities when particles are in equilibrium or close to equilibrium state. The second part is a modified GA which receives its initial population from best solutions of the modified PSO and uses adaptive mutation for introducing population diversity. In addition, the particle's location in PSO and each chromosome in GA are repaired in such a way that the radiality constraint is always satisfied. The validity and the effectiveness of the proposed method has been tested using the standard IEEE 33-bus distribution network. The results show that the proposed method is robust and delivers a minimal average power loss of independent runs with reduced computational time.

Population-based (gradient-free) methods have become attractive for solving optimization problems since they have been known to locate "optimal" (best) positions within a search space. In this study, we investigate the use of three different gradient-free optimization methods namely: Iterative Latin Hypercube Sampling (ILHS), Particle Swarm Optimization (PSO), and Genetic Algorithm (GA) for well placement and well controls optimization problem of the CO2 underground storage in a 2D saline aquifer with bound constraints on the design variables. We also consider sequential optimization of well locations and well controls using the gradient-free methods. To evaluate the performance of these algorithms, we test the methods on well-known test (or toy) problems such as the multi-dimensional (40 design variables) Rosenbrock function, as well as the Traveling Salesman Problem (TSP) with 20 cities (20 design variables). We further extend the study to a more complex problem which involves finding the optimal well types, well locations, or well controls for a CO2 injection problem in a synthetic saline aquifer compositional model built in a commercial simulator. The objective function formulated for the CO2 injection problem is the net present environmental value (NPEV) involving discrete design variables (well types and well locations) and real design variables (well controls). Results obtained from the performance comparison of these gradient-free methods on the toy problems demonstrate the superior performance of the ILHS over PSO and GA for the Rosenbrock test function, while GA outperforms ILHS and PSO in solving the TSP. We also observe that for the simple well locations optimization problems involving one or two wells, all three algorithms obtained comparable results, given the same number of samples and number of iterations. However, for more complex cases such as the sequential or simultaneous optimization problems, when multiple wells which may include injectors and producers are present, we observe significant differences in the selection of the optimal well types and well locations among the three optimizers. In the simultaneous optimization of well types, well locations, and well controls, when both injectors and producers are BHP controlled, the results obtained showed that it is more optimal for at least one producer to be present, and for the injectors to be operated at the upper bound of the injector BHP, while the producers operated at the lower bound of the producer BHP to maximize the NPEV.