An Improved Strategy of PSO for Solving Multimodal and Higher Dimensional Complicated Optimization Problems

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

The main objective of this paper is to solve the inverse convection heat transfer problems with particle swarm optimization method. An enhanced particle swarm optimization (EPSO) algorithm is proposed to overcome the shortcoming of earlier convergence of standard PSO algorithms. The performance of EPSO is tested by some benchmark functions; it is shown that EPSO has a strong antilocal trap capability especially for high dimensional multimodal optimization problems. At last, EPSO is used to identify the unknown boundary heat flux in a channel flow. According to the computational results of four test problems, it is clear that the proposed EPSO algorithm is able to estimate the unknown heat flux accurately even when the input data contain measurement error.

Aiming at the premature convergence problem of particle swarm optimization algorithm, a new particle swarm Optimization algorithm with dynamic adaptive inertia weigh was presented to solve the typical multi-peak, high dimensional function optimization problems. The dynamic adaptive strategy was introduced in this new algorithm and the change of inertia weight was formulated as an adjust function of this factor according to its impact on the search performance of the swarm. In each iteration process, the inertia weight was timely changed based on the current the swarm diversity and congregate degree, which provides the algorithm with effective dynamic adaptability. The experiments show that the proposed strategy is effectiveness.

Particle swarm optimization (PSO) algorithm is generally improved by adaptively adjusting the inertia weight or combining with other evolution algorithms. However, in most modified PSO algorithms, the random values are always generated by uniform distribution in the range of [0, 1]. In this study, the random values, which are generated by uniform distribution in the ranges of [0, 1] and [−1, 1], and Gauss distribution with mean 0 and variance 1 ( U [ 0 , 1 ] , U [ − 1 , 1 ] and G ( 0 , 1 ) ), are respectively used in the standard PSO and linear decreasing inertia weight (LDIW) PSO algorithms. For comparison, the deterministic PSO algorithm, in which the random values are set as 0.5, is also investigated in this study. Some benchmark functions and the pressure vessel design problem are selected to test these algorithms with different types of random values in three space dimensions (10, 30, and 100). The experimental results show that the standard PSO and LDIW-PSO algorithms with random values generated by U [ − 1 , 1 ] or G ( 0 , 1 ) are more likely to avoid falling into local optima and quickly obtain the global optima. This is because the large-scale random values can expand the range of particle velocity to make the particle more likely to escape from local optima and obtain the global optima. Although the random values generated by U [ − 1 , 1 ] or G ( 0 , 1 ) are beneficial to improve the global searching ability, the local searching ability for a low dimensional practical optimization problem may be decreased due to the finite particles.

This paper addresses dynamic data clustering as an optimization problem and propose techniques for finding optimal (number of) clusters in a multi-dimensional data or feature space. In order to accomplish this objective we first propose two novel techniques, which successfully address several major problems in the field of particle swarm optimization (PSO) and promise a significant breakthrough over complex, multi-modal optimization problems at high dimensions. The first one, so-called multi-dimensional (MD) PSO, re-forms the native structure of swarm particles in such a way that they can make inter-dimensional passes with a dedicated dimensional PSO process. Therefore, in a multidimensional search space where the optimum dimension is unknown, swarm particles can seek both positional and dimensional optima. This eventually removes the necessity of setting a fixed dimension a priori, which is a common drawback for the family of swarm optimizers. Nevertheless, MD PSO is still susceptible to premature convergences due to lack of divergence. To address this problem we propose fractional global best formation (FGBF) technique, which basically collects all promising dimensional components and fractionally creates an artificial global-best particle (aGB) that has the potential to be a better ldquoguiderdquo than the PSO's native gbest particle. We investigated both individual and mutual applications of the proposed techniques and demonstrated that the best clustering performance can be achieved by their mutual operation. In order to test and evaluate their clustering performance in terms of accuracy, robustness and scalability, a synthetic data-set, which contains ground-truth clusters and offers a broad range of complexity levels is used. An extensive set of experiments demonstrate that the proposed dynamic clustering technique based on MD PSO with FGBF can extract the optimal (number of) clusters by converging to the global optimum of the validity index function at the true dimension.

Particle swarm optimization (PSO) is one of the modern heuristic algorithms. PSO has attracted great attention due to its features of easy implementation, robustness to control parameters and computation efficiency compared with other existing heuristic algorithms. The performance of a PSO can depend on its parameters such as the inertia weight factors and two acceleration coefficients. The value of inertia weight can treat the balance between exploration and exploitation, so a proper control of inertia weight is very important to find the optimum solution efficiently. This paper compared several kinds of inertia weights. Experimental results demonstrate that simulated annealing inertia weight and linearly decreasing inertia weight have better convergence performance in the searching procedure. The dimension of the solution has no effect on the performance of inertia weight. The performance of the two kinds of inertia weight will change when the benchmark functions and acceleration coefficients change.

Experimental study of a new hybrid PSO with mutation for economic dispatch with non-smooth cost function

In artificial intelligence, evolutionary algorithms (EAs) have shown to be effective and robust in solving difficult optimization problems. EAs are generic populationbased metaheuristic optimization algorithms. The mechanisms used in EAs are inspired by biological evolution: reproduction, mutation, recombination, and selection. The development of EAs can be classified into two categories: single objective and multi-objective optimization. In this thesis, both single objective and multi-objective evolutionary algorithms have been studied. For single objective optimization, various niching techniques are integrated with differential evolution (DE) and particle swarm optimization (PSO) for multi-modal optimization. Multi-modal optimization deals with optimization tasks that involve finding all or most of the global/local peaks in one single run. EAs in their original forms are usually designed for locating one single global solution. To promote and maintain formation of multiple stable subpopulations within a single population, we introduced a neighborhood mutation technique to enhance DE with ability of handling multi-modal problems. We also proposed a locally informed PSO to tackle multi-modal optimization. Beside these, several existing niching techniques from the literature were modified and improved by us.

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.

Network reconfiguration for loss reduction in a distribution system is a very important way to save the electrical energy. This article proposes a hybrid evolutionary algorithm to solve the distribution feeder reconfiguration problem. The algorithm combines a fuzzy adaptive particle swarm optimization with a differential evolution algorithm, called the fuzzy adaptive particle swarm optimization–differential evolution. The fuzzy adaptive particle swarm optimization includes two parts. The first part is fuzzy adaptive binary particle swarm optimization, which determines the status of tie switches (open or closed), and the second part is fuzzy adaptive discrete particle swarm optimization, which determines the sectionalizing switch number. In the proposed algorithm, due to the results of binary particle swarm optimization and discrete particle swarm optimization algorithms that highly depend on the values of their parameters (such as the inertia weight and learning factors), a fuzzy system is employed to adaptively adjust the parameters during the search process. The differential evolution algorithm is combined with the fuzzy adaptive particle swarm optimization algorithm to improve its performance. The proposed algorithm is tested on two distribution test feeders. The results of simulation show that the proposed method is very powerful and is guaranteed to obtain the global optimization.

In many real-world optimization problems, multimodal function optimization is considered, in fact, we are faced with a multimodal optimization problem. Particle swarm optimization (PSO) and continuous ant colony optimization (ACOR) are two population-based optimization techniques that work based on probability laws. The main problem of PSO and ACOR algorithms is premature convergence and falling into local optima. One way to solve the problems is to use combinational methods. This paper presents a combinational method including PSO and ACOR in order to improve the search process. The proposed algorithm tries to solve the problem. Standard benchmark functions are used in order to evaluate the proposed algorithm, proposed method was compared with ACOR, PSO and sequential approach with the enlarged pheromone-particle table of the composition of PSO and ACOR Introduced in [8]. Results show that the proposed method is superior.

An efficient and most famous tool to enhance damping of the power system low frequency oscillations is the conventional widely used lead-lag Power System Stabilizer (PSS). To achieve the desired level of robust performance under transient situation, selecting a suitable design method for optimal tuning of PSS parameters is very important in multi-machine power system. Because, it is a multimodal and difficult combinatorial optimization problem, this paper presents a novel parameter automation strategy for Particle Swarm Optimization (PSO) called PSO with Time-Varying Acceleration Coefficients (PSO-TVAC). This optimization method has a strong ability to successfully control both global and local search in each iteration process for considerably increasing the probability of finding the global optimum solution. The PSO-TVAC algorithm is applied to optimal tuning PSS parameters problem in order to reduce the PSS design effort and find the best possible solution within a reasonable computation time. For this reason, the robustly selection of PSSs parameters is converted as an optimization problem based on the time domain-based objective function under different operating conditions. The robustness of the proposed method is demonstrated on a multi-machine power system in comparison with the classical PSO and conventional method based designed PSSs. It is shown through the nonlinear time domain simulation and some performance indices for a wide range of loading condition. The analysis of the results shows that the improved PSO-TVAC is not only very effective but also provides an excellent ability for damping low frequency oscillations and greatly enhance the dynamic stability of the power system. Moreover, the proposed PSO-TVAC algorithm is superior than that of the classical PSO one in terms of accuracy, convergence and computational effort. Key words: Power system stabilizer (PSS) design, particle swarm optimization, power system dynamics, time-varying acceleration coefficients.

Particle Swarm Optimization (PSO) is a meta-heuristic for solving high dimensional optimization problems. Due to the large number of dimensions usually employed with PSO, it is not trivial to visualize and monitor the progress of the algorithm. Because of this, adjusting the parameters that govern the dynamics of the swarm for a specific problem becomes challenging. In this article, we present SwarmViz, an open-source visualization tool for PSO. Through SwarmViz, users are able to set up PSO experiments on canonical benchmark functions or input data from external experiments (e.g., learning robotic controllers), and to visualize the optimization process with state-of-the-art visualization tools. SwarmViz has two main goals. First, to enable researchers to monitor the progress of their specific optimization problem and adjust the relevant PSO parameters. Second, to give a visual insight about PSO to students in the scope of teaching optimization techniques. We demonstrate the features of the software through examples on well-known numerical benchmark functions and a case study on the optimization of a robotic controller.

A novel hybrid particle swarm optimization for economic dispatch with valve-point loading effects

In order to overcome the basic glowworm swarm optimization (GSO) algorithm in the high dimension space function optimization effect is poor defects. This paper, we introduce the idea of the traditional complex method, with the complex method the worst part of the glowworm guidance for reflection be good glowworm swarm, so as to continuously make the worst glowworm swarm become the better glowworm swarm. Finally, an improved artificial glowworm algorithm solves high dimension space of function optimization effect improvement. And through the and basic glowworm swarm algorithm, artificial fish algorithm (AFSA) and particle swarm optimization (PSO) to eight test function optimization results are compared. The show that the efficiency of the method.