Individualism of particles in particle swarm optimization

In this paper, a new method to deal with equality or inequality constraints in constrained optimization and a new neighborhood structure for Particle Swarm Optimization (PSO) called Grouped Directed Structure (GDS) are proposed. We use the new method and GDS together with the PSO algorithm to solve the well-known 24 benchmark constrained optimization problems in the literature. The PSO algorithm is well known for its fast convergence to the possible optimal position. However, in constrained optimization, the performance of PSO is not as good as it is in unconstrained optimization, partly because PSO is not good at finding the feasible region. Due to the motivation by this weakness of PSO, we develop a method called Numerical Gradient (NG) to find the feasible region. By means of the information that NG can provide, we utilize the PSO algorithm with GDS to find the optimal position of the problem. We call this new PSO variant Numerical Gradient Particle Swarm Optimization (NGPSO). A detailed description of the mechanism for NGPSO is provided and some numerical results are presented compared with the results from the existing PSO variants dealing with constraint optimization problems.

Particle swarm optimization (PSO) algorithm has shown promising performances on various benchmark functions and engineering optimization problems. However, it is still difficult to achieve a satisfying trade-off between exploration and exploitation for all the optimization problems and different evolving stages. Furthermore, control parameters of some related mechanisms need pre-experience by the requirement of trial-and-error scheme. This paper presents a novel PSO algorithm, which adaptively adopts various search strategies, called Self-adapting Hybrid Strategy PSO (SaHSPS). Unlike some other peer PSO variants, this method dynamically changes the probabilities of different strategies according to their previous successful searching memories, without any additional control parameters. The probabilities of different strategies would be re-initialized according to a proposed dynamic probabilistic model to diverse the population. Besides, particles are updated by probabilistically selected strategies after niching PSO with Ring topology. Moreover, a dynamic updating mechanism by niching PSO is proposed to guarantee the parallel searching capability during the whole evolution process. Thus, this proposed algorithm might be problem-independent and search-stage-independent, yielding more satisfying solutions on various optimization problems. A comprehensive experimental study is conducted on 28 benchmark functions of CEC 2013 special session on real-parameter optimization, including shifted, rotated, multi-modal, high conditioned, expanded and composition problems, compared with several state-of-the-art variants of PSO and differential evolution (DE) algorithms. Comparison results show that SaHSPS obtains outstanding performances on the majority of the test problems. Moreover, a practical engineering problem, real power loss minimization of IEEE 30-bus power system, is used to further evaluate SaHSPS. The numerical results, compared with other stochastic search algorithms, show that SaHSPS could find high-quality solutions with higher probability.

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

Particle Swarm Optimization (PSO) is a population-based stochastic search technique for solving optimization problems, which has been proven to be effective in wide applications in scientific and engineering domains. However, it is inefficient when searching in complex problems spaces. Lots of improved PSO variants with different features have been proposed, such as Comprehensive Learning PSO (CLPSO). CLPSO is an enhanced PSO variant by adopting a better learning strategy that has some chance to choose other particles' historical best information to update velocity. Comparing with the standard PSO, CLPSO has successfully improved the diversity of population and hence avoids the deficiency of premature convergence and local optima. However, this algorithm causes slow convergence speed, especially during the late state of searching process. In this paper, an improved CLPSO algorithm is proposed, termed as ICLPSO, to accelerate convergence speed and keep diversity of population at the same time. We set the learning probability based on particles' own fitness and adaptively construct different learning exemplars for different particles according to particles' own features and properties, which is a more appropriate learning strategy for particles' optimization. Experimental results show that the performance of ICLPSO is better than standard CLPSO and some other peer algorithms, using the functions both on unimodal and multimodal.

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.

This paper compares the performance of two variants of the Particle Swarm Optimization (PSO) algorithm; PSO with constriction factor (PSO), and mutative PSO (MPSO) in optimizing Mel Frequency Cepstrum Coefficients (MFCC) parameters. The parameters were used to extract an optimal feature set for classifying healthy and hypothyroid infant cry using Multi-Layer Perceptrons (MLP). Specifically, the PSO variants optimize the number of filter banks and number of cepstrum coefficients in MFCC. Based on the values chosen by both PSO variants, the extracted features were then fed to a MLP classifier, which was trained to discriminate between the healthy and hypothyroid infant cry. Comparisons between the performance of PSO variants showed that MPSO managed to improve the convergence rate by 2.67% compared to PSO.

A novel orthogonal multi-swarm cooperative particle swarm optimization (PSO) algorithm with a particle trajectory knowledge base is presented in this paper. Different from the traditional PSO algorithms and other variants of PSO, the proposed orthogonal multi-swarm cooperative PSO algorithm not only introduces an orthogonal initialization mechanism and a particle trajectory knowledge base for multi-dimensional optimization problems, but also conceives a new adaptive cooperation mechanism to accomplish the information interaction among swarms and particles. Experiments are conducted on a set of benchmark functions, and the results show its better performance compared with traditional PSO algorithm in aspects of convergence, computational efficiency and avoiding premature convergence.

The quantum-behaved particle swarm optimization (QPSO) algorithm, a variant of particle swarm optimization (PSO), has been proven to be an effective tool to solve various of optimization problems. However, like other PSO variants, it often suffers a premature convergence, especially when solving complex optimization problems. Considering this issue, this paper proposes a hybrid QPSO with dynamic grouping searching strategy, named QPSO-DGS. During the search process, the particle swarm is dynamically grouped into two subpopulations, which are assigned to implement the exploration and exploitation search, respectively. In each subpopulation, a comprehensive learning strategy is used for each particle to adjust its personal best position with a certain probability. Besides, a modified opposition-based computation is employed to improve the swarm diversity. The experimental comparison is conducted between the QPSO-DGS and other seven state-of-art PSO variants on the CEC’2013 test suit. The experimental results show that QPSO-DGS has a promising performance in terms of the solution accuracy and the convergence speed on the majority of these test functions, and especially on multimodal problems.

Evolutionary optimization algorithms, including particle swarm optimization (PSO), have been successfully applied in oil industry for production planning and control. Such optimization studies are quite challenging due to large number of decision variables, production scenarios, and subsurface uncertainties. In this work, multi-stage, multi-swarm PSO (MS2PSO) algorithm is proposed to fix certain issues with canonical PSO algorithm such as premature convergence, excessive influence of global best solution, and oscillation. Multiple experiments are conducted using Olympus benchmark to compare the efficacy of algorithms. Results from canonical PSO are first compared with two PSO variations in which hyperparameters are tuned to prioritize exploration in early phase and exploitation in late phase. Firstly, linearly decreasing inertia weight (LDIW-PSO) is used to have greater weight of current particle position during initial iterations, and vice versa. Then, time-varying acceleration coefficients (TVAC-PSO) are used to have greater weight of personal best and lesser weight of global best during the initial iterations, and vice versa. Next, a two-stage multi-swarm PSO (2SPSO) is used where multiple-swarms of the first stage collapse into a single swarm in the second stage. Finally, MS2PSO with multiple stages and multiple swarms is used in which swarms recursively collapse after each stage. Multiple swarm strategy ensures that diversity is retained within the population and multiple modes are explored. Staging ensures that local optima found during initial stage does not lead to premature convergence. Optimization test case comprises of 90 control variables of which 72 are well control related and 18 are well placement related. Swarm intelligence refers to global patterns emerging from simple interactions among population. Algorithmic rules at micro level lead to social interaction at meso level, which then further leads to collective behavior at macro level. It is observed that different algorithm designs have their own benefits and drawbacks. Decreasing inertia weight in LDIW-PSO enables exploration in early stages and convergence around global best in the later stages. TVAC-PSO on the other hand restricts social learning and aids exploration in the early iterations. Social learning component is increased as run progresses, and population moves towards global best. 2SPSO aids in exploring multi-modal objective space, thus preventing premature convergence to a local optima. Swarms collapse into one group in the second stage, and run finally converges towards global best. Multiple swarms and stages in MS2PSO ensure that diversity in population is maintained throughout the run which enables continuous learning, and thus mitigates premature convergence. Both 2SPSO and MS2PSO are found to be helpful for problems with high dimensions and multiple modes where greater degree of exploration is desired. Commercial cloud computing and parallel programming were used to handle high computational workload and reduce run-time from weeks to days. Coefficients of canonical PSO are tuned in LDIW-PSO and TVAC-PSO, which helps in mitigating issues like premature convergence and oscillation. Two-stage PSO (2SPSO) where multiple swarms of first stage collapse into one in second stage, and multi-stage multi-swarm PSO (MS2PSO) where swarms recursively collapse into one are proposed. These algorithms modify the social behavior at meso scale based on number of swarms, number of stages and iterations in each stage.

Oil is one of the most precious source of energy for the world and has an important role in the global economy. Therefore, the long-term prediction of the crude oil price is an important issue in economy and industry especially in recent years. The purpose of this paper is introducing a new Particle Swarm Optimization (PSO) algorithm to forecast the oil prices. Indeed, the PSO is a population-based optimization method inspired by the flocking behavior of birds. Its original version suffers from tripping in local minima. Here, the PSO is enhanced utilizing a convergence operator, an adaptive inertia weight and linear acceleration coefficients. The numerical results of mathematical test functions, obtained by the proposed algorithm and other variants of the PSO elucidate that this new approach operates competently in terms of the convergence speed, global optimality and solution accuracy. Furthermore, the effective variables on the long-term crude oil price are regarded and utilized as input data to the algorithm. The objective function of the optimization process considered in this research study is the summation of the square of the difference between the actual and the predicted oil prices. Finally, the long-term crude oil prices are accurately forecasted by the proposed strategy which proves its reliability and competence.

Particle Swarm Optimization (PSO) is a biologically inspired computational search and optimization method developed in 1995 by Eberhart and Kennedy based on the social behaviors of birds flocking or fish schooling.A number of basic variations have been developed due to improve speed of convergence and quality of solution found by the PSO.On the other hand, basic PSO is more appropriate to process static, simple optimization problem.Modification PSO is developed for solving the basic PSO problem.The observation and review 46 related studies in the period between 2002 and 2010 focusing on function of PSO, advantages and disadvantages of PSO, the basic variant of PSO, Modification of PSO and applications that have implemented using PSO.The application can show which one the modified or variant PSO that haven't been made and which one the modified or variant PSO that will be developed.

Particle swarm optimization using dimension selection methods

Localization is a key technology in wireless sensor networks. Faced with the challenges of the sensors’ memory, computational constraints, and limited energy, particle swarm optimization has been widely applied in the localization of wireless sensor networks, demonstrating better performance than other optimization methods. In particle swarm optimization-based localization algorithms, the variants and parameters should be chosen elaborately to achieve the best performance. However, there is a lack of guidance on how to choose these variants and parameters. Further, there is no comprehensive performance comparison among particle swarm optimization algorithms. The main contribution of this paper is three-fold. First, it surveys the popular particle swarm optimization variants and particle swarm optimization-based localization algorithms for wireless sensor networks. Secondly, it presents parameter selection of nine particle swarm optimization variants and six types of swarm topologies by extensive simulations. Thirdly, it comprehensively compares the performance of these algorithms. The results show that the particle swarm optimization with constriction coefficient using ring topology outperforms other variants and swarm topologies, and it performs better than the second-order cone programming algorithm.

Particle swarm optimization (PSO) has previously been parallelized primarily by distributing the computation corresponding to particles across multiple processors. In these approaches, the only benefit of additional processors is an increased swarm size. However, in many cases this is not efficient when scaled to very large swarm sizes (on very large clusters). Current methods cannot answer well the question: “How can 1000 processors be fully utilized when 50 or 100 particles is the most efficient swarm size?” In this paper we attempt to answer that question with a speculative approach to the parallelization of PSO that we refer to as SEPSO. In our approach, we refactor PSO such that the computation needed for iteration t+1 can be done concurrently with the computation needed for iteration t. Thus we can perform two iterations of PSO at once. Even with some amount of wasted computation, we show that this approach to parallelization in PSO often outperforms the standard parallelization of simply adding particles to the swarm. SEPSO produces results that are exactly equivalent to PSO; that is, SEPSO is a new method of parallelization and not a new PSO algorithm or variant. However, given this new parallelization model, we can relax the requirement of exactly reproducing PSO in an attempt to produce better results. We present several such relaxations, including keeping the best speculative position evaluated instead of the one corresponding to the standard behavior of PSO, and speculating several iterations ahead instead of just one. We show that these methods dramatically improve the performance of parallel PSO in many cases, giving speed ups of up to six compared to previous parallelization techniques.

System identification is a ubiquitous necessity for successful applications in various fields. The area of system identification can be characterized by a small number of leading principles, e.g. to look for sustainable descriptions by proper decisions in the triangle of model complexity, information contents in the data, and effective validation. Particle Swarm Optimization (PSO) is a stochastic, population‐based optimization algorithm and many variants of PSO have been developed since, including constrained, multi objective, and discrete or combinatorial versions and applications have been developed using PSO in many fields. The basic PSO algorithm implicitly utilizes a fully connected neighborhood topology. However, local neighborhood models have also been proposed for PSO long ago, where each particle has access to the information corresponding to its immediate neighbors, according to a certain swarm topology. In this local neighborhood model of PSO, particles have information only of their own and their nearest neighbors' bests, rather than that of the entire population of the swarm. In the present work basic PSO method and two of its local neighborhood variants are utilized for determining the optimal parameters of a dc motor. The result obtain from the simulation study demonstrate the usefulness of the proposed methodology.