Fractional particle swarm optimization in multidimensional search space (original) (raw)

Fractional Particle Swarm Optimization

Mathematical Methods in Engineering, 2014

The paper addresses new perspective of the PSO including a fractional block. The local gain is replaced by one of fractional order considering several previous positions of the PSO particles. The algorithm is evaluated for several well known test functions and the relationship between the fractional order and the convergence of the algorithm is observed. The fractional order influences directly the algorithm convergence rate demonstrating a large potencial for developments.

Multi-dimensional Search via Fractional Multi-swarms in Dynamic Environments

Particle swarm optimization (PSO) was proposed as an optimization technique for static environments; however, many real problems are dynamic, meaning that the environment and the characteristics of the global optimum can change in time. In this paper, we adapt recent techniques, which successfully address several major problems of PSO and exhibit a significant performance over multi-modal and non-stationary environments. In order to address the pre-mature convergence problem and improve the rate of PSO's convergence to the global optimum, Fractional Global Best Formation (FGBF) technique is used. FGBF basically collects all the best dimensional components and fractionally creates an artificial Global Best particle (aGB) that has the potential to be a better ''guide" than the PSO's native gbest particle. To establish follow-up of local optima, we then introduce a novel multi-swarm algorithm, which enables each swarm to converge to a different optimum and use FGBF technique distinctively. Finally for the multidimensional dynamic environments where the optimum dimension also changes in time, we utilize a recent PSO technique, the multi-dimensional (MD) PSO, which re-forms the native structure of the swarm particles in such a way that they can make inter-dimensional passes with a dedicated dimensional PSO process. Therefore, in a multi-dimensional search space where the optimum dimension is unknown, swarm particles can seek for both positional and dimensional optima. This eventually pushes the frontier of the optimization problems in dynamic environments towards a global search in a multi-dimensional space, where there exists a multi-modal problem possibly in each dimension. We investigated both standalone and mutual applications of the proposed methods over the moving peaks benchmark (MPB), which originally simulates a dynamic environment in a unique (fixed) dimension. MPB is appropriately extended to accomplish the simulation of a multi-dimensional dynamic system, which contains dynamic environments active in several dimensions. An extensive set of experiments show that in traditional MPB application domain, FGBF technique applied with multi-swarms exhibits an impressive speed gain and tracks the global peak with the minimum error so far achieved with respect to the other competitive PSO-based methods. When applied over the extended MPB, MD PSO with FGBF can find optimum dimension and provide the (near-) optimal solution in this dimension. (J. Pulkkinen), moncef.gabbouj@tut.fi (M. Gabbouj).

Dynamic multi-swarm particle swarm optimization with fractional global best formation

2010

Abstract Particle swarm optimization (PSO) has been initially proposed as an optimization technique for static environments; however, many real problems are dynamic, meaning that the environment and the characteristics of the global optimum can change over time. Thanks to its stochastic and population based nature, PSO can avoid being trapped in local optima and find the global optimum.

Particle swarm optimization with fractional-order velocity

Nonlinear Dynamics, 2010

This paper proposes a novel method for controlling the convergence rate of a particle swarm optimization algorithm using fractional calculus (FC) concepts. The optimization is tested for several wellknown functions and the relationship between the fractional order velocity and the convergence of the algorithm is observed. The FC demonstrates a potential for interpreting evolution of the algorithm and to control its convergence.

Fractional Order Darwinian Particle Swarm Optimization

The Darwinian Particle Swarm Optimization (DPSO) is an evolutionary algorithm that extends the Particle Swarm Optimization (PSO) using natural selection, or survival-of-the-fittest, to enhance the ability to escape from local optima. This paper presents a method for controlling the convergence rate of the DPSO using fractional calculus (FC) concepts. The fractional order (FO) DPSO, denoted as FO-DPSO, is tested using several well-known functions and the relationship between the fractional order velocity and the convergence of the algorithm is observed.

Fractional dynamics in particle swarm optimization

Systems, Man and …, 2007

This paper studies the fractional dynamics during the evolution of a Particle Swarm Optimization (PSO). Some swarm particles of the initial population are randomly changed for stimulating the system response. After the result is compared with a reference situation. The perturbation effect in the PSO evolution is observed in the perspective of the time behavior of the fitness of the best individual position visited by the replaced particles. The dynamics is investigated through the median of a sample of experiments, while adopting the Fourier analysis for describing the phenomena. The influence of the PSO parameters upon the global dynamics is also analyzed by performing several experiments for distinct values.

Multi-dimensional particle swarm optimization in dynamic environments

2011

Particle swarm optimization (PSO) was proposed as an optimization technique for static environments; however, many real problems are dynamic, meaning that the environment and the characteristics of the global optimum can change in time. In this paper, we adapt recent techniques, which successfully address several major problems of PSO and exhibit a significant performance over multi-modal and non-stationary environments.

The perils of particle swarm optimization in high dimensional problem spaces

2005

Particle swarm optimisation (PSO) is a stochastic, population-based optimisation algorithm. PSO has been applied successfully to a variety of domains. This thesis examines the behaviour of PSO when applied to high dimensional optimisation problems. Empirical experiments are used to illustrate the problems exhibited by the swarm, namely that the particles are prone to leaving the search space and never returning. This thesis does not intend to develop a new version of PSO specifically for high dimensional problems. Instead, the thesis investigates why PSO fails in high dimensional search spaces. Four different types of approaches are examined. The first is the application of velocity clamping to prevent the initial velocity explosion and to keep particles inside the search space. The second approach selects values for the acceleration coefficients and inertia weights so that particle movement is restrained or so that the swarm follows particular patterns of movement. The third introd...

Particle swarm optimization using dimension selection methods

Applied Mathematics and Computation, 2013

Particle swarm optimization (PSO) has undergone many changes since its introduction in 1995. Being a stochastic algorithm, PSO and its randomness present formidable challenge for the theoretical analysis of it, and few of the existing PSO improvements have make an effort to eliminate the random coefficients in the PSO updating formula. This paper analyzes the importance of the randomness in the PSO, and then gives a PSO variant without randomness to show that traditional PSO cannot work without randomness. Based on our analysis of the randomness, another way of using randomness is proposed in PSO with random dimension selection (PSORDS) algorithm, which utilizes random dimension selection instead of stochastic coefficients. Finally, deterministic methods to do the dimension selection are proposed, and the resultant PSO with distance based dimension selection (PSODDS) algorithm is greatly superior to the traditional PSO and PSO with heuristic dimension selection (PSOHDS) algorithm is comparable to traditional PSO algorithm. In addition, using our dimension selection method to a newly proposed modified particle swarm optimization (MPSO) algorithm also gets improved results. The experiment results demonstrate that our analysis about the randomness is correct and the usage of deterministic dimension selection method is very helpful.