Particle Swarm Optimization with Double Learning Patterns

Particle Swarm Optimization (PSO) is an effective tool in solving optimization problems. However, PSO usually suffers from the premature convergence due to the quick losing of the swarm diversity. In this paper, we first analyze the motion behavior of the swarm based on the probability characteristic of learning parameters. Then a PSO with double learning patterns (PSO-DLP) is developed, which employs the master swarm and the slave swarm with different learning patterns to achieve a trade-off between the convergence speed and the swarm diversity. The particles in the master swarm and the slave swarm are encouraged to explore search for keeping the swarm diversity and to learn from the global best particle for refining a promising solution, respectively. When the evolutionary states of two swarms interact, an interaction mechanism is enabled. This mechanism can help the slave swarm in jumping out of the local optima and improve the convergence precision of the master swarm. The proposed PSO-DLP is evaluated on 20 benchmark functions, including rotated multimodal and complex shifted problems. The simulation results and statistical analysis show that PSO-DLP obtains a promising performance and outperforms eight PSO variants

MLGSA: Multi-Leader Gravitational Search Algorithm for Multi-Objective Optimization Problem

Recently, we have introduced Multi-Leader Particle Swarm Optimization (MLPSO) algorithm for multiobjective optimization problem. Better convergence and diversity have been observed over the conventional MultiObjective Particle Swarm Optimization. In this paper, the same concept is extended to Gravitational Search Algorithm (GSA). The performance was investigated by solving a set of ZDT test problem. An analysis was also performed by varying the value of initial gravitational constant

Particle swarm optimization with composite particles in dynamic environments

This article is placed here with the permission of IEEE - Copyright @ 2010 IEEEIn recent years, there has been a growing interest in the study of particle swarm optimization (PSO) in dynamic environments. This paper presents a new PSO model, called PSO with composite particles (PSO-CP), to address dynamic optimization problems. PSO-CP partitions the swarm into a set of composite particles based on their similarity using a "worst first" principle. Inspired by the composite particle phenomenon in physics, the elementary members in each composite particle interact via a velocity-anisotropic reflection scheme to integrate valuable information for effectively and rapidly finding the promising optima in the search space. Each composite particle maintains the diversity by a scattering operator. In addition, an integral movement strategy is introduced to promote the swarm diversity. Experiments on a typical dynamic test benchmark problem provide a guideline for setting the involved parameters and show that PSO-CP is efficient in comparison with several state-of-the-art PSO algorithms for dynamic optimization problems.This work was supported in part by the Key Program of the National Natural Science Foundation (NNSF) of China under Grant 70931001 and 70771021, the Science Fund for Creative Research Group of the NNSF of China under Grant 60821063 and 70721001, the Ph.D. Programs Foundation of the Ministry of education of China under Grant 200801450008, and by the Engineering and Physical Sciences Research Council of U.K. under Grant EP/E060722/1

Handling boundary constraints for particle swarm optimization in high-dimensional search space

Despite the fact that the popular particle swarm optimizer (PSO) is currently being extensively applied to many real-world problems that often have high-dimensional and complex fitness landscapes, the effects of boundary constraints on PSO have not attracted adequate attention in the literature. However, in accordance with the theoretical analysis in [11], our numerical experiments show that particles tend to fly outside of the boundary in the first few iterations at a very high probability in high-dimensional search spaces. Consequently, the method used to handle boundary violations is critical to the performance of PSO. In this study, we reveal that the widely used random and absorbing bound-handling schemes may paralyze PSO for high-dimensional and complex problems. We also explore in detail the distinct mechanisms responsible for the failures of these two bound-handling schemes. Finally, we suggest that using high-dimensional and complex benchmark functions, such as the composition functions in [19], is a prerequisite to identifying the potential problems in applying PSO to many real-world applications because certain properties of standard benchmark functions make problems inexplicit. © 2011 Elsevier Inc. All rights reserved

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In this study, an improved particle swarm optimization (PSO) algorithm, including 4 types of new velocity updating formulae (each is equal to the traditional PSO), was introduced. This algorithm was called the reverse direction supported particle swarm optimization (RDS-PSO) algorithm. The RDS-PSO algorithm has the potential to extend the diversity and generalization of traditional PSO by regulating the reverse direction information adaptively. To implement this extension, 2 new constants were added to the velocity update equation of the traditional PSO, and these constants were regulated through 2 alternative procedures, i.e. max min-based and cosine amplitude-based diversity-evaluating procedures. The 4 most commonly used benchmark functions were used to test the general optimization performances of the RDS-PSO algorithm with 3 different velocity updates, RDS-PSO without a regulating procedure, and the traditional PSO with linearly increasing/decreasing inertia weight. All PSO algorithms were also implemented in 4 modes, and their experimental results were compared. According to the experimental results, RDS-PSO 3 showed the best optimization performance

Improved dynamical particle swarm optimization method for structural dynamics

A methodology to the multiobjective structural design of buildings based on an improved particle swarm optimization algorithm is presented, which has proved to be very efficient and robust in nonlinear problems and when the optimization objectives are in conflict. In particular, the behaviour of the particle swarm optimization (PSO) classical algorithm is improved by dynamically adding autoadaptive mechanisms that enhance the exploration/exploitation trade-off and diversity of the proposed algorithm, avoiding getting trapped in local minima. A novel integrated optimization system was developed, called DI-PSO, to solve this problem which is able to control and even improve the structural behaviour under seismic excitations. In order to demonstrate the effectiveness of the proposed approach, the methodology is tested against some benchmark problems. Then a 3-story-building model is optimized under different objective cases, concluding that the improved multiobjective optimization methodology using DI-PSO is more efficient as compared with those designs obtained using single optimization.Peer ReviewedPostprint (published version

Adaptive particle swarm optimization

An adaptive particle swarm optimization (APSO) that features better search efficiency than classical particle swarm optimization (PSO) is presented. More importantly, it can perform a global search over the entire search space with faster convergence speed. The APSO consists of two main steps. First, by evaluating the population distribution and particle fitness, a real-time evolutionary state estimation procedure is performed to identify one of the following four defined evolutionary states, including exploration, exploitation, convergence, and jumping out in each generation. It enables the automatic control of inertia weight, acceleration coefficients, and other algorithmic parameters at run time to improve the search efficiency and convergence speed. Then, an elitist learning strategy is performed when the evolutionary state is classified as convergence state. The strategy will act on the globally best particle to jump out of the likely local optima. The APSO has comprehensively been evaluated on 12 unimodal and multimodal benchmark functions. The effects of parameter adaptation and elitist learning will be studied. Results show that APSO substantially enhances the performance of the PSO paradigm in terms of convergence speed, global optimality, solution accuracy, and algorithm reliability. As APSO introduces two new parameters to the PSO paradigm only, it does not introduce an additional design or implementation complexity

Fast multi-swarm optimization for dynamic optimization problems

This article is posted here with permission of IEEE - Copyright @ 2008 IEEEIn the real world, many applications are non-stationary optimization problems. This requires that the optimization algorithms need to not only find the global optimal solution but also track the trajectory of the changing global best solution in a dynamic environment. To achieve this, this paper proposes a multi-swarm algorithm based on fast particle swarm optimization for dynamic optimization problems. The algorithm employs a mechanism to track multiple peaks by preventing overcrowding at a peak and a fast particle swarm optimization algorithm as a local search method to find the near optimal solutions in a local promising region in the search space. The moving peaks benchmark function is used to test the performance of the proposed algorithm. The numerical experimental results show the efficiency of the proposed algorithm for dynamic optimization problems