Shi Cheng

Experimental Study on Boundary Constraints Handling in Particle Swarm Optimization: From Population Diversity Perspective

Premature convergence happens in Particle Swarm Optimization PSO for solving both multimodal problems and unimodal problems. With an improper boundary constraints handling method, particles may get stuck in the boundary. Premature convergence means that an algorithm has lost its ability of exploration. Population diversity is an effective way to monitor an algorithms ability of exploration and exploitation. Through the population diversity measurement, useful search information can be obtained. PSO with a different topology structure and a different boundary constraints handling strategy will have a different impact on particles exploration and exploitation ability. In this paper, the phenomenon of particles gets stuck in the boundary in PSO is experimentally studied and reported. The authors observe the position diversity time-changing curves of PSOs with different topologies and different boundary constraints handling techniques, and analyze the impact of these setting on the algorithms ability of exploration and exploitation. From these experimental studies, an algorithms ability of exploration and exploitation can be observed and the search information obtained; therefore, more effective algorithms can be designed to solve problems.

Brain storm optimization algorithm for multi-objective optimization problems

In this paper, a novel multi-objective optimization algorithm based on the brainstorming process is proposed(MOBSO). In addition to the operations used in the traditional multi-objective optimization algorithm, a clustering strategy is adopted in the objective space. Two typical mutation operators, Gaussian mutation and Cauchy mutation, are utilized in the generation process independently and their performances are compared. A group of multi-objective problems with different characteristics were tested to validate the effectiveness of the proposed algorithm. Experimental results show that MOBSO is a very promising algorithm for solving multi-objective optimization problems.

Brain storm optimization algorithm: a review

For swarm intelligence algorithms, each individual in the swarm represents a solution in the search space, and it also can be seen as a data sample from the search space. Based on the analyses of these data, more effective algorithms and search strategies could be proposed. Brain storm optimization (BSO) algorithm is a new and promising swarm intelligence algorithm, which simulates the human brainstorming process. Through the convergent operation and divergent operation, individuals in BSO are grouped and diverged in the search space/objective space. In this paper, the history development, and the state-of-the-art of the BSO algorithm are reviewed. In addition, the convergent operation and divergent operation in the BSO algorithm are also discussed from the data analysis perspective. Every individual in the BSO algorithm is not only a solution to the problem to be optimized, but also a data point to reveal the landscape of the problem. Swarm intelligence and data mining techniques can be combined to produce benefits above and beyond what either method could achieve alone.

Diversity control in particle swarm optimization

Population diversity of particle swarm optimization (PSO) is important when measuring and dynamically adjusting algorithms ability of “exploration” or “exploitation”. Population diversities of PSO based on L1 norm are given in this paper. Useful information on search process of an optimization algorithm could be obtained by using this measurement. Properties of PSO diversity based on L1 norm are discussed. Several methods for diversity control are tested on benchmark functions, and the method based on current position and average of current velocities has the best performance. This method could control the PSO diversity effectively and gets better performance than the standard PSO.

Population diversity based study on search information propagation in particle swarm optimization

Premature convergence happens in Particle Swarm Optimization (PSO) partially due to improper search information propagation. Fast propagation of search information will lead particles get clustered together quickly. Determining a proper search information propagation mechanism is important in optimization algorithms to balance between exploration and exploitation. In this paper, we attempt to figure out the relationship between search information propagation and the population diversity change. Firstly, we analyze the different characteristics of search information propagation in PSO with four kinds of topologies: star, ring, four clusters, and Von Neumann. Secondly, population diversities of PSO, which include position diversity, velocity diversity, and cognitive diversity, are utilized to monitor particles search during optimization process. Position diversity, velocity diversity, and cognitive diversity, represent distributions of current solutions, particles “moving potential”, and particles “moving target”, respectively. From the observation of population diversities, the effect of search information propagation on PSOs optimization performance is discussed at last.

Solution clustering analysis in brain storm optimization algorithm

In swarm intelligence algorithms, premature convergence happens partially due to the solutions getting clustered together, and not diverging again. However, solution clustering is not always harmful for optimization. The solution clustering strategy is utilized in brain storm optimization (BSO) to guide individuals to move toward the better and better areas. The information of clusters indicates the solutions distribution in the search space, which could be utilized to reveal the landscapes and other proprieties of problems being optimized. In this paper, the solution clustering, and other properties of the brain storm optimization algorithm are analyzed and discussed. Experimental results show that brain storm optimization is a very promising algorithm for solving different kinds of problems.

Particle Swarm Optimization With Interswarm Interactive Learning Strategy

The learning strategy in the canonical particle swarm optimization (PSO) algorithm is often blamed for being the primary reason for loss of diversity. Population diversity maintenance is crucial for preventing particles from being stuck into local optima. In this paper, we present an improved PSO algorithm with an interswarm interactive learning strategy (IILPSO) by overcoming the drawbacks of the canonical PSO algorithms learning strategy. IILPSO is inspired by the phenomenon in human society that the interactive learning behavior takes place among different groups. Particles in IILPSO are divided into two swarms. The interswarm interactive learning (IIL) behavior is triggered when the best particles fitness value of both the swarms does not improve for a certain number of iterations. According to the best particles fitness value of each swarm, the softmax method and roulette method are used to determine the roles of the two swarms as the learning swarm and the learned swarm. In addition, the velocity mutation operator and global best vibration strategy are used to improve the algorithms global search capability. The IIL strategy is applied to PSO with global star and local ring structures, which are termed as IILPSO-G and IILPSO-L algorithm, respectively. Numerical experiments are conducted to compare the proposed algorithms with eight popular PSO variants. From the experimental results, IILPSO demonstrates the good performance in terms of solution accuracy, convergence speed, and reliability. Finally, the variations of the population diversity in the entire search process provide an explanation why IILPSO performs effectively.

Multiple strategies based orthogonal design particle swarm optimizer for numerical optimization

In the canonical particle swarm optimization (PSO), each particle updates its velocity and position by taking its historical best experience and its neighbors? best experience as exemplars and adding them together. Its performance is largely dependent on the employed exemplars. However, this learning strategy in the canonical PSO is inefficient when complex problems are being optimized. In this paper, Multiple Strategies based Orthogonal Design PSO (MSODPSO) is presented, in which the social-only model or the cognition-only model is utilized in each particle?s velocity update, and an orthogonal design (OD) method is used with a small probability to construct a new exemplar in each iteration. In order to enhance the efficiency of OD method and obtain more efficient exemplar, four auxiliary vector generating strategies are designed. In addition, a global best mutation operator including non-uniform mutation and Gaussian mutation is employed to improve its global search ability. The MSODPSO can be applied to PSO with the global or local structure, yielding MSODPSO-G and MSODPSO-L algorithms, respectively. To verify the effectiveness of the proposed algorithms, a set of 24 benchmark functions in 30 and 100 dimensions are utilized in experimental studies. The proposed algorithm is also tested on a real-world economic load dispatch (ELD) problem, which is modelled as a non-convex minimization problem with constraints. The experimental results on the benchmark functions and ELD problems demonstrate that the proposed MSODPSO-G and MSODPSO-L can offer high-quality solutions.

Population Diversity of Particle Swarm Optimizer Solving Single and Multi-Objective Problems

Premature convergence occurs in swarm intelligence algorithms searching for optima. A swarm intelligence algorithm has two kinds of abilities: exploration of new possibilities and exploitation of old certainties. The exploration ability means that an algorithm can explore more search place to increase the possibility that the algorithm can find good enough solutions. In contrast, the exploitation ability means that an algorithm focuses on the refinement of found promising areas. An algorithm should have a balance between exploration and exploitation, that is, the allocation of computational resources should be optimized to ensure that an algorithm can find good enough solutions effectively. The diversity measures the distribution of individuals’ information. From the observation of the distribution and diversity change, the degree of exploration and exploitation can be obtained. Another issue in multiobjective is the solution metric. Pareto domination is utilized to compare between two solutions, however, solutions are almost Pareto non-dominated for multi-objective problems with more than ten objectives. In this paper, the authors analyze the population diversity of particle swarm optimizer for solving both single objective and multiobjective problems. The population diversity of solutions is used to measure the goodness of a set of solutions. This metric may guide the search in problems with numerous objectives. Adaptive optimization algorithms can be designed through controlling the balance between exploration and exploitation.

Biomimicry of parasitic behavior in a coevolutionary particle swarm optimization algorithm for global optimization

Graphical abstractDisplay Omitted HighlightsPSOPB is inspired by the phenomenon that parasitic behavior is beneficial to the natural ecosystem for the promotion of its biodiversity.The host-parasite interaction is mimicked from some aspects.Extensive experiments demonstrate the effectiveness of PSOPB.Search behavior analysis is performed through monitoring the variation of population diversity. The declining of population diversity is often considered as the primary reason for solutions falling into the local optima in particle swarm optimization (PSO). Inspired by the phenomenon that parasitic behavior is beneficial to the natural ecosystem for the promotion of its biodiversity, this paper presents a novel coevolutionary particle swarm optimizer with parasitic behavior (PSOPB). The population of PSOPB consists of two swarms, which are host swarm and parasite swarm. The characteristics of parasitic behavior are mimicked from three aspects: the parasites getting nourishments from the host, the host immunity, and the evolution of the parasites. With a predefined probability, which reflects the characteristic of the facultative parasitic behavior, the two swarms exchange particles according to particles sorted fitness values in each swarm. The host immunity is mimicked through two ways: the number of exchange particles is linearly decreased over iterations, and particles in the host swarm can learn from the global best position in the parasite swarm. Two mutation operators are utilized to simulate two aspects of the evolution of the parasites in PSOPB. In order to embody the law of survival of the fittest in biological evolution, the particles with poor fitness in the host swarm are removed and replaced by the same numbers of randomly initialized particles. The proposed algorithm is experimentally validated on a set of 21 benchmark functions. The experimental results show that PSOPB performs better than other eight popular PSO variants in terms of solution accuracy and convergence speed.