Sabine Helwig

Experimental Analysis of Bound Handling Techniques in Particle Swarm Optimization

Many practical optimization problems are constrained and have a bounded search space. In this paper, we propose and compare a wide variety of bound handling techniques for particle swarm optimization. By examining their performance on flat landscapes, we show that many bound handling techniques introduce significant search bias. Furthermore, we compare the performance of many bound handling techniques on a variety of test problems, demonstrating that the bound handling technique can have a major impact on the algorithm performance, and that the method recently proposed as the standard does not, in general, perform well.

Particle Swarm Optimization in High-Dimensional Bounded Search Spaces

When applying particle swarm optimization (PSO) to real world optimization problems, often boundary constraints have to be taken into account. In this paper, we show that the bound handling mechanism essentially influences the swarm behavior, especially in high-dimensional search spaces. In our theoretical analysis, we prove that all particles are initialized very close to the boundary with overwhelming probability, and that the global guide is expected to leave the search space in every forth dimension. Afterwards, we investigate the initialization process when optimizing the sphere function, a widely used benchmark, in more detail in order to provide a first step towards explaining previously observed phenomena. Moreover, we present a broad experimental study of commonly applied bound handling mechanisms on a variety of benchmark functions which is useful for choosing an appropriate strategy in real world applications. Finally, we derive some guidelines for the practical application of the PSO algorithm in high-dimensional bounded search spaces

Theoretical Analysis of Initial Particle Swarm Behavior

In this paper, particle trajectories of PSO algorithms in the first iteration are studied. We will prove that many particles leave the search space at the beginning of the optimization process when solving problems with boundary constraints in high-dimensional search spaces. Three different velocity initialization strategies will be investigated, but even initializing velocities to zero cannot prevent this particle swarm explosion. The theoretical analysis gives valuable insight into PSO in high-dimensional bounded spaces, and highlights the importance of bound handling for PSO: As many particles leave the search space in the beginning, bound handling strongly influences particle swarm behavior. Experimental investigations confirm the theoretical results.

Particle Swarm Optimization with Velocity Adaptation

Particle swarm optimization (PSO) algorithms have gained increasing interest for dealing with continuous optimization problems in recent years. Often such problems involve boundary constraints. In this case, one has to cope with the situation that particles may leave the feasible search space. To deal with such situations different bound handling methods have been proposed in the literature and it has been observed that the success of PSO algorithms depends on a large degree on the used bound handling method. In this paper, we propose an alternative approach to cope with bounded search spaces. The idea is to introduce a velocity adaptation mechanism into PSO algorithms that is similar to step size adaptation used in evolution strategies. Using this approach we show that the bound handling method becomes less important for PSO algorithms and that using velocity adaptation leads to better results for a wide range of benchmark functions.

Modeling and analysis of indirect communication in particle swarm optimization

Particle swarm optimization (PSO) has successfully been applied to many optimization problems. One particularly interesting aspect of these algorithms is to study the communication behavior of the particles. Often, a neighborhood topology is defined a priori and used throughout the optimization run. However, the cost of communication between particles has not been analyzed up to now. In this paper, we will propose a novel algorithm called DAPSO (distributed archives PSO) that makes use of stationary archives to establish indirect communication architecture in the swarms. Moreover, we provide analytical results of the required communication energy in such a scenario. This might be especially important in robot swarms and sensor networks. The applicability of our new methodology will be shown on some selected test cases.

Heterogeneous constraint handling for particle swarm optimization

We propose a generic, hybrid constraint handling scheme for particle swarm optimization called Heterogeneous Constraint Handling. Inspired by the notion of social roles, we assign different constraint handling methods to the particles, one for each social role. In this paper, we investigate two social roles for particles, ‘self’ and ‘neighbor’. Due to the usual particle dynamics, a powerful mixture of the two corresponding constraint handling methods emerges. We evaluate this heterogeneous constraint handling approach with respect to the complete set of the CEC 2006 benchmark instances. Our results indicate that a such a heterogeneous combination of two constraint handling methods often leads to significantly better results than running each individual constraint handling method separately and returning the best solution obtained.

Velocity Adaptation in Particle Swarm Optimization

Swarm Intelligence methods have been shown to produce good results in various problem domains. A well-known method belonging to this kind of algorithms is particle swarm optimization (PSO). In this chapter, we examine how adaptation mechanisms can be used in PSO algorithms to better deal with continuous optimization problems. In case of bound-constrained optimization problems, one has to cope with the situation that particles may leave the feasible search space. To deal with such situations, different bound handling methods were proposed in the literature, and it was observed that the success of PSO algorithms highly depends on the chosen bound handling method. We consider how velocity adaptation mechanisms can be used to cope with bounded search spaces. Using this approach we show that the bound handling method becomes less important for PSO algorithms and that using velocity adaptation leads to better results for a wide range of benchmark functions.

Design and experimental evaluation of multiple adaptation layers in self-optimizing particle swarm optimization

Particle swarm optimization (PSO) is a nature-inspired technique for solving continuous optimization problems. For a fixed optimization problem, the quality of the found solution depends significantly on the choice of the algorithmic PSO parameters such as the inertia weight and the acceleration coefficients. It is a challenging task to choose appropriate values for these parameters by hand or mathematically. In this paper, a novel self-optimizing particle swarm optimizer with multiple adaptation layers is introduced. In the new algorithm, adaptation takes place on both particle and subswarm level. The new idea of using virtual parameter swarms which hold modifiable parameter configurations each is introduced. The algorithmic PSO parameters can be mutated by using, for instance, well-known techniques from the field of evolutionary algorithms, in order to allow fine-granular parameter adaptation to the problem at hand. The new algorithm is experimentally evaluated, and compared to a standard PSO and the Tribes algorithm. The experimental study shows that our new algorithm is highly competitive to previously suggested approaches.