Tracking Changing Extrema with Modified Adaptive Particle

The purpose of this paper is to present a modified PSO (Particle Swarm Optimization) algorithm applied to the complex dynamic environment. The algorithm presented is referred as Improved Adaptive Particle Swarm Optimizer (IAPSO). A new variable-"Activity Factor" and distributed responding method are introduced by IAPSO. Several experiments based on complex dynamic environment were performed to test the performance of the algorithm. The dynamic environment used is generated by the Dynamic Function #1 (DF1). Furthermore, additional feature of setting reinitializing threshold randomly is put to the basic IAPSO to improve its performance. The experimental results indicate that IAPSO is more adaptive in complex dynamic environment than Adaptive Particle Swarm Optimizer (APSO) and other PSO-based algorithms. In this paper, a modified PSO-based method is presented and referred as Improved Particle Swarm Optimizer (IAPSO). The algorithm introduces a new variable—Activity Factor and uses distributed responding method. PSO and its variation in dynamic environment are firstly introduced in the paper. Then, IAPSO is discussed in detail. At the last of the paper, experiments are performed to test the IAPSO. The results show that IAPSO is relatively excellent comparing with other PSO-based method. II. BACKGROUND A. PSO and PSO-based method in dynamic environment The basic PSO involves casting a population of particles over the search space, each with an individual, initially random, location and velocity vector. The particles fly over the solution space, remembering the best solution encountered (referred as particle's solution). At each iteration, every particle adjusts its velocity vector, based on its momentum and the influence of both its best solution and the best solution of its neighbours (referred as global solution), then computes a new point to examine. The memory of each particle tends to keep it from being trapped by a local extremum which is not optimal, yet by each particle considering both its own memory and that of its neighbours, the entire swarm tends to converge on a global extremum (8-10). Two key modifications are needed to apply PSO in the dynamic environment. First, swarm or particles should be sensible to the change of environment. Second, some kind of responding should be taken to update the swarm or particles when change of the environment is detected. Eberhart and Carlisle have made the modification in different ways. The method proposed by Eberhart (referred as E-PSO in this paper) estimates the change by monitoring the non- changing time of the gBest value and second best gBest value. The effectiveness of the method depends seriously on the fixed frequency set beforehand. And, there are also problems with APSO. In some cases, some area among the whole searching space is static during a period of time. When the swarm converges on a global extremum which resides in a temporal stationary area, the swarm can't detect the change of environment any longer for all the sentry particles are in the stationary area. The result is that the swarm can't track the latest global extremum. B. Modification to the PSO algorithm (IAPSO)