Particle Swarm Optimization - A Survey <s> Optimization in a Dynamic Environment <s> This paper introduces an adaptive PSO, which automatically tracks various changes in a dynamic system. Different environment detection and response techniques are tested on the parabolic and Rosenbrock benchmark functions, and re-randomization is introduced to respond to the dynamic changes. Performance on the benchmark functions with various severities is analyzed. <s> BIB001 </s> Particle Swarm Optimization - A Survey <s> Optimization in a Dynamic Environment <s> Many real-world problems are dynamic, requiring an optimization algorithm which is able to continuously track a changing optimum over time. In this paper, we explore new variants of particle swarm optimization (PSO) specifically designed to work well in dynamic environments. The main idea is to split the population of particles into a set of interacting swarms. These swarms interact locally by an exclusion parameter and globally through a new anti-convergence operator. In addition, each swarm maintains diversity either by using charged or quantum particles. This paper derives guidelines for setting the involved parameters and evaluates the multiswarm algorithms on a variety of instances of the multimodal dynamic moving peaks benchmark. Results are also compared with other PSO and evolutionary algorithm approaches from the literature, showing that the new multiswarm optimizer significantly outperforms previous approaches <s> BIB002 </s> Particle Swarm Optimization - A Survey <s> Optimization in a Dynamic Environment <s> This paper proposes an improved particle swarm optimizer using the notion of species to determine its neighborhood best values for solving multimodal optimization problems and for tracking multiple optima in a dynamic environment. In the proposed species-based particle swam optimization (SPSO), the swarm population is divided into species subpopulations based on their similarity. Each species is grouped around a dominating particle called the species seed. At each iteration step, species seeds are identified from the entire population, and then adopted as neighborhood bests for these individual species groups separately. Species are formed adaptively at each step based on the feedback obtained from the multimodal fitness landscape. Over successive iterations, species are able to simultaneously optimize toward multiple optima, regardless of whether they are global or local optima. Our experiments on using the SPSO to locate multiple optima in a static environment and a dynamic SPSO (DSPSO) to track multiple changing optima in a dynamic environment have demonstrated that SPSO is very effective in dealing with multimodal optimization functions in both environments <s> BIB003
When the objective function changes dynamically, the PSO system needs to detect and adapt to the changed environment. Again, maintenance of diversity in the swarm is considered to be the key. Hu and Eberhart BIB001 propose to occasionally re-evaluate the objective function at the gbest found so far. Upon detecting the change of the objective function, re-randomization of particle positions and erasing the pbest information have been proposed for re-triggering exploration in a wide area. Blackwell and Branke BIB002 use the multiswarm which consists of multiple subswarms designated to converge to different local extrema. Diversity among the subswarms is maintained by exclusion which re-initializes a subswarm converged at an extremum already taken by another subswarm, and anti-convergence which re-initializes one of the subswarms when there are no more exploratory subswarms. Further, the diversity within the subswarm is maintained by a modeled Coulomb repulsion among particles to prevent the convergence of the subswarms. Also, as previously mentioned, the dynamic version of SPSO (DSPSO) by Parrot and Li BIB003 also successfully tracks multiple moving optima.