On the Computation of All Global Minimizers Through Particle Swarm Optimization

Multiple Roots of Systems of Equations by Repulsion Merit Functions

“…This is a system with many roots in the considered search space Ω. Figure 3 be the merit function of the system In [−5, 5] 2 , the merit function has 12 global minimizers [18]. Table 1 shows the average number of roots, N.rootsavg, the average number of function evaluations, NFEavg, and time (in seconds), Tavg, found in five experimental runs produced by our algorithm, where we implemented:…”

“…However, the same solutions may be located over and over again along the iterations and the computational effort turns out to be quite heavy. Other approaches that combine metaheuristics with techniques that modify the objective function in problem (2) have been reported in the literature [17,18,19,20]. The technique in [20] relies on the assignment of a penalty term to each previously computed root so that a repulsion area around the root is created.…”

Searching for the Best Points of Interpolation Using Swarm Intelligence Techniques

“…Based upon a mathematical description of the social behavior of swarms, it has been shown that this algorithm can be efficiently generated to find good solutions to a certain number of complicated situations such as, for instance, the static optimization problems, the topological optimization and others (Parsopoulos, K.E. et al, 2001a); (Parsopoulos, K.E.et al 2001b); (Fourie, P.C. et al, 2000); ( Fourie, P.C.…”

Compound Particle Swarm Optimization in Dynamic Environments

“…Parameters c 1 and c 2 are individual and social learning factors, and ξ and η are random numbers in the range of [0.0, 1.0]. PSO has been widely used for stationary problems [13,14,18]. In recent years, PSO has obtained an increasing concern to solve DOPs [3].…”