Abstract: Particle swarm optimization (PSO) is becoming one of
the most important swarm intelligent paradigms for solving global
optimization problems. Although some progress has been made to
improve PSO algorithms over the last two decades, additional work
is still needed to balance parameters to achieve better numerical
properties of accuracy, efficiency, and stability. In the optimal
PSO algorithm, the optimal weightings of (√ 5 − 1)/2 and (3 − √5)/2 are used for the cognitive factor and the social factor,
respectively. By the same token, the same optimal weightings have
been applied for intensification searches and diversification searches,
respectively. Perturbation and constriction effects are optimally
balanced. Simulations of the de Jong, the Rosenbrock, and the
Griewank functions show that the optimal PSO algorithm indeed
achieves better numerical properties and outperforms the canonical
PSO algorithm.
Abstract: Ant colony optimization (ACO) and its variants are
applied extensively to resolve various continuous optimization
problems. As per the various diversification and intensification
schemes of ACO for continuous function optimization, researchers
generally consider components of multidimensional state space to
generate the new search point(s). However, diversifying to a new
search space by updating only components of the multidimensional
vector may not ensure that the new point is at a significant distance
from the current solution. If a minimum distance is not ensured
during diversification, then there is always a possibility that the
search will end up with reaching only local optimum. Therefore, to
overcome such situations, a Mahalanobis distance-based
diversification with Nelder-Mead simplex-based search scheme for
each ant is proposed for the ACO strategy. A comparative
computational run results, based on nine nonlinear standard test
problems, confirms that the performance of ACO is improved
significantly with the integration of the proposed schemes in the
ACO.