Population diversity of particle swarm optimizer solving single-and multi-objective problems

Premature convergence occurs in swarm intelligence algorithms searching for optima. A swarm intelligence algorithm has two kinds of abilities: exploration of new possibilities and exploitation of old certainties. The exploration ability means that an algorithm can explore more search places to increase the possibility that the algorithm can find good enough solutions. In contrast, the exploitation ability means that an algorithm focuses on the refinement of found promising areas. An algorithm should have a balance between exploration and exploitation, that is, the allocation of computational resources should be optimized to ensure that an algorithm can find good enough solutions effectively. The diversity measures the distribution of individuals' information. From the observation of the distribution and diversity change, the degree of exploration and exploitation can be obtained. Another issue in multiobjective is the solution metric. Pareto domination is utilized to compare two solutions; however, solutions are almost Pareto non-dominated for multiobjective problems with more than ten objectives. In this chapter, the authors analyze the population diversity of a particle swarm optimizer for solving both single objective and multiobjective problems. The population diversity of solutions is used to measure the goodness of a set of solutions. This metric may guide the search in problems with numerous objectives. Adaptive optimization algorithms can be designed through controlling the balance between exploration and exploitation.