In the later period of optimization by particle swarm optimization (PSO) algorithm, the diversity scarcity of population easily causes the algorithm fall into the local optimum. Therefore, an improved PSO (IPSO) algorithm is presented, in which each particle has the ability of keeping its inertia motion and learning from another randomly selected particle with better performance; moreover, for the particle with better performance, the inertia weight will be larger and the learning coefficient will be smaller. Thus, for the particles sorted in order of decreasing performance, the inertia weights are decreased and the learning rate coefficients are increased gradually. The new learning approach develops the diversity of the population, while the new parameters setting approach develops the adaptability of the population. Comparison results with the basic PSO on the examination of some well-known benchmark functions show that the IPSO algorithm has higher searching speed and stronger global searching ability.

Shuffled frog leaping algorithm (SFLA) is mainly used for the discrete space optimization. For SFLA, the population is divided into several memeplexes, several frogs of each memeplex are selected to compose a submemeplex for local evolvement, according to the mechanism that the worst frog learns from the best frog in submemeplex or the best frog in population, and the memeplexes are shuffled for the global evolvement after some generations of each memeplex. Derived by the discrete SFLA, a new SFLA for continuous space optimization is presented, in which the population is divided based on the principle of uniform performance of memeplexes, and all the frogs participate in the evolvement by keeping the inertia learning behaviors and learning from better ones selected randomly. The simulation results of searching minima of several multi-peak continuous functions show that the improved SFLA can effectively overcome the problems of premature convergence and slow convergence speed, and achieve high optimization precision.