The particle swarm optimization (PSO) algorithm is a new population based search strat-

egy, which has exhibited good performance on well-known numerical test problems. How-

ever, on strongly multi-modal test problems the PSO tends to suffer premature

convergence. This is due to a decrease of diversity in search space that leads to a to-

tal implosion and ultimately fitness stagnation of the swarm. An accepted hypothesis

is that maintenance of high diversity is crucial for preventing premature convergence in

multi-modal optimization.-The particle swarm optimization (PSO) algorithm is a new population based search strat-

egy, which has exhibited good performance on well-known numerical test problems. How-

ever, on strongly multi-modal test problems the PSO tends to suffer　premature

convergence. This is due to a decrease of diversity in search space that leads to a to-

tal implosion and ultimately fitness stagnation of the swarm. An accepted hypothesis

is that maintenance of high diversity is crucial for preventing premature convergence in

multi-modal optimization.