Abstract Bat algorithm (BA) is a heuristic optimization algorithm based on swarm intelligence and the inspiration from the nature behavior of bats. It has some advantages including fast solving speed, high precision and only few parameters need to be adjusted. However, BA is easy to fall into local optima and has unstable optimization results due to low global exploration ability. In order to overcome these weakness, a new bat algorithm based on iterative local search and stochastic inertia weight (ILSSIWBA) is proposed in this paper. A kind of local search algorithm, called iterative local search (ILS) is introduced into the proposed algorithm. The ILS algorithm disturbs the local optimum and do some local re-search, so that the ILSSIWBA has strong ability to jump out of the local optima. In addition, a weight updating method, called stochastic inertia weight (SIW) is also introduced into the proposed algorithm. Considering the SIW in the velocity updating equation can enhance the diversity and flexibility of bat population, so that the ILSSIWBA has stable optimization results. Meanwhile, the pulse rate and loudness are modified to enhance the balance performance between global and local search. Moreover, the global convergence of ILSSIWBA is proved by the convergence criteria of stochastic algorithm. In the end, the ILSSIWBA is compared with directional bat algorithm (DBA) and other algorithms on 10 classic benchmark functions, CEC 2005 benchmark suite, and two real-world problems. The results show that ILSSIWBA has remarkable advantages in optimization accuracy, solving speed and convergence stability. This algorithm lays a solid foundation for solving modeling, optimization and control problems of complex systems.