We present the parallel and interacting stochastic approximation annealing (PISAA) algorithm, a stochastic simulation procedure for global optimisation, that extends and improves the stochastic approximation annealing (SAA) by using population Monte Carlo ideas. The efficiency of standard SAA algorithm crucially depends on its self-adjusting mechanism which presents stability issues in high dimensional or rugged optimisation problems. The proposed algorithm involves simulating a population of SAA chains that interact each other in a manner that significantly improves the stability of the self-adjusting mechanism and the search for the global optimum in the sampling space, as well as it inherits SAA desired convergence properties when a square-root cooling schedule is used. It can be implemented in parallel computing environments in order to mitigate the computational overhead. As a result, PISAA can address complex optimisation problems that it would be difficult for SAA to satisfactory address. We demonstrate the good performance of the proposed algorithm on challenging applications including Bayesian network learning and protein folding. Our numerical comparisons suggest that PISAA outperforms the simulated annealing, stochastic approximation annealing, and annealing evolutionary stochastic approximation Monte Carlo.