Aiming at the problems of low efficiency and difficulty in constructing acceleration devices in traditional interval optimization algorithms (IOAs), this paper constructs a valid acceleration device based on a more concise point evolutionary strategy (ES), and then proposes a novel hybrid IOA (HIOA) with no requirement on the derivative of the objective function. The HIOA first divides the initial search area into $N$ equal parts, randomly selects multiple point individuals in each subinterval to represent their information, and performs the optimization with fewer iterations using ES for all point individuals to make them closer to the optima; then selects reliable subintervals containing more point individuals to split, and deletes unreliable subintervals without any point individuals; finally, provides a reliable upper bound to direct the pruning operation to further improve the search efficiency. Furthermore, the convergence property of the proposed algorithm is analyzed. Extensive numerical experiments on several typical test functions and the application to the bounded error parameter estimation demonstrate the superiority of HIOA by comparing it with the existing conventional algorithms, which confirms the effectiveness and applicability of the suggested algorithm.