Metaheuristic algorithms are a class of optimization techniques that have revolutionized problem-solving across various domains. These algorithms provide a versatile and powerful approach to finding near-optimal solutions for complex, combinatorial, and computationally intensive problems. They draw inspiration from natural processes, such as evolution, swarm behavior, or annealing, to iteratively refine solutions by intelligently navigating the problem space. Metaheuristics have become indispensable tools in both academia and industry, helping researchers and practitioners address real-world problems efficiently and effectively. The Pelican optimization algorithm (POA) is a recently developed metaheuristic algorithm that simulates the hunting behavior of pelicans. In complex optimization problems, an POA may have slow convergence or fall in sub-optimal regions, especially in high complex ones. In this paper, Levy flight is integrated into the exploration phase to enhance its search capabilities. Furthermore, a novel exponential parameter has been introduced to enhance the algorithm's overall performance by facilitating a smoother shift between exploration and exploitation phases. These modifications are intended to keep the algorithm from being locked in local optima. The developed algorithm named as IPOA was tested using widely recognized twenty-three benchmark functions with a variety of characteristics, a set of CEC2022 test suites, and five different engineering constrained problems. The results demonstrate the superiority and effectiveness of IPOA in tackling function optimization and constrained design engineering problems.