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Barrier coverage in wireless sensor networks (WSNs) is a well-known model for military security applications in IoTs, in which sensors are deployed to detect every movement over the predefined border. The fundamental sub-problem of barrier coverage in WSNs is the minimal exposure path (MEP) problem. The MEP refers to the worst-case coverage path where an intruder can move through the sensing field with the lowest capability to be detected. Knowledge about MEP is useful for network designers to identify the worst coverage in WSNs. Most prior research focused on this problem with the assumption that the WSN has an ideal deployment environment without obstacles, causing existing gaps between theoretical and practical WSNs systems. To overcome this drawback, we investigate a systematic and generic MEP problem under real-world environment networks by presenting obstacles called Obstacle-Evasion-MEP (hereinafter OE-MEP). We propose an algorithm to create several types of arbitrary-shaped obstacles inside the deployment area of WSNs. The OE-MEP problem is an NP-Hard with high dimension, non-differentiation, non-linearity, and constraints. Based upon its characteristics, we then devise an elite algorithm namely Family System based Evolutionary Algorithm (FEA) with our newly-proposed concepts of Family System, tailored to efficiently solve the OE-MEP. We also build an extension to a custom-made simulation environment to integrate a variety of network topologies as well as obstacles. Experimental results on numerous instances indicate that the proposed algorithm is suitable for the converted OE-MEP problem and performs better in solution accuracy than existing approaches. • Formulate the obstacles-evade minimal exposure path problem in WSNs. • Model and devise a method to randomly generate obstacles in different forms. • Propose the Family System based on Evolutionary Algorithm for solving this problem. • Conduct a number of systematic simulations and analyze the experimental results. [ABSTRACT FROM AUTHOR]