Distance-Gradient-Based Convex Optimization for Efficient Near-Optimal Coverage in WSNs

Coverage optimization in Wireless Sensor Networks is a fundamental yet NP-hard problem that directly affects monitoring quality and efficiency. Existing solutions mainly rely on meta-heuristic algorithms that use fitness-based evaluations, which often incur high computational overhead, slow convergence, and limited scalability, particularly in real-time or high-precision monitoring scenarios. In this paper, we examine the relationship between effective coverage area and redundant distances in an analytical manner. We then propose reformulating WSN coverage optimization as a Distance-Gradient based convex optimization problem, which can be subsequently solved using the first-order Gradient Descent algorithm or the second-order quasi-Newton algorithm. Extensive comparative experiments against five representative meta-heuristic methods, the Virtual Force Algorithm (VFA) and a general convex optimization algorithm (CVX), demonstrate that our approach achieves near-optimal coverage while preserving network connectivity within milliseconds, highlighting its advantages over existing methods for WSNs coverage optimization.