RETRACTED: Multi-target point path planning for inspection robots based on improved GWO and A* algorithms

Abstract

Multi-target path planning in structured environments remains challenging due to local-optimal trapping, high computational burden, and the incompatibility of classical A* with multi-objective constraints. This paper proposes a two-layer hybrid framework, IGWO-I-A*, integrating an Improved Gray Wolf Optimizer (IGWO) with an enhanced multi-objective A* (I-A*) to simultaneously optimize traversal order and the actual navigation path. In the upper layer, IGWO incorporates (i) IAM-TSP–based population initialization and (ii) a dynamic elite-based 2-Opt operator. These strategies reduce the average tour cost on TSPLIB benchmarks by 12.08%, 10.24%, 5.01%, 27.32%, 18.32%, and 27.55% for Att48, Eil101, Ch130, Pr136, Ch150, and Rand200, respectively, compared with basic GWO. IGWO also achieves near-optimal error rates of 0–0.15%, significantly outperforming ACO (0.54–3.50%), PSO (4.39–7.67%), SA (10.67–21.36%) and GA (95–186%). In the lower layer, the enhanced A* incorporates weighted objectives for path length, turning energy, and safety cost. Across grid-based robot-inspection scenarios, I-A* reduces the comprehensive cost by 21.8% (Scenario 1) and 29.4% (Scenario 2) versus classical A*. Moreover, the proposed IGWO-I-A* produces stable convergence, avoiding premature stagnation and achieving up to 133–250% lower error compared to GWO-I-A*. Simulation results in four representative environments confirm that IGWO-I-A* generates inspection paths with fewer turns, higher safety, and significantly faster convergence than competing approaches, demonstrating its suitability for multi-target robot inspection tasks.