Improved NSGA-II for Multi-Objective Optimization of Acoustic Array GDOP under Physical Constraints

Abstract

To address the issue of restricted array layout in wide-area acoustic monitoring, an improved NSGA-II multi-objective optimization algorithm that integrates the feasible region hard constraint initialization (FDHCI) strategy is proposed. This algorithm aims to minimize the geometric accuracy factor (GDOP) and minimize the violation degree of constraints, with two objectives of minimizing GDOP and performing the lowest violation degree. Through the rejection sampling mechanism of the FDHCI strategy, the algorithm ensures that the initial population completely falls within the feasible region, avoiding the waste of resources in repairing infeasible solutions in the early stage. In a monitoring scenario of 200×180m with 4 building obstacles, 32 sensors were deployed as FDHCI-optimized array, basic NSGA-II-optimized array, and traditional-optimized uniform array. The results show that the initial violation degree of constraints of the FDHCI-optimized array (10⁰) is 6 orders of magnitude less than that of the basic NSGA-II (10⁶); the proportion of high-precision positioning area is more than that of the basic NSGA-II and traditional optimized arrays by 4.2% and 4.4% points respectively. The study indicates that constraint compliance and positioning accuracy of the array is optimized significantly by the FDHCI strategy which improving the feasibility of the initial population and the evolutionary efficiency, providing data support for the performance improvement of the acoustic TDOA positioning system.