This paper introduces evolutionary optimization as a grid-free training-free continuous-domain search mechanism for near-field multi-source localization, addressing the major limitations of grid-based subspace methods such as MUSIC and data-driven deep learning approaches. To this end, we develop two complementary evolutionary localization frameworks that operate directly on the continuous spherical-wave signal model and support arbitrary array geometries without requiring labeled data, discretized angle-range grids, or architectural constraints. The first framework, termed NEar-field MultimOdal DE (NEMO-DE) associates each individual in the evolutionary population to a single source and optimizes a residual least-squares objective in a sequential manner, updating the data residual and enforcing spatial separation to estimate multiple source locations. To overcome the limitation of NEMO-DE under large power imbalances among the sources, we propose the second framework, named NEar-field Eigen-subspace Fitting DE (NEEF-DE), which jointly encodes all source locations and minimizes a subspace-fitting criterion that aligns a model-based array response subspace with the received signal subspace. The proposed formulations are not intrinsically tied to a specific optimizer; however, this work adopts differential evolution (DE) as a representative evolutionary search strategy because of its simple implementation, small number of control parameters, and strong empirical performance in continuous nonconvex optimization problems. Numerical results show that the proposed frameworks provide competitive accuracy compared with MUSIC-type baselines while avoiding pre-defined grid construction and labeled training data. This work establishes evolutionary computation as a powerful and flexible paradigm for model-based near-field localization, paving the way for future innovations in this domain.

翻译：本文介绍演化优化作为一种无网格、免训练、连续域搜索机制，用于近场多源定位，解决了基于网格的子空间方法（如MUSIC）和数据驱动的深度学习方法的局限性。为此，我们开发了两个互补的演化定位框架，它们直接基于连续球面波信号模型运行，支持任意阵列几何结构，无需标注数据、离散化角度-距离网格或架构约束。第一个框架称为近场多模态差分演化（NEMO-DE），将演化种群中的每个个体关联到一个单一信源，以序贯方式优化残差最小二乘目标，更新数据残差并强制空间分离以估计多个信源位置。为克服NEMO-DE在信源间功率严重不平衡时的局限性，我们提出第二个框架，名为近场特征子空间拟合差分演化（NEEF-DE），该框架联合编码所有信源位置，并最小化一个子空间拟合准则，将基于模型的阵列响应子空间与接收信号子空间对齐。所提出的公式化方法并不固有地绑定于特定优化器；然而，本文采用差分演化（DE）作为代表性演化搜索策略，因其实现简单、控制参数少，且在连续非凸优化问题中表现出色。数值结果表明，所提框架相比MUSIC类基线提供了竞争性精度，同时避免了预定义网格构建和标注训练数据。本文将演化计算确立为基于模型的近场定位的强大灵活范式，为该领域的未来创新铺平了道路。