A Primer on Evolutionary Optimization Frameworks for Near-Field Multi-Source Localization

Abstract

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.