LHEMO: LLM-based heuristic evolution for multi-objective sensor-weapon-target assignment

The multi-objective sensor–weapon–target assignment (SWTA) problem requires the coordinated allocation of heterogeneous sensing and action resources under conflicting objectives such as mission effectiveness, resource consumption, and response time. Existing SWTA solvers, including classical multi-objective evolutionary algorithms and recent large language model (LLM)-based automated heuristic design (AHD) methods, either rely heavily on hand-crafted search components or transfer poorly to SWTA because of its heterogeneous entities, strict feasibility requirements, and Pareto-oriented feedback. To address these challenges, we propose LHEMO, an LLM-based heuristic evolution framework for multi-objective SWTA. LHEMO adopts a bi-level architecture: an outer level evolves executable heuristic programs through LLM-guided operators, and an inner multi-objective solver evaluates each candidate. Two reconstruction operators expand exploration through line- and module-level code regeneration, a validation-and-repair mechanism recovers invalid candidates, a cross-generation reflection mechanism reuses evolutionary experience, and a seeded initialization anchors early-stage search. A Pareto-oriented fitness built on per-instance normalized hypervolume and a feasibility penalty guides the evolution toward high-quality trade-off solutions. Experiments on a benchmark ranging from 8 to 320 targets show that LHEMO attains the best hypervolume among nine compared methods on every instance with at least 64 targets and improves upon the strongest hand-crafted baseline by up to 178.9%. Heuristics evolved on a single 12-target training instance retain about 85% of this performance on instances up to 26.7 times larger. These results establish LLM-driven heuristic evolution as a practical paradigm for constraint-intensive multi-objective resource allocation.