Heuristic optimization algorithms play an important role in solving complex, nonlinear, multimodal, or high-dimensional optimization problems. This paper proposes a heuristic optimization algorithm based on the hunting behavior of falcons, called the Falcon-Inspired Heuristic Optimization (FIH). This algorithm achieves efficient global search and local fine-grained search capabilities by simulating the falcon's swooping hunting, prey prediction, energy management and strategy switching, and swarm perception mechanisms. The algorithm's core mechanisms include speed-distance adaptive swooping, local intelligent search, energy hopping strategy, and swarm information fusion. This paper systematically describes and analyzes the algorithm through mathematical formulas and discusses its applicability to high-dimensional continuous optimization, constrained optimization, multimodal optimization, and combinatorial optimization problems.