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Plant root foraging exhibits complex behaviors analogous to those of animals, including the adaptability to continuous changes in soil environments. In this work, we adapt the optimality principles in the study of plant root foraging behavior to create one possible bio-inspired optimization framework for solving complex engineering problems. This provides us with novel models of plant root foraging behavior and with new methods for global optimization. This framework is instantiated as a new search paradigm, which combines the root tip growth, branching, random walk, and death. We perform a comprehensive simulation to demonstrate that the proposed model accurately reflects the characteristics of natural plant root systems. In order to be able to climb the noise-filled gradients of nutrients in soil, the foraging behaviors of root systems are social and cooperative, and analogous to animal foraging behaviors.