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The classical Load Balancing Problem (LBP) is to map tasks to processors so as to minimize the maximum load. Solving the LBP successfully would lead to better utilization of resources and better performance. The LBP has been proven to be NP-hard, thus generating the exact solutions in a tractable amount of time becomes infeasible when the problems become large.We present a new nature-inspired approximation algorithm based on the Particle Mechanics (PM) model to compute in parallel approximate efficient solutions for LBPs. Just like other Nature-inspired Algorithms (NAs) drawing from observations of physical processes that occur in nature, the PM algorithm is inspired by physical models of particle kinematics and dynamics. The PM algorithm maps the classical LBP to the movement of particles in a force field by a corresponding mathematical model in which all particles move according to certain defined rules until reaching a stable state. By anti-mapping the stable state, the solution to LBP can be obtained.