Metaheuristics algorithms are competitive methods for solving assignment problems. This paper reports on nature inspired algorithms approach which is the particle swarm optimization (PSO) method hybrid with a local search (LS) algorithm for solving the quadratic three-dimensional assignment problem (Q3AP) where population-based metaheuristics like PSO or GA failed to solve. Q3AP is one of the combinatorial problems proven to be NP-Hard. It is an extension of the quadratic assignment problem (QAP). Solving the Q3AP consists of finding an optimal symbol mapping over two vectors, whereas solving the QAP consists of finding an optimal symbol mapping over one vector only. The authors tested the proposed hybrid algorithm on many instances where some of them haven't been used in the previous works for solving Q3AP. The results show that compared with the PSO algorithm and the genetic algorithm (GA), the proposed hybrid PSO-ILS (TS) algorithm is promising for finding the optimal/best known solution.