The generalized quadratic assignment problem (GQAP) is one of the hardest problems to solve in the operations research area. The GQAP addressed in this work is defined as the task of minimizing the assignment and transportation costs of assigning a set of facilities to a set of locations. The facilities have different space requirements, and the locations have different space capacities. Multiple facilities can be assigned to each location if the space capacity is not violated. In this work, three instances of GQAP in different situations are presented. Then, a genetic algorithm is developed to solve the GQAP instances. Finally, the local neighborhood search with the steepest descend strategy is constructed and applied to the final solution obtained by the GA, and the final solution is compared with the best solution found by MPL/CPLEX software and reference papers. The results show that the developed GA heuristic is effective for solving the GQAP.

翻译：广义二次分配问题（GQAP）是运筹学领域最难求解的问题之一。本文研究的GQAP定义为最小化将一组设施分配到一组位置所产生的分配与运输成本。各设施具有不同的空间需求，而各位置则具有不同的空间容量。在不超过空间容量的条件下，可将多个设施分配至同一位置。本文给出了三种不同场景下的GQAP实例，随后开发了一种遗传算法对这些实例进行求解。最后，构建了基于最速下降策略的局部邻域搜索，并将其应用于遗传算法所得最终解，通过将该解与MPL/CPLEX软件及参考文献中的最优解进行对比。结果表明，所开发的遗传算法启发式方法对求解GQAP具有有效性。