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）是运筹学领域中最难求解的问题之一。本工作研究的GQAP定义为：在将一组设施分配到一组位置的过程中，最小化分配成本与运输成本的任务。各设施具有不同的空间需求，而各位置具有不同的空间容量。若空间容量未被违反，则每个位置可分配多个设施。本文提出三种不同情境下的GQAP实例，随后开发了一种遗传算法来求解这些GQAP实例。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，同时将该解与MPL/CPLEX软件及参考文献中的最优解进行比较。结果表明，所开发的遗传算法启发式方法能有效求解GQAP。