This work treats the so-called Generalized Quadratic Assignment Problem. Solution methods are based on heuristic and partially LP-optimizing ideas. Base constructive results stem from a simple 1-pass heuristic and a tree-based branch-and-bound type approach. Then we use a combination of Tabu Search and Linear Programming for the improving phase. Hence, the overall approach constitutes a type of mat- and metaheuristic algorithm. We evaluate the different algorithmic designs and report computational results for a number of data sets, instances from literature as well as own ones. The overall algorithmic performance gives rise to the assumption that the existing framework is promising and worth to be examined in greater detail.