We consider a class of problems where a given number p of facility locations must be selected from a set of s potential locations so as to optimize a pre-determined fitness function. There exist outstanding location problems in this class, such as the p-median, max-covering, MAXCAP, and MAXPROFIT problems. These location problems may contain more than a single global optimal solution. Obtaining multiple global optimal solutions allows us to consider other characteristics in the process of selecting the preferred solution. In [B. Pelegrín, J. Redondo, P. Fernández, I. García, and P. Ortigosa, GASUB: Finding global optima to discrete location problems by a genetic-like algorithm, J. Glob. Optim. 38 (2007), pp. 249–264], a new ‘multimodal’ algorithm (gasub) was presented for solving the previously mentioned location problems. In the paper, the algorithm was fine-tuned to obtain a single global optimum (with 100% success) as fast as possible, and it was compared with two widely used techniques, that is, the standard optimizer Xpress-MP [Xpress-MP, Dashoptimization, 2004.] and the Multi Start Heuristic. In this paper, we propose a new set of parameter values so that gasub can explore the space more deeply and consequently find several alternative global optimal solutions. Moreover, two coarse-grain parallelizations of gasub are presented, cggasub and cggasub_mo. cggasub is able to reduce the computational time of gasub where solutions of the same quality are generated, while cggasub_mo finds more alternative global optima than the sequential version and spending similar computational time in the process. gasub, with the new parameter setting and also the parallel algorithms, will be evaluated using a comprehensive computational set of experiments. Additionally, some criteria can also be used to select one of the known global optimal solutions when several alternatives optimize the corresponding objective function.