Obtaining Simultaneous Equation Models through a Unified Shared-Memory Scheme of Metaheuristics

A Simultaneous Equation Model represents simultaneous dependencies in a set of variables. These models are normally created by experts in the field, but in some cases it is difficult to obtain such a model, for example due to a large number of variables, to unclear dependencies, etc. Furthermore, sometimes it is necessary to evaluate models composed of different variables before to obtain the values of the variables in the model and subsequently a satisfactory model. It is possible to develop metaheuristics to help the expert in the automatic generation of satisfactory models. But it is necessary to experiment with several metaheuristics and tune them for the problem. Furthermore, inside a metaheuristic a large number of models are evaluated, and when the number of variables is large, the evaluation of the models is very time consuming. This paper presents some metaheuristics for obtaining Simultaneous Equation Models from a set of values of the variables. A unified shared-memory scheme for metaheuristics is used, which allows the easy application and tuning of different metaheuristics and combinations of them. Shared-memory versions of the metaheuristics are developed to reduce the execution time. To obtain parallel versions of the metaheuristics quickly, the unified metaheuristic scheme is used, so obtaining a unified parallel scheme for metaheuristics. The different functions in the scheme are parallelized independently, and each function is parameterized with a different number of threads, which allows us to select a different number of threads for each function and metaheuristic, so adapting the parallel scheme to the metaheuristic, the computational system and the problem. Experiments with GRASP, genetic algorithms, scatter search and combinations of them are shown.