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People from a variety of industrial domains are beginning to realise that appropriate use of machine learning techniques for their data mining projects could bring great benefits. End-users now have to face the new problem of how to choose a combination of data processing tools and algorithms for a given dataset. This problem is usually termed the Full Model Selection (FMS) problem. Extended from our previous work [10], in this paper, we introduce a framework for designing FMS algorithms. Under this framework, we propose a novel algorithm combining both genetic algorithms (GA) and particle swarm optimization (PSO) named GPS (which stands for GA-PSO-FMS), in which a GA is used for searching the optimal structure for a data mining solution, and PSO is used for searching optimal parameters for a particular structure instance. Given a classification dataset, GPS outputs a FMS solution as a directed acyclic graph consisting of diverse data mining operators that are available to the problem. Experimental results demonstrate the benefit of the algorithm. We also present, with detailed analysis, two model-tree-based variants for speeding up the GPS algorithm