Abstract

Segmentation is a tool presented for representation and approximation of data, according to a set of appropriate models. These procedures have applications to many different domains, such as time series analysis, polygonal approximation, Air Traffic Control,... Different heuristic and metaheuristic proposals have been introduced to deal with this issue. This thesis provides a novel multiobjective evolutionary method, analyzing the required general tools for the application evolutionary algorithms to real problems and the specific modifications required over the different steps of general proposals to adapt them to the segmentation domain. An introduction to the domain is presented by means of the design of a specific heuristic for segmentation of Air Traffic Control (ATC) data. This domain has a series of characteristics which make it difficult to be faced with traditional techniques: noisy data and a large number of measurements. The proposal works on two phases, using a pre-segmentation which introduces available domain information and applying a standard technique over this initial technique's results. Its results according to the presented domain, tested with a set of eight different representative trajectories, show competitive advantages compared to general approaches, which oversegmentate noisy data and, in some cases, exhibit poor scalability. This heuristic proposal shows the costly process of adapting available approaches and designing specific ones, along with the multi-objective nature of the problem, which requires the use of quality indicators for a proper comparison process. Applying evolutionary algorithms to segmentation provides several advantages, highlighting the fact that the problem dependance of heuristics make it costly to adapt these heuristics to new domains, as introduced by the designed heuristic to ATC. However, the practical application of these algorithms requires the study of a topic which has received little research effort from the community: stopping criteria. An evolutionary approach should contain a dynamic procedure which can determine when stagnation has taken place and stop the algorithm accordingly (as opposed to a-priori cost budgets, either in function evaluations or generations, which are usually applied for test datasets). Stopping criteria have been faced for single and multi-objective cases in this thesis. Single-objective stopping criteria have been approached proposing an active role of the stopping criteria, actively increasing the diversity in the variable space while tracking the updates in the fitness function. Thus, the algorithm reuses the information obtained for the stopping decision and feeds it to a stopping prevention mechanism in order to prevent problematic situations such as early convergence. The presented algorithm has been tested according to a set of 27 different functions, with different characteristics regarding their dimensionality, search space, local minima... The results show that the introduced mechanisms enhance the robustness of the results, due to the improved exploration and the early convergence prevention. Multi-objective stopping criteria are faced with the use of progress indicators (comparison measures of the quality of the evolution results at different generations) and an associated data gathering tool. The final proposal uses three different progress indicators, (hypervolume, epsilon and Mutual Dominance Rate) and considers them jointly according to a decision fusion architecture. The stagnation analysis is based on the least squares regression parameters of the indicators values, including a normality analysis as well. The online nature of these algorithms is highlighted, preventing the recomputation of the indicators values which were present in other available alternatives, and also focusing on the simplicity of the final proposal, in order to reduce the cost of introducing it into available algorithms. The proposal has been tested with instances of the DTLZ algorithm family, obtaining satisfactory stops with a standard set of configuration values for the technique. However, there is a lack of quantitative measures to determine the objective quality of a stop and to properly compare its value to other alternatives. The multi-objective nature of the segmentation problem is analyzed to propose a multiobjective evolutionary algorithm (MOEA) to deal with it. This nature is analyzed according to a selection of available approaches, highlighting the difficulties which had to be faced in the parameter configuration in order to guide the processes to the desired solution values. A multi-objective a-posteriori approach such as the one presented allows the decision maker to choose from the front of possible final solutions the one which suits him best, simplifying this process. The presented approach chooses SPEA2 as its underlying MOEA, analyzing different representation and initialization proposals. The results have been validated against a representative set of heuristic and metaheuristic techniques, using three widely extended curves from the polygonal approximation domain (chromosome, leaf and semicircle), obtaining statistically better results for almost all the different test cases. This initial MOEA approach had unresolved issues, such as the archiving technique complexity order, and also lacked the proper specific design considerations to adapt it to the application domain. These issues have been faced according to different improvements. First of all, an alternative representation is proposed, including partial fitness information and associated fitness-aware transformation operators (transformation operators which compute children fitness values according to their changes and the parents partial values). A novel archiving procedure is introduced according to the bi-objective nature of the domain, being one of them discrete. This leads to a relaxed Pareto dominance check, named epsilon glitches. Multi-objective local search versions of the traditional algorithms are proposed and tested for the initialization of the algorithm, along with the stopping criterion proposal which has also been adapted to the problem characteristics. The archive size in this case is big enough to contain all the different individuals in the optimal front, such that quality assessment is simplified and a simpler mechanism can be introduced to detect stagnation, according to the improvements in each of the possible individuals. The final evolutionary proposal is scalable, requires few configuration parameters and introduces an efficient dynamic stopping criterion. Its results have been tested against the original technique and the set of heuristic and metaheuristic techniques previously used, including the three original curves and also more complex versions of them (obtained with an introduced generation mechanism according to these original shapes). Even though the stopping results are very satisfactory, the obtained results are slightly worse than the original MOEA for the three simpler problem instances with the established configuration parameters (as was expected, due to the computational effort of the a-priori established number of generations and population size, based on the analysis of the algorithm's results). However, the comparison versus the alternative techniques stills shows the same statistically better results, and its reduced computational cost allows its application to a wider set of problems.