Evolutionary Multiobjective Optimization: Review, Algorithms, and Applications
Roman Denysiuk · Portuguese National Funding Agency for Science, Research and Technology (RCAAP Project by FCT) · 2014
Many mathematical problems arising from diverse elds of human activity can be formulated as optimization problems. The majority of real-world optimization problems involve several and con icting objectives. Such problems are called multiobjective optimization problems (MOPs). The presence of multiple con icting objectives that have to be simultaneously optimized gives rise to a set of trade-o solutions, known as the Pareto optimal set. Since this set of solutions is crucial for e ective decision-making, which generally aims to improve the human condition, the availability of e cient optimization methods becomes indispensable. Recently, evolutionary algorithms (EAs) have become popular and successful in approximating the Pareto set. The population-based nature is the main feature that makes them especially attractive for dealing with MOPs. Due to the presence of two search spaces, operators able to e ciently perform the search in both the decision and objective spaces are required. Despite the wide variety of existing methods, a lot of open research issues in the design of multiobjective evolutionary algorithms (MOEAs) remains. This thesis investigates the use of evolutionary algorithms for solving multiobjective optimization problems. Innovative algorithms are developed studying new techniques for performing the search either in the decision or the objective space. Concerning the search in the decision space, the focus is on the combinations of traditional and evolutionary optimization methods. An issue related to the search in the objective space is studied in the context of many-objective optimization. Application of evolutionary algorithms is addressed solving two di erent real-world problems, which are modeled using multiobjective approaches. The problems arise from the mathematical modelling of the dengue disease transmission and a wastewater treatment plant design. The obtained results clearly show that multiobjective modelling is an e ective approach. The success in solving these challenging optimization problems highlights the practical relevance and robustness of the developed algorithms.