Design of an Algorithm for Multiobjective Optimization with Differential Evolution

In many real-world optimization problems the quality of solutions is determined with several fundamentally different objectives, such as, for example, cost, performance and profit. These objectives are often mutually conflicting thus yielding several optimal solutions, where each of them represents a different tradeoff between the objectives. Classicalmethods solve multiobjective optimization problems by first transforming all objectives into a single one (often using the weighted sum approach) and then optimizing the resulting objective. Evolutionary algorithms, on the other hand, treat all objectives independently and provide as a result a set of tradeoff solutions. Several state-of-the-art multiobjective evolutionary algorithms, such as NSGA-II, SPEA2 and IBEA use the same genetic algorithm to search solutions and differ only in the procedure used for selecting the best solutions, called environmental selection. In this thesis, a novel algorithm DEMO (Differential Evolution for Multiobjective Optimization) is presented, which can incorporate an arbitrary environmental selection procedure and generates the solutions with differential evolution—an evolutionary algorithm that often outperforms genetic algorithms on singleobjective optimization problems. DEMO was implemented in four variants with different environmental selection procedures and was compared to the corresponding algorithms NSGA-II, SPEA2 and IBEA (in two variants). Results of extensive experiments show that DEMO variants are significantly better than the compared algorithms on most test problems. Therefore, we can conclude that differential evolution is more efficient than genetic algorithms also on multiobjective optimization problems. Finally, the DEMO variant which achieves the best distribution of vectors in the objective space is used on the practical problem of setting the parameters of decision tree building algorithms in such away that the obtained trees are as accurate and small as possible. On the tested machine learning domains DEMO finds good tradeoffs between accurate and small decision trees thus enabling the users to easily choose the most desired solution.