Criterion Space Search Algorithms for Nonlinear Integer Multiobjective programs

Most real-world optimization problems in the areas of applied sciences, engineering and economics involve multiple, often conflicting, goals. In the mathematical modeling of these problems, under the necessity of reflecting discrete quantities, logical relationships or decisions, integer and 0-1 variables need to be considered. On the other hand, real-world applications rely on non-linear functions for the definition of the inner relations of a model. In this context, the aim of this thesis concerns the solution of Multiobjective Integer Programs (MOIP), with possibly non-linear convex objectives and constraints. The challenging nature of MOIPs and the need for methods with guaranteed performance motivated the development of exact solution approaches. To the best of our knowledge, algorithms for multiobjective optimization can be divided into three categories: decision space search algorithms (i.e. approaches searching in the space of feasible solutions), criterion space search algorithms (i.e. methods searching in the space of objective function values) and hybrid methods, which try to combine the previous two. In this thesis, all these categories are discussed and new competitive criterion space search algorithms are introduced. The analysis is supported by numerical evidence.