Improved Formulations and Computational Strategies for the Solution and Nonconvex Generalized Disjunctive Programs

Many optimization problems require the modelling of discrete and continuous variables, giving rise to mixed-integer linear and mixed-integer nonlinear programming (MILP / MINLP). An alternative representation of MINLP is Generalized Disjunctive Programming (GDP)1. GDP models are represented through continuous and Boolean variables, and involve algebraic equations, disjunctions, and logic propositions. This higher level representation facilitates the modelling process while keeping the logic structure of the problem. GDP models are typically reformulated as MINLP problems to exploit the developments in these solvers. The two traditional GDP-to-MINLP reformulations are the Big-M (BM) and Hull-reformulation (HR). Alternatively to direct MINLP reformulations, special techniques can help to improve the performance in solving GDP problems. There are two main contributions in this thesis. The first contribution involves the development of reformulations and methods that generate improved MINLP models form GDP problems. This development is achieved by exploiting the logic-nature of GDP, as well as alternative GDP-to-MINLP reformulations, to obtain relatively small MINLP models with tight continuous relaxations. The second contribution of this thesis is the improvement of existing GDP solution methods by the use of novel concepts. In particular, we improve the linear disjunctive branch and bound through the use of a Lagrangean relaxation of the HR. Also, we extend the logic-based outer-approximation to nonconvex problems, and develop a novel method to obtain cutting planes that improves the linear relaxation of the nonconvex problem. In the thesis, we first present a new Big-M reformulation of GDPs. Unlike the traditional