Logic-Based Outer-Approximation Algorithm for Solving Discrete-Continuous Dynamic Optimization Problems

Abstract

In this work we present an extension of the Logic Outer-Approximation algorithm for dealing with disjunctive discrete-continuous optimal control problems whose dynamic behavior is modeled in terms of differential-algebraic equations. Although the proposed algorithm can be applied to a wide variety of discrete-continouos optimal control problems we are mainly interested in problems where disjunctions are also present. Disjunctions are included to take into account only certain parts of the underlying model which become relevant under some processing conditions. By doing so the numerical robustness of the optimization algorithm improves since those parts of the model that are not active are discarded leading to a reduced size problem and avoiding potential model singularities. We test the proposed algorithm using 3 examples of different complex dynamic behavior. In all the case studies the number of iterations and the computational load required to get the optimal solutions is modest and the solutions are relatively easy to find

Optimal plate design problem in steel production

“…Logic-based outer approximation (L-OA) algorithm was first proposed by Türkay and Grossmann (1996) to solve the optimal synthesis problem of process networks and had been generalized to many applications in industrial optimization problems (Ruiz-Femenia et al, 2014;Yeomans and Grossmann, 2000). L-OA algorithm could be viewed as an extension of normal outer approximation algorithm which is one of the most common methods of MINLP problems.…”