Nested Heuristic and Gradient-based Method for Generalized Disjunctive Programming

Abstract

The Generalized Disjunctive Programming (GDP) has been proposed as an alternative to the mixed integer nonlinear programming (MINLP) for applications in process synthesis. It is straightforward in conditional modelling. Besides, it can reduce the complexity of the NLP sub-problems. In this paper, a nested method combining heuristic algorithm and gradient-based optimizer is proposed to solve the GDPs. It is generally a two-layer method, where the heuristic algorithm such as Tabu Search (TS) or Genetic Algorithm (GA) performs master iterations in the outer loop dealing with the logical variables of GDPs, and a gradient-based NLP solver such as Sequential Quadratic Programming (SQP) is applied in the inner layer dealing with the sub-NLP problems. In each call by the outer-layer heuristic algorithm, a set of logic values is specified and passed to the inner-layer. The general GDP model can thus be transformed into a reduced NLP sub-problem by automatically eliminating a number of equations based on the logic disjunction, nonlinear ones in some cases. After the execution of the gradient-based NLP solver, the result of each NLP sub-problem is returned to the outer-layer for further iterations. The heuristic method is responsible to find the global optimum of logic variables. Good performance has been demonstrated by applying the combined method into process synthesis such as heat exchanger networks (HEN) and the integrated water systems.