Integration of logic and heuristic knowledge in discrete optimization techniques for process systems

This thesis deals with the development of effective techniques to integrate logic and heuristic knowledge with discrete mathematical optimization methods for the design and synthesis of chemical systems. Conventional mathematical optimization approaches for process synthesis do not fully exploit the logic structure of the problem nor do they apply engineering heuristics used by designers to simplify the solution space. To deal with this problem, the thesis has studied the role of logic in the modelling and solution of discrete optimization problems and proposed techniques to integrate logic within mathematical optimization methods both at the quantitative and symbolic level.; At the quantitative level, logical relationships and engineering heuristics can be expressed as equivalent linear inequalities. The logical inference problem is shown to be solvable as a Mixed-Integer linear programming problem. Strategies to integrate the logic and heuristic knowledge, in the form of these linear inequalities, with MINLP approaches are proposed at the levels of both model formulation and algorithmic search. Extensive numerical results are reported with these methods.; At the symbolic level, a propositional logic based representation is developed for representing the interconnections between units in a process network and a modified branch and bound algorithm is then proposed that performs symbolic inference on these logical relationships simultaneously with the numerical tree search. It is shown that reductions of more than an order of magnitude can be obtained on MILP separation systems synthesis problems. The suggested approach has been automated within the Optimization Subroutine Library.; Finally, the issue of representing general discrete optimization problems has been studied and a modelling framework has been presented for this class of problems in which mixed-integer relationships are expressed as disjunctions while others are expressed as algebraic constraints. A theoretical characterization of disjunctive constraints is proposed which can serve as a criterion for deciding whether a disjunction should be transformed into equation form or handled symbolically. A solution algorithm is presented for solving the problem in this form.