Disjunctive-Genetic Programming Approach to Synthesis of Process Networks

Abstract

In this work, disjunctive-genetic programming (D-GP), based on the integration of genetic algorithm (GA) with the disjunctive formulations of generalized disjunctive programming (GDP) for the optimization of process networks, has been proposed. Discrete optimization problems, which give rise to the conditional modeling of equations through representations as logic based disjunctions, are very important and often appear in all scales of chemical engineering process network design and synthesis. The decomposition of the resulting mixed integer nonlinear programming (MINLP) problem obtained from the relaxation of the disjunctive formulation of the original problem results in alternating solutions of mixed integer linear programming (MILP) master problems and nonlinear programming (NLP) subproblems. With the increase in the problem scale, dealing with such alternating routes becomes difficult due to increased computational load and possible entanglement of the results in suboptimal solutions due to infeasibilities in the MILP space. In this work, the genetic algorithm (GA) has been used as a jumping operator to the different terms of the discrete search space and for the generation of different feasible fixed configurations. This proposed approach eliminates the need for the reformulation of the discrete/discontinuous optimization problems into direct MINLP problems, thus allowing for the solution of the original problem as a continuous optimization problem but only at each individual discrete and reduced search space. Segment-based mutation (SBM) and segment-based floating crossover (SBFC) strategies were proposed for the efficient handling of the population of chromosomes comprising the coded terms of the disjunctions. The effectiveness of D-GP as shown on various benchmark problems involving heat exchange equipment design and network problems as well as a classical process network problem shows this may be a promising approach in dealing with process network problems with large discontinuous objective and/or constraint functions.