Abstract
The P-graph framework was originally developed to address Process Network Synthesis (PNS) problems in the preliminary design of chemical plants. P-graph provides a mathematically rigorous and computationally efficient framework for solving PNS problems via the maximal structure generation (MSG), solution structure generation (SSG) and accelerated branch-and-bound (ABB) algorithms. MSG ensures rigorous generation of the maximal structure, while the ad hoc generation of a superstructure as basis for a mathematical programming model can lead to significant modelling errors. In addition, SSG allows the generation of combinatorially feasible network structures that can be utilized for practical decision-making by designers. For very large problems, ABB can reduce the computational effort of reaching globally optimal solutions by multiple orders of magnitude compared to conventional branch-and-bound solvers for Mixed Integer Linear Programming (MILP) models. In addition to conventional PNS problems, P-graph has been applied to the optimization of separation processes, Heat Exchanger Networks (HENs), Combined Heat and Power (CHP) systems, chemical reaction pathways, polygeneration plants, biorefineries, and supply chains. Further non-conventional applications have also been reported, such as the optimisation of office processes, human resource networks, and economic structures at the level of cities or regions. In addition to synthesis and design problems, P-graph has also been applied to operational problems, such as determining the best abnormal operating conditions for process networks. These diverse applications suggest the potential for applying the P-graph framework as a problem-solving strategy for a broad class of generalized process networks, beyond the traditional PNS problems in chemical plant design. This paper surveys recent trends in the P-graph literature and uses bibliometric analysis to identify promising trends and discusses potential directions for novel applications for optimization of generalized process networks, particularly for applications that address critical sustainability issues.
