Heat Integration (Part 3)

3 fevereiro 2022, 11:00 • Pedro Castro

Part 3 deals with the minimisation of the total investment cost of the heat exchanger network. The problem can be formulated as a non-convex NLP that is built from a superstructure that includes all heat-exchanger possibilities between any pair of hot and cold streams.

Implementation of the model in GAMS, followed by its solution for the complete network and the regions above and below the pinch. The results are interesting in the sense that the option with the fewest heat exchangers is not the one leading to the lowest total cost. 

Heat Integration (Part 2)

1 fevereiro 2022, 08:30 • Pedro Castro

MILP model to minimize the number of heat exchanger units. Implementation and solution in GAMS for the complete network as well as for the regions above and below the pinch.

Heat Integration (Part 1)

31 janeiro 2022, 11:00 • Pedro Castro

3rd MAP45 - Implementing missing constraints of the Wastewater Treatment Network (WTN) design problem, given the Excel file, and then solving the problem to local optimality (trying different initialisations).
Mathematical programming for improving energy efficiency in the chemical industry. Synthesis of heat exchanger networks through a sequential approach.
Part 1 deals with LP transshipment model for minimising total utility cost. Exercise to implement model in GAMS with emphasis on with dynamic sets to obtain a general model that works with different data.

Global Optimization Algorithms for NLPs

27 janeiro 2022, 11:00 • Pedro Castro

Two-stage MILP/NLP decomposition algorithms for QCPs. Spatial brand-and-bound for general problems.
The wastewater treatment network (WTN) design problem. NLP formulation and three relaxation models (of different strengths). Illustration by solving a WTN problem in GAMS. Comparison of performance to commercial global optimization solver BARON.

Piecewise Relaxation of Quadratically Constrained Problems (QCPs)

25 janeiro 2022, 08:30 • Pedro Castro

Linear Programming relaxation of the bilinear terms in a QCP using the McCormick envelopes. Mixed-Integer Linear Programming relaxations from piecewise McCormick envelopes and the Multiparametric Disaggregation Technique.
QCP formulation for the design of water-using networks (WUN).
Solving a WUN design problem for a multi-contaminant system using Excel (starting from a file with the flowrate and mass balance constraints over the unit's inlet mixers missing; constrains in the solver window also missing). Importance of initialisation of model variables for convergence (from network with no re-use and recycling).