Review of Mixed-Integer Nonlinear and Generalized Disjunctive Programming Methods

A feasible path-based branch and bound algorithm for strongly nonconvex MINLP problems

In this paper, a feasible path-based branch and bound (B&B) algorithm is proposed to solve mixed-integer nonlinear programming problems with highly nonconvex nature through integration of the previously proposed hybrid feasible-path optimisation algorithm and the branch and bound method. The main advantage of this novel algorithm is that our previously proposed hybrid steady-state and time-relaxation-based optimisation algorithm is employed to solve a nonlinear programming (NLP) subproblem at each node during B&B. The solution from a parent node in B&B is used to initialize the NLP subproblems at the child nodes to improve computational efficiency. This approach allows circumventing complex initialisation procedure and overcoming difficulties in convergence of process simulation. The capability of the proposed algorithm is illustrated by several process synthesis and intensification problems using rigorous models.

Data Driven Control of Vagus Nerve Stimulation for the Cardiovascular System: An in Silico Computational Study

Vagus nerve stimulation is an emerging therapy that seeks to offset pathological conditions by electrically stimulating the vagus nerve through cuff electrodes, where an electrical pulse is defined by several parameters such as pulse amplitude, pulse width, and pulse frequency. Currently, vagus nerve stimulation is under investigation for the treatment of heart failure, cardiac arrhythmia and hypertension. Through several clinical trials that sought to assess vagus nerve stimulation for the treatment of heart failure, stimulation parameters were determined heuristically and the results were inconclusive, which has led to the suggestion of using a closed-loop approach to optimize the stimulation parameters. A recent investigation has demonstrated highly specific control of cardiovascular physiology by selectively activating different fibers in the vagus nerve. When multiple locations and multiple stimulation parameters are considered for optimization, the design of closed-loop control becomes considerably more challenging. To address this challenge, we investigated a data-driven control scheme for both modeling and controlling the rat cardiovascular system. Using an existing in silico physiological model of a rat heart to generate synthetic input-output data, we trained a long short-term memory network (LSTM) to map the effect of stimulation on the heart rate and blood pressure. The trained LSTM was utilized in a model predictive control framework to optimize the vagus nerve stimulation parameters for set point tracking of the heart rate and the blood pressure in closed-loop simulations. Additionally, we altered the underlying in silico physiological model to consider intra-patient variability, and diseased dynamics from increased sympathetic tone in designing closed-loop VNS strategies. Throughout the different simulation scenarios, we leveraged the design of the controller to demonstrate alternative clinical objectives. Our results show that the controller can optimize stimulation parameters to achieve set-point tracking with nominal offset while remaining computationally efficient. Furthermore, we show a controller formulation that compensates for mismatch due to intra-patient variabilty, and diseased dynamics. This study demonstrates the first application and a proof-of-concept for using a purely data-driven approach for the optimization of vagus nerve stimulation parameters in closed-loop control of the cardiovascular system.

New Algorithm to Solve Mixed Integer Quadratically Constrained Quadratic Programming Problems Using Piecewise Linear Approximation

Techniques and methods of linear optimization underwent a significant improvement in the 20th century which led to the development of reliable mixed integer linear programming (MILP) solvers. It would be useful if these solvers could handle mixed integer nonlinear programming (MINLP) problems. Piecewise linear approximation (PLA) is one of most popular methods used to transform nonlinear problems into linear ones. This paper will introduce PLA with brief a background and literature review, followed by describing our contribution before presenting the results of computational experiments and our findings. The goals of this paper are (a) improving PLA models by using nonuniform domain partitioning, and (b) proposing an idea of applying PLA partially on MINLP problems, making them easier to handle. The computational experiments were done using quadratically constrained quadratic programming (QCQP) and MIQCQP and they showed that problems under PLA with nonuniform partition resulted in more accurate solutions and required less time compared to PLA with uniform partition.

Innovative Application of Model-Based Predictive Control for Low-Voltage Power Distribution Grids with Significant Distributed Generation

In past decades, the deployment of renewable-energy-based power generators, namely solar photovoltaic (PV) power generators, has been projected to cause a number of new difficulties in planning, monitoring, and control of power distribution grids. In this paper, a control scheme for flexible asset management is proposed with the aim of closing the gap between power supply and demand in a suburban low-voltage power distribution grid with significant penetration of solar PV power generation while respecting the different systems’ operational constraints, in addition to the voltage constraints prescribed by the French distribution grid operator (ENEDIS). The premise of the proposed strategy is the use of a model-based predictive control (MPC) scheme. The flexible assets used in the case study are a biogas plant and a water tower. The mixed-integer nonlinear programming (MINLP) setting due to the water tower ON/OFF controller greatly increases the computational complexity of the optimisation problem. Thus, one of the contributions of the paper is a new formulation that solves the MINLP problem as a smooth continuous one without having recourse to relaxation. To determine the most adequate size for the proposed scheme’s sliding window, a sensitivity analysis is carried out. Then, results given by the scheme using the previously determined window size are analysed and compared to two reference strategies based on a relaxed problem formulation: a single optimisation yielding a weekly operation planning and a MPC scheme. The proposed problem formulation proves effective in terms of performance and maintenance of acceptable computational complexity. For the chosen sliding window, the control scheme drives the power supply/demand gap down from the initial one up to 38%.

Modern Modeling Paradigms Using Generalized Disjunctive Programming

Models involving decision variables in both discrete and continuous domain spaces are prevalent in process design. Generalized Disjunctive Programming (GDP) has emerged as a modeling framework to explicitly represent the relationship between algebraic descriptions and the logical structure of a design problem. However, fewer formulation examples exist for GDP compared to the traditional Mixed-Integer Nonlinear Programming (MINLP) modeling approach. In this paper, we propose the use of GDP as a modeling tool to organize model variants that arise due to characterization of different sections of an end-to-end process at different detail levels. We present an illustrative case study to demonstrate GDP usage for the generation of model variants catered to process synthesis integrated with purchasing and sales decisions in a techno-economic analysis. We also show how this GDP model can be used as part of a hierarchical decomposition scheme. These examples demonstrate how GDP can serve as a useful model abstraction layer for simplifying model development and upkeep, in addition to its traditional usage as a platform for advanced solution strategies.

Integrating Genome-Scale and Superstructure Optimization Models in Techno-Economic Studies of Biorefineries

Genome-scale models have become indispensable tools for the study of cellular growth. These models have been progressively improving over the past two decades, enabling accurate predictions of metabolic fluxes and key phenotypes under a variety of growth conditions. In this work, an efficient computational method is proposed to incorporate genome-scale models into superstructure optimization settings, introducing them as viable growth models to simulate the cultivation section of biorefinaries. We perform techno-economic and life-cycle analyses of an algal biorefinery with five processing sections to determine optimal processing pathways and technologies. Formulation of this problem results in a mixed-integer nonlinear program, in which the net present value is maximized with respect to mass flowrates and design parameters. We use a genome-scale metabolic model of Chlamydomonas reinhardtii to predict growth rates in the cultivation section. We study algae cultivation in open ponds, in which exchange fluxes of biomass and carbon dioxide are directly determined by the metabolic model. This formulation enables the coupling of flowrates and design parameters, leading to more accurate cultivation productivity estimates with respect to substrate concentration and light intensity.

Process intensification

Process intensification (PI) is a rapidly growing field of research and industrial development that has already created many innovations in chemical process industry. PI is directed toward substantially smaller, cleaner, more energy-efficient technology. Furthermore, PI aims at safer and sustainable technological developments. Its tools are reduction of the number of devices (integration of several functionalities in one apparatus), improving heat and mass transfer by advanced mixing technologies and shorter diffusion pathways, miniaturization, novel energy techniques, new separation approaches, integrated optimization and control strategies. This review discusses many of the recent developments in PI. Starting from fundamental definitions, microfluidic technology, mixing, modern distillation techniques, membrane separation, continuous chromatography, and application of gravitational, electric, and magnetic fields will be described.

Recent Developments and Challenges in Optimization-Based Process Synthesis

This article first reviews recent developments in process synthesis and discusses some of the major challenges in the theory and practice in this area. Next, the article reviews key concepts in optimization-based conceptual design, namely superstructure representations, multilevel models, optimization methods, and modeling environments. A brief review of the synthesis of major subsystems and flowsheets is presented. Finally, the article closes with a critical assessment and future research challenges for the process synthesis area.