A unified framework for model-based multi-objective linear process and energy optimisation under uncertainty

Process and energy models provide an invaluable tool for design, analysis and optimisation. These models are usually based upon a number of assumptions, simplifications and approximations, thereby introducing uncertainty in the model predictions. Making model based optimal decisions under uncertainty is therefore a challenging task. This issue is further exacerbated when more than one objective is to be optimised simultaneously, resulting in a Multi-Objective Optimisation (MO2MO2) problem. Even though, some methods have been proposed for MO2MO2 problems under uncertainty, two separate optimisation techniques are employed; one to address the multi-objective aspect and another to take into account uncertainty. In the present work, we propose a unified optimisation framework for linear MO2MO2 problems, in which the uncertainty and the multiple objectives are modelled as varying parameters. The MO2MO2 under uncertainty problem (MO2U2)(MO2U2) is thus reformulated and solved as a multi-parametric programming problem. The solution of the multi-parametric programming problem provides the optimal solution as a set of parametric profiles

Game theoretic optimisation in process and energy systems engineering: A review

Game theory is a framework that has been used by various research fields in order to represent dynamic correlation among stakeholders. Traditionally, research within the process and energy systems engineering community has focused on the development of centralised decision making schemes. In the recent years, decentralised decision-making schemes have attracted increasing attention due to their ability to capture multi-stakeholder dynamics in a more accurate manner. In this article, we survey how centralised and decentralised decision making has been facilitated by game theoretic approaches. We focus on the deployment of such methods in process systems engineering problems and review applications related to supply chain optimisation problems, design and operations, and energy systems optimisation. Finally, we analyse different game structures based on the degree of cooperation and how fairness criteria can be employed to find fair payoff allocations

Multi-parametric mixed integer linear programming under global uncertainty

Major application areas of the process systems engineering, such as hybrid control, scheduling and synthesis can be formulated as mixed integer linear programming (MILP) problems and are naturally susceptible to uncertainty. Multi-parametric programming theory forms an active field of research and has proven to provide invaluable tools for decision making under uncertainty. While uncertainty in the right-hand side (RHS) and in the objective function's coefficients (OFC) have been thoroughly studied in the literature, the case of left-hand side (LHS) uncertainty has attracted significantly less attention mainly because of the computational implications that arise in such a problem. In the present work, we propose a novel algorithm for the analytical solution of multi-parametric MILP (mp-MILP) problems under global uncertainty, i.e. RHS, OFC and LHS. The exact explicit solutions and the corresponding regions of the parametric space are computed while a number of case studies illustrates the merits of the proposed algorithm

Explicit Model Predictive Control of Hybrid Systems using Multi-parametric Mixed Integer Polynomial Programming

Hybrid systems are dynamical systems characterized by the simultaneous presence of discrete and continuous variables. Model-based control of such systems is computationally demanding. To this effect, explicit controllers which provide control inputs as a set of functions of the state variables have been derived, using multiparametric programming mainly for the linear systems. Hybrid polynomial systems are considered resulting in a Mixed Integer Polynomial Programming problem. Treating the initial state of the system as a set of bounded parameters, the problem is reformulated as a multiparametric Mixed Integer Polynomial optimization (mp-MIPOPT) problem. A novel algorithm for mp-MIPOPT problems is proposed and the exact explicit control law for polynomial hybrid systems is computed. The key idea is the computation of the analytical solution of the optimality conditions while the binary variables are treated as relaxed parameters. Finally, using symbolic calculations exact nonconvex critical regions are compute

Multi-parametric linear programming under global uncertainty

Multi-parametric programming has proven to be an invaluable tool for optimisation under uncertainty. Despite the theoretical developments in this area, the ability to handle uncertain parameters on the left-hand side remains limited and as a result, hybrid, or approximate solution strategies have been proposed in the literature. In this work, a new algorithm is introduced for the exact solution of multi-parametric linear programming problems with simultaneous variations in the objective function's coefficients, the right-hand side and the left-hand side of the constraints. The proposed methodology is based on the analytical solution of the system of equations derived from the first order Karush–Kuhn–Tucker conditions for general linear programming problems using symbolic manipulation. Emphasis is given on the ability of the proposed methodology to handle efficiently the LHS uncertainty by computing exactly the corresponding nonconvex critical regions while numerical studies underline further the advantages of the proposed methodology, when compared to existing algorithms

Nonlinear Model-Based Process Operation under Uncertainty Using Exact Parametric Programming

In the present work, two new, (multi-)parametric programming (mp-P)-inspired algorithms for the solution of mixed-integer nonlinear programming (MINLP) problems are developed, with their main focus being on process synthesis problems. The algorithms are developed for the special case in which the nonlinearities arise because of logarithmic terms, with the first one being developed for the deterministic case, and the second for the parametric case (p-MINLP). The key idea is to formulate and solve the square system of the first-order Karush-Kuhn-Tucker (KKT) conditions in an analytical way, by treating the binary variables and/or uncertain parameters as symbolic parameters. To this effect, symbolic manipulation and solution techniques are employed. In order to demonstrate the applicability and validity of the proposed algorithms, two process synthesis case studies are examined. The corresponding solutions are then validated using state-of-the-art numerical MINLP solvers. For p-MINLP, the solution is given by an optimal solution as an explicit function of the uncertain parameters

Multi set-point explicit model predictive control for nonlinear process systems

In this article, we introduce a novel framework for the design of multi set-point nonlinear explicit controllers for process systems engineering problems where the set-points are treated as uncertain parameters simultaneously with the initial state of the dynamical system at each sampling instance. To this end, an algorithm for a special class of multi-parametric nonlinear programming problems with uncertain parameters on the right-hand side of the constraints and the cost coefficients of the objective function is presented. The algorithm is based on computed algebra methods for symbolic manipulation that enable an analytical solution of the optimality conditions of the underlying multi-parametric nonlinear program. A notable property of the presented algorithm is the computation of exact, in general nonconvex, critical regions that results in potentially great computational savings through a reduction in the number of convex approximate critical regions

Implementation ;performance investigation of dicode PPM over dispersive optical channels

This work is concerned with the development and investigation of a Dicode PPM (DiPPM) system. A DiPPM coder was developed to code any input PCM signal into DiPPM format. A further investigation took place on the DiPPM spectrum and associated output. Software simulation and mathematical analysis of this PPM code was considered and comparison with previous theoretical results presented. Results show that DiPPM is an advantageous PPM code for optic communication; DiPPM spectrum is not concentrated near to DC and it is possible to extract the DiPPM framerate component directly from the pulse stream. A timing extraction circuit that recovers the clock from a DiPPM sequence and synchronises the slots within the frames, was constructed successfully. This enabled transmission through fibre optics and Free Space Optics (FSO). The technique used for the timing extraction circuit of the DiPPM scheme gives an advantage over many of the PPM formats. An optical transmitter/receiver system was developed and the DiPPM scheme was investigated through optical channels. Results show that the DiPPM sequence transferred through the optic system was not changed and the clock had been recovered. A DiPPM decoder was constructed and the received DiPPM signal returned to its original PCM form without errors. Both DiPPM coder and decoder were developed in VHDL and measurements were taken. The timing extraction was programmed in VHDLAMS with the use of digital, analogue and mathematical equations. DiPPM MLSD was also constructed in VHDL. Simulation results proved the theoretical expectations.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

A game-theoretic optimisation approach to fair customer allocation in oligopolies

Under the ever-increasing capital intensive environment that contemporary process industries face, oligopolies begin to form in mature markets where a small number of companies regulate and serve the customer base. Strategic and operational decisions are highly dependent on the firms’ customer portfolio and conventional modelling approaches neglect the rational behaviour of the decision makers, with regards to the problem of customer allocation, by assuming either static competition or a leader-follower structure. In this article, we address the fair customer allocation within oligopolies by employing the Nash bargaining approach. The overall problem is formulated as mixed integer program with linear constraints and a nonlinear objective function which is further linearised following a separable programming approach. Case studies from the industrial liquid market highlight the importance and benefits of the proposed game theoretic approach