A mixed integer quadratic programming formulation for the economic dispatch of generators with prohibited operating zones

In this paper, an optimisation-based approach is proposed using a mixed integer quadratic programming model for the economic dispatch of electrical power generators with prohibited zones of operation. The main advantage of the proposed approach is its capability to solve case studies from the literature to global optimality quickly and without any targeting of solution procedures. (c) 2006 Elsevier B.V. All rights reserved

Piecewise Regression through the Akaike Information Criterion using Mathematical Programming

In machine learning, regression analysis is a tool for predicting the output variables from a set of known independent variables. Through regression analysis, a function that captures the relationship between the variables is fitted to the data. Many methods from literature tackle this problem with various degrees of difficulty. Some simple methods include linear regression and least squares, while some are more complicated such as support vector regression. Piecewise or segmented regression is a method of analysis that partitions the independent variables into intervals and a function is fitted to each interval. In this work, the Optimal Piecewise Linear Regression Analysis (OPLRA) model is used from literature to tackle the problem of segmented analysis. This model is a mathematical programming approach that is formulated as a mixed integer linear programming problem that optimally partitions the data into multiple regions and calculates the regression coefficients, while minimising the Mean Absolute Error of the fitting. However, the number of regions is a known priori. For this work, an extension of the model is proposed that can optimally decide on the number of regions using information criteria. Specifically, the Akaike Information Criterion is used and the objective is to minimise its value. By using the criterion, the model no longer needs a heuristic approach to decide on the number of regions and it also deals with the problem of overfitting and model complexity

Medium-term optimization-based approach for the integration of production planning, scheduling and maintenance

A medium-term optimization-based approach is proposed for the integration of production planning, scheduling and maintenance. The problem presented in this work considers a multiproduct single-stage batch process plant with parallel units and limited resources. An MILP continuous-time formulation is developed based on the main ideas of travelling salesman problem and precedence-based constraints to deal with, sequence-dependent unit performance decay, flexible recovery operations, resource availability and product lifetime. Small scheduling examples have been solved and compared with adapted formulations from the literature, based on discrete-time and global-time events, demonstrating the effectiveness of the proposed solution approach. Additional planning and scheduling problems have been proposed by considering several time periods. Multi-period examples have been efficiently solved by the model showing the applicability of the solution approach for medium-size problems

Optimal Antibody Purification Strategies Using Data-Driven Models

This work addresses the multiscale optimization of the purification processes of antibody fragments. Chromatography decisions in the manufacturing processes are optimized, including the number of chromatography columns and their sizes, the number of cycles per batch, and the operational flow velocities. Data-driven models of chromatography throughput are developed considering loaded mass, flow velocity, and column bed height as the inputs, using manufacturing-scale simulated datasets based on microscale experimental data. The piecewise linear regression modeling method is adapted due to its simplicity and better prediction accuracy in comparison with other methods. Two alternative mixed-integer nonlinear programming (MINLP) models are proposed to minimize the total cost of goods per gram of the antibody purification process, incorporating the data-driven models. These MINLP models are then reformulated as mixed-integer linear programming (MILP) models using linearization techniques and multiparametric disaggregation. Two industrially relevant cases with different chromatography column size alternatives are investigated to demonstrate the applicability of the proposed models

Tree regression models using statistical testing and mixed integer programming

Regression analysis is a statistical procedure that fits a mathematical function to a set of data in order to capture the relationship between dependent and independent variables. In tree regression, tree structures are constructed by repeated splits of the input space into two subsets, creating if-then-else rules. Such models are popular in the literature due to their ability to be computed quickly and their simple interpretations. This work introduces a tree regression algorithm that exploits an optimisation model of an existing literature method called Mathematical Programming Tree (MPtree) to optimally split nodes into subsets and applies a statistical test to assess the quality of the partitioning. Additionally, an approach of splitting nodes using multivariate decision rules is explored in this work and compared in terms of performance and computational efficiency. Finally, a novel mathematical model is introduced that performs subset selection on each node in order to select an optimal set of variables to considered for splitting, that improves the computational performance of the proposed algorithm

Key aspects in the strategic development of synthetic natural gas (BioSNG) supply chains

This work investigates the impact of pretreatment technologies in the design of BioSNG supply chains at a regional and national scale. For this purpose, an optimisation-based framework is proposed to account for two possible routes for BioSNG production. The first route considers processing of raw biomass and production of BioSNG in integrated facilities. The second route consists of pretreatment technologies, transportation of intermediate products, and upgrading facilities. The main objective is to investigate the trade-off between capital investment and reduction of transportation costs, and their impact on the economic performance of a BioSNG supply chain. Moreover, the impact of government subsidisation is further investigated through a parametric analysis in which the tariff is varied from £0/MWh up to £100/MWh. Finally, the major contributing factors in the design of BioSNG supply chains are identified through the implementation of a rigorous global sensitivity analysis (GSA). The results suggest that inclusion of pretreatment technologies improve considerably the economic performance, however, their impact is not enough to detach the development from government subsidisation which influences tremendously the possibility of a large-scale deployment

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

An optimisation framework for the strategic design of synthetic natural gas (BioSNG) supply chains

A general optimisation framework based on a spatially-explicit multiperiod mixed integer linear programming (MILP) model is proposed to address the strategic design of BioSNG supply chains. The framework considers procurement of feedstocks, plantation of energy crops, and different modes for transportation of feedstocks and final products. The mathematical framework allows researches and policy makers to investigate scenarios that promote the development of BioSNG supply chains in a regional and/or national context. The capabilities of the proposed model are illustrated through the implementation of a set of case studies based on the UK. The results revealed that domestic resources in the UK can supply up to 21.4% of the total gas demand projected by the UK National Grid in the scenario “Slow progression” for a planning horizon of 20 years. However, despite the considerable potential for production of BioSNG, the role of the government through subsidisation schemes such as feed-in tariff and Renewable Obligation Certificates (ROCs) is crucial in order to make the development of these resources economically attractive for private sectors

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

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