Data-driven scenario generation for two-stage stochastic programming

Optimisation under uncertainty has always been a focal point within the Process Systems Engineering (PSE) research agenda. In particular, the efficient manipulation of large amount of data for the uncertain parameters constitutes a crucial condition for effectively tackling stochastic programming problems. In this context, this work proposes a new data-driven Mixed-Integer Linear Programming (MILP) model for the Distribution & Moment Matching Problem (DMP). For cases with multiple uncertain parameters a copula-based simulation of initial scenarios is employed as preliminary step. Moreover, the integration of clustering methods and DMP in the proposed model is shown to enhance computational performance. Finally, we compare the proposed approach with state-of-the-art scenario generation methodologies. Through a number of case studies we highlight the benefits regarding the quality of the generated scenario trees by evaluating the corresponding obtained stochastic solutions

Module detection in complex networks using integer optimisation

<p>Abstract</p> <p>Background</p> <p>The detection of <it>modules or community structure </it>is widely used to reveal the underlying properties of complex networks in biology, as well as physical and social sciences. Since the adoption of modularity as a measure of network topological properties, several methodologies for the discovery of community structure based on modularity maximisation have been developed. However, satisfactory partitions of large graphs with modest computational resources are particularly challenging due to the NP-hard nature of the related optimisation problem. Furthermore, it has been suggested that optimising the modularity metric can reach a resolution limit whereby the algorithm fails to detect smaller communities than a specific size in large networks.</p> <p>Results</p> <p>We present a novel solution approach to identify community structure in large complex networks and address resolution limitations in module detection. The proposed algorithm employs modularity to express network community structure and it is based on mixed integer optimisation models. The solution procedure is extended through an iterative procedure to diminish effects that tend to agglomerate smaller modules (resolution limitations).</p> <p>Conclusions</p> <p>A comprehensive comparative analysis of methodologies for module detection based on modularity maximisation shows that our approach outperforms previously reported methods. Furthermore, in contrast to previous reports, we propose a strategy to handle resolution limitations in modularity maximisation. Overall, we illustrate ways to improve existing methodologies for community structure identification so as to increase its efficiency and applicability.</p

Stable optimisation-based scenario generation via game theoretic approach

Systematic scenario generation (SG) methods have emerged as an invaluable tool to handle uncertainty towards the efficient solution of stochastic programming (SP) problems. The quality of SG methods depends on their consistency to generate scenario sets which guarantee stability on solving SPs and lead to stochastic solutions of good quality. In this context, we delve into the optimisation-based Distribution and Moment Matching Problem (DMP) for scenario generation and propose a game-theoretic approach which is formulated as a Mixed-Integer Linear Programming (MILP) model. Nash bargaining approach is employed and the terms of the objective function regarding the statistical matching of the DMP are considered as players. Results from a capacity planning case study highlight the quality of the stochastic solutions obtained using MILP DMP models for scenario generation. Furthermore, the proposed game-theoretic extension of DMP enhances in-sample and out-of-sample stability with respect to the challenging problem of user-defined parameters variability

Optimisation as a Tool for Gaining Insight: An Application to the Built Environment

The design of heating systems for dwellings using new technologies, or new versions of old technologies, requires the ability to predict the temperatures in a dwelling. The temperature behaviour can be modelled, typically by differential equations which incorporate thermal driving forces and the thermal inertia of a dwelling. The development and characterisation of these models is usually based on fitting data accumulated over sufficient time to capture the behaviour of the dwelling under different conditions (summer, winter, etc.). Model fitting relies on assumptions about the behaviour of the system. Optimisation can be used to examine these assumptions and gain insight into this behaviour. This paper describes the application of a nature inspired algorithm, known as the Plant Propagation Algorithm, a variant of a Variable Neighbourhood Search algorithm, to the problem of modelling a dwelling heated by an air source heat pump. The algorithm is evaluated using different population evolution strategies and implemented using a simple parallel computing paradigm on a multi-core desktop system. The results are used to identify potential sources of missing data which could explain the observed behaviour of the dwelling. </jats:p

A rolling horizon approach for optimal management of microgrids under stochastic uncertainty

This work presents a Mixed Integer Linear Programming (MILP) approach based on a combination of a rolling horizon and stochastic programming formulation. The objective of the proposed formulation is the optimal management of the supply and demand of energy and heat in microgrids under uncertainty, in order to minimise the operational cost. Delays in the starting time of energy demands are allowed within a predefined time windows to tackle flexible demand profiles. This approach uses a scenario-based stochastic programming formulation. These scenarios consider uncertainty in the wind speed forecast, the processing time of the energy tasks and the overall heat demand, to take into account all possible scenarios related to the generation and demand of energy and heat. Nevertheless, embracing all external scenarios associated with wind speed prediction makes their consideration computationally intractable. Thus, updating input information (e.g., wind speed forecast) is required to guarantee good quality and practical solutions. Hence, the two-stage stochastic MILP formulation is introduced into a rolling horizon approach that periodically updates input information

Optimal Piecewise Linear Regression Algorithm for QSAR Modelling

Quantitative Structure‐Activity Relationship (QSAR) models have been successfully applied to lead optimisation, virtual screening and other areas of drug discovery over the years. Recent studies, however, have focused on the development of models that are predictive but often not interpretable. In this article, we propose the application of a piecewise linear regression algorithm, OPLRAreg, to develop both predictive and interpretable QSAR models. The algorithm determines a feature to best separate the data into regions and identifies linear equations to predict the outcome variable in each region. A regularisation term is introduced to prevent overfitting problems and implicitly selects the most informative features. As OPLRAreg is based on mathematical programming, a flexible and transparent representation for optimisation problems, the algorithm also permits customised constraints to be easily added to the model. The proposed algorithm is presented as a more interpretable alternative to other commonly used machine learning algorithms and has shown comparable predictive accuracy to Random Forest, Support Vector Machine and Random Generalised Linear Model on tests with five QSAR data sets compiled from the ChEMBL database

Optimisation Models for Pathway Activity Inference in Cancer

BACKGROUND: With advances in high-throughput technologies, there has been an enormous increase in data related to profiling the activity of molecules in disease. While such data provide more comprehensive information on cellular actions, their large volume and complexity pose difficulty in accurate classification of disease phenotypes. Therefore, novel modelling methods that can improve accuracy while offering interpretable means of analysis are required. Biological pathways can be used to incorporate a priori knowledge of biological interactions to decrease data dimensionality and increase the biological interpretability of machine learning models. METHODOLOGY: A mathematical optimisation model is proposed for pathway activity inference towards precise disease phenotype prediction and is applied to RNA-Seq datasets. The model is based on mixed-integer linear programming (MILP) mathematical optimisation principles and infers pathway activity as the linear combination of pathway member gene expression, multiplying expression values with model-determined gene weights that are optimised to maximise discrimination of phenotype classes and minimise incorrect sample allocation. RESULTS: The model is evaluated on the transcriptome of breast and colorectal cancer, and exhibits solution results of good optimality as well as good prediction performance on related cancer subtypes. Two baseline pathway activity inference methods and three advanced methods are used for comparison. Sample prediction accuracy, robustness against noise expression data, and survival analysis suggest competitive prediction performance of our model while providing interpretability and insight on key pathways and genes. Overall, our work demonstrates that the flexible nature of mathematical programming lends itself well to developing efficient computational strategies for pathway activity inference and disease subtype prediction

An integrated platform for intuitive mathematical programming modeling using LaTeX

This paper presents a novel prototype platform that uses the same LaTeX mark-up language, commonly used to typeset mathematical content, as an input language for modeling optimization problems of various classes. The platform converts the LaTeX model into a formal Algebraic Modeling Language (AML) representation based on Pyomo through a parsing engine written in Python and solves by either via NEOS server or locally installed solvers, using a friendly Graphical User Interface (GUI). The distinct advantages of our approach can be summarized in (i) simplification and speed-up of the model design and development process (ii) non-commercial character (iii) cross-platform support (iv) easier typo and logic error detection in the description of the models and (v) minimization of working knowledge of programming and AMLs to perform mathematical programming modeling. Overall, this is a presentation of a complete workable scheme on using LaTeX for mathematical programming modeling which assists in furthering our ability to reproduce and replicate scientific work

Biopharmaceutical capacity planning for batch and semi-continuous bioprocesses under various strategic criteria

Biopharmaceutical companies with expanding portfolios of commercial therapeutics face increasing pressure to meet market demands whilst minimising costs and capital expenditure. Attaining optimal production plans is made more problematic by portfolios containing products with different production modes: batch and semi-continuous. Semi-continuous perfusion-mode products often exhibit a distinct separation of upstream and downstream manufacturing via an intermediate freezing step. This flexibility adds further complexity which needs to be efficiently overcome during the optimisation process. An added complexity to having different process modes is that changeover times are different, leading to computationally expensive sequence-dependent changeover times. Considering the implications of incorrect capacity planning from a business perspective, a framework which can help manufacturers predict capacity bottlenecks whilst concurrently satisfying multiple objectives has great industrial importance. This presentation describes the development of a mixed integer linear program that incorporates both perfusion and batch processes to produce capacity plans and manufacturing schedules. The mathematical model has expanded on previous work and has been reformulated to consist of a more computationally efficient state task network (STN) which can solve problems faster and obtain lower manufacturing costs. The model aims to help manufacturers decide whether to outsource to a contract manufacturing organisation (CMO), build a new facility, or do both as capacity limits are reached. The advantages of retrofitting existing facilities to accommodate different products as opposed to outsourcing capacity are examined. These different approaches of increasing manufacturing capacity each have trade-offs in terms of cost, time and risks. The complexity of the model is increased by considering the multi-objective nature of this problem, such as optimising the manufacturing cost whilst maintaining facility utilisation targets, or limiting the number of product changeovers so as to minimise contamination risks. An industrial case study is presented with results showing how these factors, including varying the changeover times between perfusion and fed-batch campaigns, can impact the different objectives and manufacturing schedules

Investigating the Trade-Off between Design and Operational Flexibility in Continuous Manufacturing of Pharmaceutical Tablets: A Case Study of the Fluid Bed Dryer

Market globalisation, shortened patent lifetimes and the ongoing shift towards personalised medicines exert unprecedented pressure on the pharmaceutical industry. In the push for continuous pharmaceutical manufacturing, processes need to be shown to be agile and robust enough to handle variations with respect to product demands and operating conditions. In this paper we examine the use of operational envelopes to study the trade-off between the design and operational flexibility of the fluid bed dryer at the heart of a tablet manufacturing process. The operating flexibility of this unit is key to the flexibility of the full process and its supply chain. The methodology shows that for the fluid bed dryer case study there is significant effect on flexibility of the process at different drying times with the optimal obtained at 700 s. The flexibility is not affected by the change in volumetric flowrate, but only by the change in temperature. Here the method used a black box model to show how it could be done without access to the full model equation set, as this often needs to be the case in commercial settings