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

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

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

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

Novel drug-target interactions via link prediction and network embedding

BACKGROUND: As many interactions between the chemical and genomic space remain undiscovered, computational methods able to identify potential drug-target interactions (DTIs) are employed to accelerate drug discovery and reduce the required cost. Predicting new DTIs can leverage drug repurposing by identifying new targets for approved drugs. However, developing an accurate computational framework that can efficiently incorporate chemical and genomic spaces remains extremely demanding. A key issue is that most DTI predictions suffer from the lack of experimentally validated negative interactions or limited availability of target 3D structures. RESULTS: We report DT2Vec, a pipeline for DTI prediction based on graph embedding and gradient boosted tree classification. It maps drug-drug and protein–protein similarity networks to low-dimensional features and the DTI prediction is formulated as binary classification based on a strategy of concatenating the drug and target embedding vectors as input features. DT2Vec was compared with three top-performing graph similarity-based algorithms on a standard benchmark dataset and achieved competitive results. In order to explore credible novel DTIs, the model was applied to data from the ChEMBL repository that contain experimentally validated positive and negative interactions which yield a strong predictive model. Then, the developed model was applied to all possible unknown DTIs to predict new interactions. The applicability of DT2Vec as an effective method for drug repurposing is discussed through case studies and evaluation of some novel DTI predictions is undertaken using molecular docking. CONCLUSIONS: The proposed method was able to integrate and map chemical and genomic space into low-dimensional dense vectors and showed promising results in predicting novel DTIs. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1186/s12859-022-04650-w

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

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

AbstractUnder 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.</jats:p