Songsong Liu

A mixed integer optimisation approach for integrated water resources management

In areas lacking substantial freshwater resources, the utilisation of alternative water sources, such as desalinated seawater and reclaimed water, is a sustainable alternative option. This paper presents an optimisation approach for the integrated management of water resources, including desalinated seawater, wastewater and reclaimed water, for insular water deficient areas. The proposed mixed integer linear programming (MILP) model takes into account the subdivided regions on the island, the subsequent localised needs for water use (including water quality) and wastewater production, as well as geographical aspects. In addition, the integration of potable and non-potable water systems is considered. The optimal water management decisions, including the location of desalination, wastewater treatment, and reclamation plants, as well as the conveyance infrastructure for desalinated water, wastewater and reclaimed water, are obtained by minimising the annualised total capital and operating costs. Finally, the proposed approach is applied to two Greek islands: Syros and Paros-Antiparos, for case study and scenario analysis.

Integrated Management of Non-conventional Water Resources in Anhydrous Islands

Anhydrous islands are dependent either on non-conventional water resources, such as desalinated seawater or reclaimed water from wastewater, or on water importation from the mainland. The latter option is often expensive and non-sustainable. Desalinated water can be used for potable and non-potable water applications, while reclaimed water can be used for non-potable water applications. Thus all water needs can be satisfied by an optimal blend of desalinated and reclaimed water. It is important to calculate the optimal capacities and locations of seawater desalination plants, wastewater treatment plants and water reclamation plants, and to estimate the water/wastewater conveyance system, in order to minimise water production and distribution costs. Mathematical modelling and optimisation techniques can be employed for calculating the optimum scenario: the satisfaction of all water needs at minimum cost. In this article, we have estimated the water demands taking into account water quality for the anhydrous Greek island of Syros, in the Aegean Sea. Syros has been subdivided into 6 regions, taking into account geographical and population distribution criteria. All water needs are to be satisfied by desalinated seawater and reclaimed water. A mixed-integer linear programming algorithm is used here to calculate the optimal scenario (location and capacities of desalination plants and wastewater treatment and water reclamation plants, as well as the desalinated water, reclaimed water and wastewater conveyance infrastructure needed) by minimising the annualised total cost including capital and operating costs.

Designing cost‐effective biopharmaceutical facilities using mixed‐integer optimization

Chromatography operations are identified as critical steps in a monoclonal antibody (mAb) purification process and can represent a significant proportion of the purification material costs. This becomes even more critical with increasing product titers that result in higher mass loads onto chromatography columns, potentially causing capacity bottlenecks. In this work, a mixed‐integer nonlinear programming (MINLP) model was created and applied to an industrially relevant case study to optimize the design of a facility by determining the most cost‐effective chromatography equipment sizing strategies for the production of mAbs. Furthermore, the model was extended to evaluate the ability of a fixed facility to cope with higher product titers up to 15 g/L. Examination of the characteristics of the optimal chromatography sizing strategies across different titer values enabled the identification of the maximum titer that the facility could handle using a sequence of single column chromatography steps as well as multi‐column steps. The critical titer levels for different ratios of upstream to dowstream trains where multiple parallel columns per step resulted in the removal of facility bottlenecks were identified. Different facility configurations in terms of number of upstream trains were considered and the trade‐off between their cost and ability to handle higher titers was analyzed. The case study insights demonstrate that the proposed modeling approach, combining MINLP models with visualization tools, is a valuable decision‐support tool for the design of cost‐effective facility configurations and to aid facility fit decisions.

MILP-based approaches for medium-term planning of single-stage continuous multiproduct plants with parallel units

In this paper, we address the problem of medium-term planning of single-stage continuous multiproduct plants with multiple processing units in parallel. Sequence-dependent changeover times and costs occur when switching from one type of product to another. A traveling salesman problem (TSP)-based mixed-integer linear programming (MILP) model is proposed based on a hybrid discrete/continuous time representation. We develop additional constraints and variables to ensure that subtours do not occur in the solution. The model is successfully applied to an example of a polymer processing plant to illustrate its applicability. In order to solve larger model instances and planning horizons, a rolling horizon approach is developed to reduce the computational expense. Finally, the proposed model is compared to a recently published approach through literature examples, and the results show that the computational performance of the proposed model is superior.

Optimising chromatography strategies of antibody purification processes by mixed integer fractional programming techniques

Abstract The strategies employed in chromatography steps play a key role in downstream processes for monoclonal antibody (mAb) manufacture. This work addresses the integrated optimisation of chromatography step sequencing and column sizing in mAb purification processes. Chromatography sequencing decisions include the resin selection at each typical step, while the column sizing decisions include the number of columns, the column diameter and bed height, and number of cycles per batch. A mixed integer nonlinear programming (MINLP) model was developed and then reformulated as a mixed integer linear fractional programming (MILFP) model. A literature approach, the Dinkelbach algorithm, was adopted as the solution method for the MILFP model. Finally, an industrially-relevant case study was investigated for the applicability of the proposed models and approaches.

Mathematical programming for piecewise linear regression analysis

A novel piece-wise linear regression method has been proposed in this work.The method partitions samples into multiple regions from a single attribute.Each region is fitted with a linear regression function.An optimisation model is proposed to decide break-points and regression functions.Benchmark examples have been used to demonstrate its efficiency. In data mining, regression analysis is a computational tool that predicts continuous output variables from a number of independent input variables, by approximating their complex inner relationship. A large number of methods have been successfully proposed, based on various methodologies, including linear regression, support vector regression, neural network, piece-wise regression, etc. In terms of piece-wise regression, the existing methods in literature are usually restricted to problems of very small scale, due to their inherent non-linear nature. In this work, a more efficient piece-wise linear regression method is introduced based on a novel integer linear programming formulation. The proposed method partitions one input variable into multiple mutually exclusive segments, and fits one multivariate linear regression function per segment to minimise the total absolute error. Assuming both the single partition feature and the number of regions are known, the mixed integer linear model is proposed to simultaneously determine the locations of multiple break-points and regression coefficients for each segment. Furthermore, an efficient heuristic procedure is presented to identify the key partition feature and final number of break-points. 7 real world problems covering several application domains have been used to demonstrate the efficiency of our proposed method. It is shown that our proposed piece-wise regression method can be solved to global optimality for datasets of thousands samples, which also consistently achieves higher prediction accuracy than a number of state-of-the-art regression methods. Another advantage of the proposed method is that the learned model can be conveniently expressed as a small number of if-then rules that are easily interpretable. Overall, this work proposes an efficient rule-based multivariate regression method based on piece-wise functions and achieves better prediction performance than state-of-the-arts approaches. This novel method can benefit expert systems in various applications by automatically acquiring knowledge from databases to improve the quality of knowledge base.

Mixed integer optimisation of antibody purification processes

Abstract Chromatographic operations are identified as critical steps in a monoclonal antibody (mAb) purification process and can represent a significant proportion of the purification material costs. The optimisation of chromatography equipment sizing strategies is therefore crucial to improve the cost-effectiveness of mAb manufacture. In this work, a mixed-integer linear programming model (MILP) was developed to determine the optimal chromatography column sizing decisions, so as to minimise the cost of goods per gram (COG/g) of the whole mAb manufacturing process. Modelling challenges related with non-linearities involving the multiplication of decision variables were addressed by the use of linearisation techniques allowing the resulting model to determine global process performance metrics (e.g. chromatography processing time, COG/g). The application of the MILP model to an industrially-relevant case study combined with the use of visualisation methods proved to be a valuable tool to explore the characteristics of the optimal sizing strategies across different scenarios and to facilitate decision-making.

DETECTION OF DISJOINT AND OVERLAPPING MODULES IN WEIGHTED COMPLEX NETWORKS

Community structure detection is widely accepted as a means of elucidating the functional properties of complex networks. The problem statement is ever evolving, with the aim of developing more flexible and realistic modeling procedures. For example, a first step in developing a more informative model is the inclusion of weighted interactions. In addition to the standard community structure problem, interest has increased in the detection of overlapping communities. Adopting such constraints may, in some cases, represent a more true to life abstraction of the system under study. In this paper, two novel mathematical programming algorithms for module detection are presented. First, disjoint modules in weighted and unweighted networks are detected by formulating modularity maximization as a mixed integer nonlinear programming (MINLP) model. The solution obtained is then used to detect overlapping modules through a further MINLP model. The inclusion of two parameters controlling the extent of overlapping offers flexibility in user requirements. Comparative results show that these methodologies perform competitively to previously proposed methods. The methodologies proposed here promote the detection of topological relationships in complex systems. Together with the amenable nature of mathematical programming models, we show that both algorithms offer a versatile solution to the community detection problem.

A regression tree approach using mathematical programming

This work proposes a novel tree model for multivariate regression analysis.Both node splitting and regression coefficients are optimised in this model.The proposed method achieves improved prediction accuracy than literature methods.The resultant trees are at least as simple as the ones from previous methods. Regression analysis is a machine learning approach that aims to accurately predict the value of continuous output variables from certain independent input variables, via automatic estimation of their latent relationship from data. Tree-based regression models are popular in literature due to their flexibility to model higher order non-linearity and great interpretability. Conventionally, regression tree models are trained in a two-stage procedure, i.e. recursive binary partitioning is employed to produce a tree structure, followed by a pruning process of removing insignificant leaves, with the possibility of assigning multivariate functions to terminal leaves to improve generalisation. This work introduces a novel methodology of node partitioning which, in a single optimisation model, simultaneously performs the two tasks of identifying the break-point of a binary split and assignment of multivariate functions to either leaf, thus leading to an efficient regression tree model. Using six real world benchmark problems, we demonstrate that the proposed method consistently outperforms a number of state-of-the-art regression tree models and methods based on other techniques, with an average improvement of 760% on the mean absolute errors (MAE) of the predictions.

An Optimisation-based Approach for Integrated Water Resources Management

This paper considers an integrated water management problem for a region lacking fresh and ground water resources, which comprises (a) the optimal placement of desalination, water reclamation and wastewater treatment plants, (b) the calculation of the optimal capacities of the above facilities, and (c) the calculation of the optimal conveyance system for desalinated, reclaimed water and wastewater. This problem is formulated as a mixed-integer linear programming (MILP) model, with an objective to minimise the annualised total cost including capital and operating costs. Finally, the proposed model is applied to a real case for the Greek island of Syros in the Aegean Sea.