Pump scheduling in drinking water distribution networks with an LP/NLP-based branch and bound

This paper offers a novel approach for computing globally optimal solutions to the pump scheduling problem in drinking water distribution networks. A tight integer linear relaxation of the original non-convex formulation is devised and solved by branch and bound where integer nodes are investigated through non-linear programming to check the satisfaction of the non-convex constraints and compute the actual cost. This generic method can tackle a large variety of networks , e.g. with variable-speed pumps. We also propose to specialize it for a common subclass of networks with several improving techniques, including a new primal heuristic to repair near-feasible integer relaxed solutions. Our approach is numerically assessed on various case studies of the literature and compared with recently reported results

Process optimization of a lignocellulosic multi-product biorefinery

2014 - 2015A methodology to reduce the complexity of the process optimization was applied to multiproduct biorefinery fed by lignocellulosic biomass. A process superstructure was built to consider alternative process pathways to levulinic acid, succinic acid and ethanol. A Mixed Integer Non-Linear Problem was obtained and transformed in a Mixed Integer Linear Problem by means of a discretization procedure of the non-linear variables. Rigorous design methods accounting for complete kinetics schemes for hydrolysis and fermentation reactors for the production of levulinic acid, succinic acid and ethanol were included in a biorefinery superstructure optimization. A discretization method was applied to obtain a MILP approximation of the resulting MINLP master problem. The optimal flowsheet of a biorefinery with hardwood feedstock, obtained by maximizing the Net Present Value, yields comparable biomass allocation to levulinic acid and succinic acid (more than 40% each) and the its balance to ethanol. A sensitivity analysis highlighted that the optimal flowsheet and the relevant technical and economic performances are significantly dependent on the economic scenario (chemical products selling price, discount rate) and on the plant scale. Finally, process optimization achieved by maximizing two different economic objective functions, Net Present Value and Internal Rate of Return, provided different optimal flowsheets and biomass allocation to chemical products. The effect of the change of the biomass type and composition on the plant was also considered. Results highlight that the composition of the biomass feedstock in terms of cellulose, hemicellulose and lignin has a significant effect on the biomass allocation to the three product production processes and on the relevant optimal flowsheet. Case studies with a combined use of different seasonal biomass types during the year were also studied to provide a methodology to find the optimal biorefinery flowsheet in real scenarios. In the season based scenario studied, product yield distribution and overall productivity of the plant varies during the different periods provided a constant biomass feed rate. [edited by Author]XIV n.s

Branching strategies for mixed-integer programs containing logical constraints and decomposable structure

Decision-making optimisation problems can include discrete selections, e.g. selecting a route, arranging non-overlapping items or designing a network of items. Branch-and-bound (B&B), a widely applied divide-and-conquer framework, often solves such problems by considering a continuous approximation, e.g. replacing discrete variable domains by a continuous superset. Such approximations weaken the logical relations, e.g. for discrete variables corresponding to Boolean variables. Branching in B&B reintroduces logical relations by dividing the search space. This thesis studies designing B&B branching strategies, i.e. how to divide the search space, for optimisation problems that contain both a logical and a continuous structure. We begin our study with a large-scale, industrially-relevant optimisation problem where the objective consists of machine-learnt gradient-boosted trees (GBTs) and convex penalty functions. GBT functions contain if-then queries which introduces a logical structure to this problem. We propose decomposition-based rigorous bounding strategies and an iterative heuristic that can be embedded into a B&B algorithm. We approach branching with two strategies: a pseudocost initialisation and strong branching that target the structure of GBT and convex penalty aspects of the optimisation objective, respectively. Computational tests show that our B&B approach outperforms state-of-the-art solvers in deriving rigorous bounds on optimality. Our second project investigates how satisfiability modulo theories (SMT) derived unsatisfiable cores may be utilised in a B&B context. Unsatisfiable cores are subsets of constraints that explain an infeasible result. We study two-dimensional bin packing (2BP) and develop a B&B algorithm that branches on SMT unsatisfiable cores. We use the unsatisfiable cores to derive cuts that break 2BP symmetries. Computational results show that our B&B algorithm solves 20% more instances when compared with commercial solvers on the tested instances. Finally, we study convex generalized disjunctive programming (GDP), a framework that supports logical variables and operators. Convex GDP includes disjunctions of mathematical constraints, which motivate branching by partitioning the disjunctions. We investigate separation by branching, i.e. eliminating solutions that prevent rigorous bound improvement, and propose a greedy algorithm for building the branches. We propose three scoring methods for selecting the next branching disjunction. We also analyse how to leverage infeasibility to expedite the B&B search. Computational results show that our scoring methods can reduce the number of explored B&B nodes by an order of magnitude when compared with scoring methods proposed in literature. Our infeasibility analysis further reduces the number of explored nodes.Open Acces

Integration of solar energy with industrial processes

Solar energy offers a great potential for integration with industrial processes, which conventionally rely on fossil fuels to provide energy. The seasonal, daily, and regional dependence of solar energy alongside the scarcity of space or financial resources in many territories constitute great challenges. These may be overcome by efficient solar energy use through optimal integration methods. Such methods should address multiple aspects including accurate solar technology models and identification of the "true" process requirements. Beyond that, optimal design of the integrated systems and quantification of the added value of solar integration, particularly with regard to competing technologies, is crucial. This thesis explores this multi-dimensional problem formulation through elaboration ofmethodologies tailored to the low-temperature processing industries. The intricacies behind this goal are addressed in four main chapters. (a) The first chapter examines options for solar technology modeling in view of industrial integration. A design approach is developed which allows estimation of solar system performance at sufficient precision and constrained computational effort. (b) In the second chapter, a comprehensive method is proposed which addresses simultaneous optimization of the process heat recovery, the conventional utilities, and the renewable utility system (including thermal storage) using e-constrained parametric optimization. (c) The promising results from the third chapter motivate a more thorough analysis of industrial heat pump systems, which is addressed the following chapter presenting a novel generic heat pump superstructure-based synthesis method for industrial applications based on mathematical programming. (d) The subsequent two chapters address generalization of the derived methods to estimate potentials of relevant technologies at national and international scale from the perspective of multiple stakeholders. The derived method generates a database of solutions by applying generalized optimization techniques. The proposed methods are applied to the dairy industry and results reveal that solar energy should be considered as part of a series of efficiency measures. It is shown that in many cases heat pumping or mechanical vapor re-compression lead to more efficient and less costly solutions, which may be extended with solar thermal energy or complimented with solar electricity

Channel Equalization using GA Family

High speed data transmissions over communication channels distort the trans- mitted signals in both amplitude and phase due to presence of Inter Symbol Inter- ference (ISI). Other impairments like thermal noise, impulse noise and cross talk also cause further distortions to the received symbols. Adaptive equalization of the digital channels at the receiver removes/reduces the e®ects of such ISIs and attempts to recover the transmitted symbols. Basically an equalizer is an inverse ¯lter which is placed at the front end of the receiver. Its transfer function is inverse to the transfer function of the associated channel. The Least-Mean-Square (LMS), Recursive-Least-Square (RLS) and Multilayer perceptron (MLP) based adaptive equalizers aim to minimize the ISI present in the digital communication channel. These are gradient based learning algorithms and therefore there is possibility that during training of the equalizers, its weights do not reach to their optimum values due to ..

Proceedings of the XIII Global Optimization Workshop: GOW'16

[Excerpt] Preface: Past Global Optimization Workshop shave been held in Sopron (1985 and 1990), Szeged (WGO, 1995), Florence (GO’99, 1999), Hanmer Springs (Let’s GO, 2001), Santorini (Frontiers in GO, 2003), San José (Go’05, 2005), Mykonos (AGO’07, 2007), Skukuza (SAGO’08, 2008), Toulouse (TOGO’10, 2010), Natal (NAGO’12, 2012) and Málaga (MAGO’14, 2014) with the aim of stimulating discussion between senior and junior researchers on the topic of Global Optimization. In 2016, the XIII Global Optimization Workshop (GOW’16) takes place in Braga and is organized by three researchers from the University of Minho. Two of them belong to the Systems Engineering and Operational Research Group from the Algoritmi Research Centre and the other to the Statistics, Applied Probability and Operational Research Group from the Centre of Mathematics. The event received more than 50 submissions from 15 countries from Europe, South America and North America. We want to express our gratitude to the invited speaker Panos Pardalos for accepting the invitation and sharing his expertise, helping us to meet the workshop objectives. GOW’16 would not have been possible without the valuable contribution from the authors and the International Scientific Committee members. We thank you all. This proceedings book intends to present an overview of the topics that will be addressed in the workshop with the goal of contributing to interesting and fruitful discussions between the authors and participants. After the event, high quality papers can be submitted to a special issue of the Journal of Global Optimization dedicated to the workshop. [...

Data-Driven Mixed-Integer Optimization for Modular Process Intensification

High-fidelity computer simulations provide accurate information on complex physical systems. These often involve proprietary codes, if-then operators, or numerical integrators to describe phenomena that cannot be explicitly captured by physics-based algebraic equations. Consequently, the derivatives of the model are either absent or too complicated to compute; thus, the system cannot be directly optimized using derivative-based optimization solvers. Such problems are known as “black-box” systems since the constraints and the objective of the problem cannot be obtained as closed-form equations. One promising approach to optimize black-box systems is surrogate-based optimization. Surrogate-based optimization uses simulation data to construct low-fidelity approximation models. These models are optimized to find an optimal solution. We study several strategies for surrogate-based optimization for nonlinear and mixed-integer nonlinear black-box problems. First, we explore several types of surrogate models, ranging from simple subset selection for regression models to highly complex machine learning models. Second, we propose a novel surrogate-based optimization algorithm for black-box mixed-integer nonlinear programming problems. The algorithm systematically employs data-preprocessing techniques, surrogate model fitting, and optimization-based adaptive sampling to efficiently locate the optimal solution. Finally, a case study on modular carbon capture is presented. Simultaneous process optimization and adsorbent selection are performed to determine the optimal module design. An economic analysis is presented to determine the feasibility of a proposed modular facility.Ph.D

Development of a techno-economic energy model for low carbon business parks

To mitigate climate destabilisation, global emissions of human-induced greenhouse gases urgently need to be reduced, to be nearly zeroed at the end of the century. Clear targets are set at European level for the reduction of greenhouse gas emissions and primary energy consumption and for the integration of renewable energy. Carbon dioxide emissions from fossil fuel combustion in the industry and energy sectors account for a major share of greenhouse gas emissions. Hence, a low carbon shift in industrial and business park energy systems is called for. Low carbon business parks minimise energy-related carbon dioxide emissions by enhanced energy efficiency, heat recovery in and between companies, maximal exploitation of local renewable energy production, and energy storage, combined in a collective energy system. Moreover, companies with complementary energy profiles are clustered to exploit energy synergies. The design of low carbon energy systems is facilitated using the holistic approach of techno-economic energy models. These models take into account the complex interactions between the components of an energy system and assist in determining an optimal trade-off between energetic, economic and environmental performances. In this work, existing energy model classifications are scanned for adequate model characteristics and accordingly, a confined number of energy models are selected and described. Subsequently, a practical categorisation is proposed, existing of energy system evolution, optimisation, simulation, accounting and integration models, while key model features are compared. Next, essential features for modelling energy systems at business park scale are identified: As a first key feature, a superstructure-based optimisation approach avoids the need for a priori decisions on the system’s configuration, since a mathematical algorithm automatically identifies the optimal configuration in a superstructure that embeds all feasible configurations. Secondly, the representation of time needs to incorporate sufficient temporal detail to capture important characteristics and peaks in time-varying energy demands, energy prices and operation conditions of energy conversion technologies. Thirdly, energy technologies need to be accurately represented at equipment unit level by incorporating part-load operation and investment cost subject to economy of scale in the model formulation. In addition, the benefits of installing multiple units per technology must be considered. A generic model formulation of technology models facilitates the introduction of new technology types. As a fourth important feature, the potential of thermodynamically feasible heat exchange between thermal processes needs to be exploited, while optimally integrating energy technologies to fulfil remaining thermal demands. For this purpose, thermal streams need to be represented by heat –temperature profiles. Moreover, restrictions to direct heat exchange between process streams need to be taken into account. Finally, the possibility for energy storage needs to be included to enhance the integration of non-dispatchable renewable energy technologies and to bridge any asynchrony between cooling and heating demands. Starting from these essential features, a techno-economic optimisation model (Syn-E-Sys), is developed customised for the design of low carbon energy systems on business park scale. The model comprises two sequential stages. In the first stage, heat recovery within the system is maximised, while energy supply and energy storage technologies are optimally integrated and designed to fulfil remaining energy requirements at minimum total annualised costs. Predefined variations in thermal and electrical energy demand and supply are taken into account, next to a carbon emission cap. At the same time, heat networks can be deployed to transfer heat between separate parts of the system. In the second stage, the model generates an optimal multi-period heat exchanger network enabling all required heat exchanges. Syn-E-Sys builds upon a multi-period energy integration model that can deal with restrictions in heat exchange. It is combined with a generic technology model, that features part-load operation as well as investment cost subject to economy of scale, and a generic energy storage model. The technology model can be manipulated to represent various thermal or electrical energy conversion technology units, and serves as a building block to model more complex technologies. The storage model covers electrical as well as thermal energy storage, taking into account the effect of hourly energy losses on the storage level, without increasing the number of time steps to be analysed. For this purpose, time sequence is introduced by dividing the year into a set of time slices and assigning them to a hierarchical time structure. In addition, a more complex model for storage of sensible heat is integrated, consisting of a stack of interconnected virtual tanks. To enable the optimisation of the number of units per technology in the energy system configuration, an automated superstructure expansion procedure is incorporated. Heat transfer unit envelope curves are calculated to facilitate the choice of appropriate temperature levels for heat networks. Heat networks that are embedded within this envelope, completely avoid the increase in energy requirements that would result from the heat exchange restrictions between separated parts of the energy system. Finally, the heat exchanger network is automatically generated using a multi-period stage-wise superstructure. Two problems inherent to the heat cascade formulation are encountered during model development. As a first issue, heat networks can form self-sustaining energy loops if their hot and cold streams are not completely embedded within the envelope. This phenomenon is referred to in this work as phantom heat. As a second issue, the heat cascade formulation does not prevent that a thermal storage releases its heat to a cooling technology. To demonstrate the specific features of Syn-E-Sys and its holistic approach towards the synthesis of low carbon energy systems, the model is applied to a generic case study and to a case study from literature. The generic case study is set up to demonstrate the design of an energy system including non-dispatchable renewable energy and energy storage, subject to a carbon emission cap. For this purpose, the year is subdivided into a set of empirically defined time slices that are connected to a hierarchical time structure composed of seasons, daytypes and intra-daily time segments. The results obtained by Syn-E-Sys show a complex interaction between energy supply, energy storage and energy import/export to fulfil energy demands, while keeping carbon emissions below the predefined cap. The model enables optimisation of the intra-annual charge pattern and the capacity of thermal and electrical storage. Moreover, an optimal heat exchanger network is automatically generated. In the second case study, heat recovery is optimised for a drying process in the paper industry. To avoid the energy penalty due to heat exchange restrictions between two separated process parts, heat transfer units need to be optimally integrated. Firstly, a simplified version of the original problem is set up in Syn-E-Sys and the obtained results correspond well to literature. Subsequently, the original problem is extended to demonstrate the optimal integration of heat transfer units in a multi-period situation. In conclusion, Syn-E-Sys facilitates optimal design of low carbon energy systems on business park scale, taking into account the complex time-varying interactions between thermal and electrical energy demand, supply and storage, while the potential for heat recovery is fully exploited