Computational Optimisation Group

Seminar: Development and application of automatic force field parameterization software for molecular simulation
2012-04-26 14:00 UTC
Title: Development and application of automatic force field parameterization software for molecular simulationSpeaker: Dr. Lee-Ping WangAffiliation: Stanford UniversityLocation: Room 218Time: 2:00pm
Abstract. Force fields are empirical potential energy functions that describe molecules and their interactions; they constitute the physical foundation for simulations of atomic and molecular motion. The accuracy of a force field is determined by empirical parameters, and the choice of optimal parameters has been a difficult challenge for decades. The molecular simulation community is in need of an automatic and systematic method for force field parameterization, which would revolutionize the field by providing greatly improved simulation accuracy and reproducibility of force field development. With this goal in mind, I have developed an open-source software package called ForceBalance to perform automatic force field parameterization. The software is built around a standardized procedure for force field development, interfaces easily with classical and quantum simulation codes, and has the ability to produce force fields that are optimized to reproduce any experimental or theoretical reference data. I will introduce the concepts and implementation of ForceBalance, provide a simple demonstration of the software, and discuss opportunities for collaboration.
About the speaker. Lee-Ping Wang graduated from U.C Berkeley with a B.A. in Physics in 2006. He entered graduate school in the chemistry department at MIT, where he worked with Prof. Troy Van Voorhis on various topics in theoretical chemistry such as water splitting catalysis, QM/MM methods, and force field development, graduating with a Ph.D. in 2011. Lee-Ping is now working as a postdoctoral fellow at Stanford University with Profs. Todd Martinez and Vijay Pande where he is continuing to refine force field development methods and applying them to biomolecular simulation.

Seminar: Lifting Methods for Generalized Semi-Infinite Programs
2012-03-22 15:00
Title: Lifting Methods for Generalized Semi-Infinite ProgramsSpeaker: Dr. Boris HouskaAffiliation: Centre for Process Systems Engineering at Imperial CollegeLocation: Room 217 Huxley BuildingTime: 3:00pm
Abstract. In this talk we present numerical solution strategies for generalized semi-infinite optimization problems (GSIP), a class of mathematical optimization problems which occur naturally in the context of design centering problems, robust optimization problems, and many fields of engineering science. GSIPs can be regarded as bilevel optimization problems, where a parametric lower-level maximization problem has to be solved in order to check feasibility of the upper level minimization problem. In this talk we discuss three strategies to reformulate a class lower-level convex GSIPs into equivalent standard minimization problems by exploiting the concept of lower level Wolfe duality. Here, the main contribution is the discussion of the non-degeneracy of the corresponding formulations under various assumptions. Finally, these non-degenerate re-formulations of the original GSIP allow us to apply standard nonlinear optimization algorithms.
About the speaker. Boris Houska studied mathematics and physics at the university of Heidelberg in 2003-2008. He obtained his Ph.D. in 2011 in Electrical Engineering at the Optimization in Engineering Center (OPTEC) at K.U. Leuven. Since 2012 he is a postdoctoral researcher at the Centre of Process Systems Engineering at Imperial College. His research interests include numerical optimization and optimal control, robust optimization, as well as fast MPC algorithms.

Seminar: Payment Rules through Discriminant-Based Classifiers
2012-03-21 14:00
Title: Payment Rules through Discriminant-Based ClassifiersSpeaker: Prof. David ParkesAffiliation: School of Engineering and Applied Sciences at Harvard UniversityLocation: Room 217-218 Huxley BuildingTime: 2:00pm
Abstract. In mechanism design it is typical to impose incentive compatibility and then derive an optimal mechanism subject to this constraint. By replacing the incentive compatibility requirement with the goal of minimizing expected ex-post regret, we are able to adapt techniques of statistical machine learning to the design of payment rules. This computational approach to mechanism design is applicable to domains with multi- dimensional types and situations where computational efficiency is a concern. Specifically, given an outcome rule and access to a type distribution, we train a support vector machine with a special discriminant function structure such that it implicitly establishes a payment rule with desirable incentive properties. We discuss applications to a multi-minded combinatorial auction with a greedy winner-determination algorithm and to an assignment problem with egalitarian outcome rule. Experimental results demonstrate both that the construction produces payment rules with low ex-post regret, and that penalizing classification errors is effective in preventing failures of ex-post individual rationality.
About the speaker. David C. Parkes is the Gordon McKay Professor of Computer Science in the School of Engineering and Applied Sciences at Harvard University. He was the recipient of the NSF Career Award, the Alfred P. Sloan Fellowship, the Thouron Scholarship, the Harvard University Roslyn Abramson Award for Teaching. Parkes received his Ph.D. degree in Computer and Information Science from the University of Pennsylvania in 2001, and an M.Eng. (First class) in Engineering and Computing Science from Oxford University in 1995. At Harvard, Parkes founded the Economics and Computer Science research group. His research interests include mechanism design, electronic commerce, market design, and social computing. Parkes is editor of Games and Econonic Behavior, and on the editorial boards of JAAMAS, ACM TEAC and INFORMS J. Computing. Parkes also serves as the Chair of the ACM SIG on Electronic Commerce and was the Program Chair of ACMEC’07 and AAMAS’08, and General Chair of ACMEC’10.

Seminar: The Long-run Impact of Wind Power on Electricity Prices and Generating Capacity (joint work with Nicholas Vasilakos)
2012-03-08 14:00
Title: The Long-run Impact of Wind Power on Electricity Prices and Generating Capacity (joint work with Nicholas Vasilakos)Speaker: Prof. Richard Green – Alan and Sabine Howard Professor of Sustainable Energy Business at Imperial College Business SchoolAffiliation: Imperial College LondonLocation: Room 344A Huxley BuildingTime: 2:00pm
Abstract. This paper uses a market equilibrium model to calculate how the mix of generating capacity would change if large amounts of intermittent renewables are built in Great Britain, and what this means for operating patterns and the distribution of prices over time. If generators bid their marginal costs, we find that the changes to the capacity mix are much greater than the changes to the pattern of prices. Thermal capacity falls only slightly in response to the extra wind capacity, and there is a shift towards power stations with higher variable costs (but lower fixed costs). The changes to the pattern of prices, once capacity has adjusted, are relatively small. In an oligopolistic setting, strategic generators will choose lower levels of capacity. If wind output does not receive the market price, then mark-ups on thermal generation will be lower in a system with large amounts of wind power.
About the speaker. Richard Green is the Alan and Sabine Howard Professor of Sustainable Energy Business at Imperial College Business School. He was previously Professor of Energy Economics and Director of the Institute for Energy Research and Policy at the University of Birmingham, and Professor of Economics at the University of Hull. He started his career at the Department of Applied Economics and Fitzwilliam College, Cambridge. He has spent time on secondment to the Office of Electricity Regulation and has held visiting appointments at the World Bank, the University of California Energy Institute and the Massachusetts Institute of Technology. He has been studying the economics and regulation of the electricity industry for over 20 years. He has written extensively on market power in wholesale electricity markets and has also worked on transmission pricing. More recently, the main focus of his work has been on the impact of low-carbon generation (nuclear and renewables) on the electricity market, and the business and policy implications of this.

Seminar: Enclosing with Simple Bodies
2012-02-23 14:00
Title: Enclosing with Simple BodiesSpeaker: Dr. Selin Damla Ahipasaoglu – research officerAffiliation: Management Science Group at LSELocation: Room 217 Huxley BuildingTime: 2:00pm
Abstract. The Minimum Volume Enclosing Ellipsoid and Minimum Enclosing Ball problems are related to covering a given set of points with an ellipsoid or a ball with the smallest volume possible. These problems have many applications, especially in statistics. We will survey recent theoretical results and take a look at efficient algorithms for solving these problems. We will show that these algorithms can be used for very large data sets.
About the speaker. Selin Damla Ahipasaoglu received her PhD in 2009 from Cornell University under the supervision of Prof. Mike Todd. After her PhD, she worked as a postdoctoral researcher at Princeton University and London School of Economics. She specialises in developing algorithms for large scale optimization problems, in particular first-order methods for convex problems. She is also working on auctions and game theory. In April 2012, she will be joining the Singapore University of Technology and Design as an assistant professor.

Seminar: Complexity and heuristics in stochastic optimization
2012-02-15 14:00
Title: Complexity and heuristics in stochastic optimizationSpeaker: Prof. Teemu Pennanen – Professor of Mathematical Finance Probability and StatisticsAffiliation: King’s College LondonLocation: Room 218 Huxley BuildingTime: 2:00pm
Abstract. Combining recent results on numerical integration and convex optimization, we derive a polynomial bound on the worst case complexity of a class of static stochastic optimization problems. We then describe a technique for reducing dynamic problems to static ones. The reduction technique is only a heuristic but it can effectively employ good guesses for good solutions. This is illustrated on an 82-period problem coming from pension insurance industry.
About the speaker. Teemu Pennanen is the Professor of Mathematical Finance, Probability and Statistics at King’s College, London. Before joining KCL, Professor Pennanen worked as Managing Director at QSA Quantitative Solvency Analysts Ltd, with a joint appointment as Professor of Stochastics at University of Jyvaskyla, Finland. His earlier appointments include a research fellowship of the Finnish Academy and several visiting positions in universities abroad.

Seminar: Performance-Based Contracts for Outpatient Medical Services
2012-02-08 14:00
Title: Performance-Based Contracts for Outpatient Medical ServicesSpeaker: Dr. Houyuan Jiang – Senior Lecturer in Management ScienceAffiliation: Judge Business School – University of CambridgeLocation: Room 218 Huxley BuildingTime: 2:00pm
Abstract. In recent years, the performance-based approach to contracting for medical services has been gaining popularity across different healthcare delivery systems, both in the US (under the name of “Pay-for-Performance”, or P4P), and abroad (“Payment-by-Results”, or PbR, in the UK). The goal of our research is to build a unified performance-based contracting (PBC) framework that incorporates patient access-to-care requirements and that explicitly accounts for the complex outpatient care dynamics facilitated by the use of an online appointment scheduling system. We address the optimal contracting problem in a principal-agent framework where a service purchaser (the principal) minimizes her cost of purchasing the services and achieves the performance target (a waiting time target) while taking into account the response of the provider (the agent) to the contract terms. Given the incentives offered by the contract, the provider maximizes his payoff by allocating his outpatient service capacity among three patient groups: urgent patients, dedicated advance patients and flexible advance patients. We model the appointment dynamics as that of an M=D=1 queue and analyze several contracting approaches under adverse selection (asymmetric information) and moral hazard (private actions) settings. We study the first-best and the second-best solutions, as well as their specific contracting implementation schemes. Our results show that simple and popular schemes used in practice cannot implement the first-best solution and that the linear PBC cannot implement the second-best solution. In order to overcome these limitations, we propose a threshold-penalty PBC approach and show that it coordinates the system for an arbitrary patient mix and that it achieves the second-best performance for the setting where all advance patients are dedicated.
About the speaker.

Seminar: A Stochastic Capacity Expansion Model for the UK Electricity System
2012-01-26 17:30
Title: A Stochastic Capacity Expansion Model for the UK Electricity SystemSpeaker: Angelos GeorghiouAffiliation: Department of Computing – Imperial College LondonLocation: Room 217-218 Huxley BuildingTime: 5:30pm
Abstract. Energy markets are currently undergoing one of their most radical changes in history. On one hand, market liberalisation leads to a shift from state-owned utilities with a focus on failure resilience towards competitive markets where reliability is traded off with costs. This will result in a much higher utilisation of generation and transmission facilities, which in turn leads to a less predictable system behaviour and more frequent outages. Moreover, predictions about climate change dictate the gradual replacement of non-renewable energy sources with renewable alternatives such as solar or wind power. Contrary to non-renewable energy, the electricity delivered from renewable sources is highly uncertain due to the intermittency of solar radiation, wind etc. Both developments highlight the need to accommodate uncertainty in the design and management of future energy systems. This work aims to identify the most cost-efficient expansion of the UK energy grid, given a growing future demand for energy and the target to move towards a more sustainable energy system. To this end, we develop a multi-stage stochastic program where the investment decisions (generation units and transmission lines that should be built) are taken here-and-now, whereas the operating decisions are taken in hourly time stages over a horizon of 30 years. The resulting problem contains several thousand time stages and is therefore severely intractable. We develop a novel problem reformulation, based on the concept of time randomization, that allows us to equivalently reformulate the problem as a two-stage stochastic program. By taking advantage of the simple structure of the decision rule approximation scheme, we can model and solve a problem that optimises the entire UK energy grid with nearly 400 generators and 1000 transmission lines.
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Seminar: Multistage Stochastic Portfolio Optimisation in Deregulated Electricity Markets Using Linear Decision Rules
2012-01-26 17:00
Title: Multistage Stochastic Portfolio Optimisation in Deregulated Electricity Markets Using Linear Decision RulesSpeaker: Paula RochaAffiliation: Department of Computing – Imperial College LondonLocation: Room 217-218 Huxley BuildingTime: 5:00pm
Abstract. The deregulation of electricity markets often poses great financial risks to retailers who procure electric energy on the spot market to satisfy their customers’ electricity demand. To hedge against this risk exposure, retailers often hold a portfolio of electricity derivative contracts. In this talk, we present a multistage stochastic mean-variance optimisation model for the management of such a portfolio. To reduce computational complexity, we perform two approximations: stage-aggregation and linear decision rules (LDR). The LDR approach consists of restricting the space of recourse decisions to those affine in the history of the random parameters. When applied to mean-variance optimisation models, it leads to convex quadratic programs. Since their size grows typically only polynomially with the number of decision stages, they are amenable to efficient numerical solution. Our numerical experiments highlight the value of adaptivity inherent in the LDR method and its potential for enabling scalability to portfolio optimisation problems with many decision stages.
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Seminar: Universal decision rule approximations for dynamic decision-making under uncertainty
2012-01-25 17:00
Title: Universal decision rule approximations for dynamic decision-making under uncertaintySpeaker: Phebe VayanosAffiliation: Department of Computing – Imperial College LondonLocation: Room 217-218 Huxley BuildingTime: 5:00pm
Abstract.
About the speaker.

Seminar: Steam Engines Jet Fighters and Credit Crises
2012-01-12 14:00
Title: Steam Engines Jet Fighters and Credit Crises Speaker: Dr George CooperAffiliation: BlueCrest Capital Location: Room 217-218 Huxley BuildingTime: 2:00pm
Abstract. The talk will discuss some of the underlying causes of the financial crisis with particular focus on financial market instability, monetary policy and the influence of the Efficient Market Hypothesis.
About the speaker. George Cooper is a fund manager at BlueCrest Capital in London. Prior to joining BlueCrest George was the head of European interest rate research at JP Morgan and has also worked for both Deutsche Bank and Goldman Sachs. George’s book “The Origin of Financial Crises: Central Banks, Credit Bubbles and the Efficient Market Fallacy” was published in August 2008 and has now been translated into over a dozen languages. George holds a PhD in engineering from Durham University.

Seminar: Robust Optimization of Dynamic Systems and Its Applications.
2012-01-06 15:00
Title: Robust Optimization of Dynamic Systems and Its Applications.Speaker: Dr. Boris Houska Affiliation: Location: CPSE Seminar room (C616 Roderic Hill)Time: 3:00pm
Abstract. This talk gives an introduction to numerical methods for the robust optimization of uncertain dynamic systems. In contrast to standard differential equations, which describe the propagation of a single vector-valued trajectory in time, uncertain dynamic systems propagate a set valued function: the uncertainty tube. For the case that control inputs are available this uncertainty tube can be influenced and optimized such that certain robustness criteria are met. The aim of the first part of the talk is to explain how to formulate and solve such tube-based robust optimal control problems.The second part of the talk is about the software environment and algorithm collection ACADO Toolkit, which implements tools for automatic control and dynamic optimization. It provides a general framework for using a great variety of algorithms for direct optimal control, including robust optimal control and model predictive control. The ACADO Toolkit is implemented as a selfcontained C++ code, while the object-oriented design allows for convenient coupling of existing optimization packages and for extending it with user-written optimization routines. We present numerical examples from the field of mechanics and biochemical engineering.
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Seminar: Decision rules for information discovery in multi-stage stochastic programming
2011-12-08 17:00
Title: Decision rules for information discovery in multi-stage stochastic programmingSpeaker: Phebe VayanosAffiliation: Department of Computing – Imperial College LondonLocation: CPSE Seminar room (C615 Roderic Hill)Time: 5:00pm
Abstract. Stochastic programming and robust optimization are disciplines concerned with optimal decision-making under uncertainty over time. Traditional models and solution algorithms have been tailored to problems where the order in which the uncertainties unfold is independent of the controller actions. Nevertheless, in numerous real-world decision problems, the time of information discovery can be influenced by the decision maker, and uncertainties only become observable following an (often costly) investment. Such problems can be formulated as mixed-binary multi-stage stochastic programs with decision-dependent non-anticipativity constraints. Unfortunately, these problems are severely computationally intractable. We propose an approximation scheme for multi-stage problems with decision-dependent information discovery which is based on techniques commonly used in modern robust optimization. In particular, we obtain a conservative approximation in the form of a mixed-binary linear program by restricting the spaces of measurable binary and real-valued decision rules to those that are representable as piecewise constant and linear functions of the uncertain parameters, respectively. We assess our approach on a problem of infrastructure and production planning in offshore oil fields from the literature.
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Seminar: A Scenario Approach for Estimating the Suboptimality of Linear Decision Rules in Two-Stage Robust Optimization
2011-12-08 17:00
Title: A Scenario Approach for Estimating the Suboptimality of Linear Decision Rules in Two-Stage Robust Optimization Speaker: Michael HadjiyiannisAffiliation: Department of Computing – Imperial College LondonLocation: CPSE Seminar room (C615 Roderic Hill)Time: 5:00pm
Abstract. Robust dynamic optimization problems involving adaptive decisions are computationally intractable in general. Tractable upper bounding approximations can be obtained by requiring the adaptive decisions to be representable as linear decision rules (LDRs). In this presentation we investigate families of tractable lower bounding approximations, which serve to estimate the degree of suboptimality of the best LDR. These approximations are obtained either by solving a dual version of the robust optimization problem in LDRs or by utilizing an inclusion-wise discrete approximation of the problem’s uncertainty set. The quality of the resulting lower bounds depends on the distribution assigned to the uncertain parameters or the choice of the discretization points within the uncertainty set, respectively. We prove that identifying the best possible lower bounds is generally intractable in both cases and propose an efficient procedure to construct suboptimal lower bounds. The resulting instance-wise bounds outperform known worst-case bounds in the majority of our test cases.
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Seminar: Scenario-Free Stochastic Programming with Polynomial Decision Rules
2011-12-08 17:00
Title: Scenario-Free Stochastic Programming with Polynomial Decision RulesSpeaker: Dimitra BampouAffiliation: Department of Computing – Imperial College LondonLocation: CPSE Seminar room (C615 Roderic Hill)Time: 5:00pm
Abstract. Multi-stage stochastic programming provides a versatile framework for optimal decision making under uncertainty, but it gives rise to hard functional optimization problems since the adaptive recourse decisions must be modeled as functions of some or all uncertain parameters. We propose to approximate these recourse decisions by polynomial decision rules and show that the best polynomial decision rule of a fixed degree can be computed efficiently. We also show that the suboptimality of the best polynomial decision rule can be estimated efficiently by solving a dual version of the stochastic program in polynomial decision rules.
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Seminar: How IBM enables industries to better leverage optimisation technology?
2011-12-01 14:00
Title: How IBM enables industries to better leverage optimisation technology?Speaker: Dr. Mozafar Hajian Affiliation: Location: 219A William Penney Lab (entrance from walkway) Time: 2:00pm
Abstract. IBM ILOG CPLEX Optimisation Studio is used by leading academic & business institutions to rapidly create both mathematical programming and constraint programming models. It is used to build efficient optimisation models and state-of-the-art applications for the full range of planning and scheduling problems. The tool provides a powerful Integrated Development Environment (IDE) using the Optimisation Programming Language (OPL) language, programmatic APIs, or indeed other 3rd party modelling interfaces. This makes it easy to evaluate different modelling approaches and to integrate external data. With its built-in development tools, it supports the entire model development process.In addition, IBM ILOG ODM Enterprise provides an enterprise scale platform for developing and deploying highly effective optimisation based analytical planning and scheduling solutions for business decision makers across a variety of industries. In this presentation, you will find out, how IBM is providing a powerful platform to enable, a) better scenario management, b) faster decision making process, c) distributed planning processes for large scale applications, and d) a role based planning and collaboration environment.
About the speaker. Mozafar Hajian completed his Ph.D. at Brunel University of West London in Combinatorial Optimisation, before joining IC-Parc at Imperial College as a Senior Research Fellow. During this period, he collaborated with both Computing and Manufacturing departments to pioneer new methods in solving combinatorial optimisation problems and distributed Supply Chain Optimisation. Outside of academia, he has held senior roles at ILOG, SAP and IBM, including senior business development manager for Supply Chain Optimisation at SAP. He is presently a certified Client Technical Advisor for IBM ILOG Optimisation & Supply Chain solutions.

Seminar: Coordinating Flexible Responsive Electricity Demand via Smart Grids
2011-11-25 14:00
Title: Coordinating Flexible Responsive Electricity Demand via Smart Grids Speaker: Dr. Daniel Livengood Affiliation: Location: CPSE Seminar room (C615 Roderic Hill)Time: 2:00pm
Abstract. As the electric grid evolves into a ‘smart’ grid, there is renewed interest in developing and implementing strategies for integrating flexible, responsive electric demand into the perpetual task of balancing electricity supply and demand on the grid. Pilot programs and research have demonstrated that automated energy management systems, particularly for residential customers, are instrumental in increasing the response of flexible demand from customers participating in these strategies. This talk will begin with a discussion of the potential benefits to a single residence when coordinating electricity consumption, distributed generation and storage with an automated energy management system under time-varying pricing and uncertain weather conditions. A discussion of the open questions involving what may happen when large numbers of automated energy management systems are installed on the smart grid will follow.
About the speaker. Daniel is a postdoctoral research fellow at the Massachusetts Institute of Technology, where he recently completed his Ph.D. in Engineering Systems. Daniel’s research focuses on automated home energy management systems as part of future smart grids, with a particular interest in developing algorithms that coordinate energy consumption, distributed generation and storage in response to time-varying pricing and uncertain weather forecasts. Along with his ongoing academic research, Daniel is working on energy and thermal algorithms with the startup Coincident, Inc., as part of their energy management appliance. Daniel is also an advisor to the startup Grid Solutions, Inc., and has worked as an intern at the demand response company EnerNOC, analyzing baseline calculation methods for demand response programs.

Seminar: Large Scale Numerical Shape Optimisation
2011-11-24 16:30
Title: Large Scale Numerical Shape Optimisation Speaker: Dr. Stephan Schmidt Affiliation: Location: CPSE Seminar room (C615 Roderic Hill)Time: 4:30pm
Abstract. Shape Optimisation problems are a special sub-class of optimisation problems with PDE constraints, where the domain in which the PDE is defined becomes the unknown to be found. The Hadamard Theorem states that given sufficient regularity, one can always find a representation of the shape gradient that exists on the surface of the unknown domain alone, thereby offering the potential to create very efficient numerical schemes. Unless the structure of a shape optimisation problem is exploited in some fashion, the resulting need to include the deformation of the surrounding domain can potentially become prohibitively expensive. The desire to create higher order methods like SQP also necessitates studies about second order shape derivatives. The talk will also focus on applications in aerodynamic design and the shaping of wave emitters.
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Seminar: LAROS: a convex optimization approach for feature extraction
2011-11-17 15:00
Title: LAROS: a convex optimization approach for feature extractionSpeaker: Dr. Xuan Vinh Doan Affiliation: Warwick Business School – University of WarwickLocation: Room 572A Huxley BuildingTime: 3:00pm
Abstract. We propose a convex optimization formulation using nuclear norm and $ell_1$-norm to find a large approximately rank-one submatrix (LAROS) for a given matrix. We are able to characterize the low-rank and sparsity structure of the resulting solutions. We show that our model can recover low-rank submatrices for matrices with subgaussian random noises. We solve the proposed model using a proximal point algorithm and show that it can be applied to applications in feature extraction. This is joint work with Stephen Vavasis and Kim-Chuan Toh.
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Seminar: Optimization under Uncertainty - Recent Advances in Multi-Parametric Mixed Integer Linear Programming and its Applications
2011-11-10 16:00
Title: Optimization under Uncertainty – Recent Advances in Multi-Parametric Mixed Integer Linear Programming and its Applications Speaker: Martina Wittmann-Hohlbein Affiliation: CPSE – Department of Chemical Engineering – Imperial College LondonLocation: 219A William Penney Lab (entrance from walkway)Time: 4:00pm
Abstract. In optimization under uncertainty, multi-parametric programming is a powerful tool to account for the presence of uncertainty in mathematical models. Its objective is to derive the optimal solution as a function of the parameters without exhaustively enumerating the parameter space. We consider the general multi-parametric mixed integer linear programming (mp-MILP) problem. The presence of uncertainty in mixed integer linear programming models employed in widespread application fields, including planning/scheduling, process synthesis and hybrid control, significantly increases the complexity and computational effort in retrieving optimal solutions. A particular difficulty arises when uncertainty is simultaneously present in the coefficients of the objective function, the constraint matrix and the constraint vector, which transforms the original linear model into a nonlinear and non-convex one with respect to both the optimization variables and the parameters. Here, we discuss two novel methods for the solution of the general mp-MILP problem. The first approach deals with the global solution of the general mp-MILP model. Exploiting the special structure of the problem, we outline the steps of a parametric branch and bound procedure. The second approach is a two-stage method for the approximate solution of the general mp-MILP problem which combines state-of-the-art robust optimization and multi-parametric programming techniques. The two-stage method is applied to short-term batch process scheduling under uncertainty and we demonstrate its potential in the construction of a pro-active scheduling policy.
About the speaker. Martina Wittmann-Hohlbein obtained a Diploma in Mathematics and Economics at Martin-Luther-University Halle-Wittenberg, Germany, in 2007. She joined CPSE at Imperial College in 2009.
