PGMODAYS 2017

 

 

Aharon BEN-TAL (Technion, Tel-Aviv)

 Regaining tractability in some large scale/uncertain engineering optimization problems

 The need to solve real-life optimization problems poses frequently a severe challenge, as the underlying mathematical programs threatens to be intractable.  The intractability can be attributed to any of the following properties:  large dimensionality of the design dimension; lack of convexity; parameters affected by  uncertainty.  In problems of designing optimal mechanical structures (truss topology design, shape design, free material optimization), the mathematical programs typically have hundreds of thousands of variables, a fact which rules out the use of advanced modern solution methods, such as Interior Point method.  Some Signal Processing and Estimation problems may result in nonconvex formulations.  In the wide area of optimization under uncertainty classical approaches, such as chance (probabilistic) constraints, give rise to nonconvex NP-hard problems. Nonconvexity also occurs in some Robust Control problems.

In all the above applications we explain how the difficulties were resolved.  In some cases this was achieved by mathematical analysis, which converted the problems (or its dual) to a tractable convex program.  In other cases novel approximation schemes, based on Robust Optimization, are used to address intractable probability inequalities.  In the case of large-scale convex programs, novel first order algorithms were employed.  In the Robust Control example, a parameterization scheme is developed under which the problem is converted to a tractable deterministic convex program.

Presentation

Roberto COMINETTI (UAI, Santiago)

Optimization and Games in Congested Networks

In this talk we will survey the use of optimization and game theory models in urban transport and telecommunications. After a brief review of equilibrium flows in congested networks, we will describe our recent work on stochastic traffic equilibrium, risk-averse route choice, dynamic equilibrium, and the limiting behavior of the Price-of-Anarchy under heavy congestion. 

Presentation 1

Presentation 2

 

Frauke LIERS (FAU Erlangen-Nürnberg)

Robust Solution Approaches for Challenging Network Optimization and Air-Traffic Management Problems

 One way of protecting against uncertainties that occur in real-world applications is to apply and to develop methodologies from robust optimization. The latter takes these uncertainties into account already in the mathematical model. Then, the task is to determine solutions that are feasible for all considered   realizations of the uncertain parameters, and among them one with best guaranteed solution value. In this talk, we give an overview over some robust approaches for real-world applications, and also talk about recent advances.

In particular, we study dynamic network flows with uncertain input data under a robust optimization perspective, where protection is sought against uncertain travel times. For operating gas networks, we present robust approaches for protecting against uncertain physical parameters. Already in the stationary case, gas network operation is complex as nonconvex quadratic optimization taks need to be solved. Robust approaches are presented for their operation that differ in the level of adjustability of the physical state variables such as pressures and flows in the network.

Finally, we will also cover an application of robust combinatorial optimization in air-traffic management. For the runway scheduling problem, we will point out modelling and solution techniques using recoverable robust solution approaches. 

(Robust dynamic flows is joint with C. Gottschalk, A. Koster, B. Peis, D. Schmand, and A. Wierz. Robust gas networks is joint with D. Aßmann, M. Stingl, and J. Vera. Robust runway scheduling is joint with A. Heidt, M. Kapolke, and A. Martin.)

Presentation

 

Andrzej  RUSZCZYNSKI (Rutgers University)

Risk-Averse Control of Markov Systems

We shall focus on risk-averse control of discrete-time and continuous-time Markov systems. We shall refine the concept of time consistency for such systems, introduce the class of Markovian risk measures, and derive their structure. This will allow us to derive a risk-averse couterpart of dynamic programming equations. Then we shall extend these ideas continuous-time Markov chains and derive the structure of risk measures and dynamic programming equations in these cases as well. In the last part of the talk, we shall discuss risk-averse control of diffusion processes and present a risk-averse counterpart of the Hamilton--Bellman--Jacobi equation. Finally, we provide brief information o n current research on partially-observable problems in discrete and continuous time.

 

Henri SANSON (ORANGE)

Stakes and overview of research works in Artificial Intelligence and Operations Research at Orange

The object of the presentation is to explain how Artificial Intelligence and Operations Research techniques permit to answer operator Orange ’s big stakes in terms of  infrastructure performances, operational efficiency and customer relationship. After introducing these stakes, we will review some of our major research works in Artificial Intelligence and Operations Research contributing directly to these objectives, mainly in the field of networks optimization, data mining as well as content and interaction technologies.

Presentation