Invited Session Mon.1.MA 376

Monday, 10:30 - 12:00 h, Room: MA 376

Cluster 22: Stochastic optimization [...]

Decisions policies and estimation techniques in a stochastic environment


Chair: Fabian Bastin



Monday, 10:30 - 10:55 h, Room: MA 376, Talk 1

Alwin Haensel
A SP approach for decision-dependent uncertainty in production planning under non-compliance risk

Coauthor: Marco Laumanns


Governmental regulation pressure on production quality and standards is increasing in many areas, especially in the chemical, food and pharmaceutical industries. Therefore, a production plan needs to consider the risks of failing the quality inspection by the authority agency. Inspection realizations are clearly dependent on the previous production planning decisions. Normally stochastic programs assume the random process to be independent of the optimization decision. This dependency increases the complexity of the underlying problem significantly. The uncertain inspection realizations are modelled by scenarios, which are generated according given product-site hazards. We propose a general scenario based stochastic programming approach and start initially with a risk-neutral model maximizing the expected revenue. The model is extended to account for more risk-averse attitudes of the decision maker by introducing probabilistic constraints. The main focus is on a direct CVaR (conditional value-at-risk) optimization formulation.



Monday, 11:00 - 11:25 h, Room: MA 376, Talk 2

Fabian Bastin
On the combination of Hessian approximations for data estimation

Coauthors: Anh Tien Mai, Michel Toulouse


Data estimation is increasingly more computing intensive as more data becomes available, and as it is used with always more complex models. Typical estimation procedures have however very specific structures, even when the models are nonlinear, and we aim to exploit them, but this may compromise convergence when we get close to the solution. In particular, we revisit optimization techniques relying on multiple Hessian approximation update schemes, with a specific focus on maximum likelihood techniques involving expensive objective functions. Such functions can for instance be constructed as Monte Carlo samples on some population and some inner expectations, as considered in fields like discrete choice theory. Using a trust-region approach, we show that combinations of standard secant updates (SR1 and BFGS) and statistical approximations (here the BHHH update), can dramatically decrease the time required to converge to the solution, and that it is possible to build strategies aimed to minimize the number of objective function evaluations using a retrospective approach. Numerical experiments on real data are presented in order to demonstrate the approach potential.



Monday, 11:30 - 11:55 h, Room: MA 376, Talk 3

Xinan Yang
Approximate dynamic programming with Bézier curves/surfaces for top-percentile traffic routing

Coauthor: Andreas Grothey


Multi-homing is used by Internet Service Providers to connect to the Internet via different network providers. This study develops a routing strategy under multi-homing in the case where network providers charge ISPs according to top-percentile pricing (i.e. based on the θ-th highest volume of traffic). We call this problem the Top-percentile Traffic Routing Problem (TpTRP).
To overcome the curse of dimensionality in Stochastic Dynamic Programming, in previous work we have suggested to use Approximate Dynamic Programming (ADP) to construct value function approximations, which allow us to work in continuous state space. The resulting ADP model provides well performing routing policies for medium sized instances. In this work we extend the ADP model, by using B{é}zier Curves/Surfaces to obtain continuous-time approximations of the time-dependent ADP parameters. This modification reduces the number of regression parameters to estimate and thus accelerates the efficiency of parameter training in the solution of the ADP model, which makes realistically sized TpTRP instances tractable. We argue that our routing strategy is near optimal by giving bounds.


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