Contributed Session Tue.3.MA 144

Tuesday, 15:15 - 16:45 h, Room: MA 144

Cluster 22: Stochastic optimization [...]

Nonlinear stochastic optimization

 

Chair: Marcus Poggi

 

 

Tuesday, 15:15 - 15:40 h, Room: MA 144, Talk 1

Kathrin Klamroth
Modeling uncertainties in location-allocation problems: A stochastic programming approach

Coauthor: Markus Kaiser

 

Abstract:
Knowledge about the future development of the planning area and the environmental conditions is highly important for location decisions.
We consider continuous location-allocation problems with Weber objectives where uncertainty not only occurs in the demand of the existing facilities (that is, in the location objective), but also in the constraints of the problem such as the size and the shape of the feasible region. The trade-off between the cost of a solution on one hand and its robustness with respect to the uncertain data on the other hand is analyzed, which naturally motivates a multiple objective formulation of the problem. A two-stage stochastic programming model is obtained as a scalarization of the multiple objective model, and the relations to single-objective location-allocation problems are discussed. We use geometric arguments to derive discretization results for the case that distances are measured by block norms or polyhedral gauges. An efficient location-allocation heuristic for problems with uncertain feasible sets is suggested and tested on problem data with up to 2000 demand nodes, 10 different scenarios and 10 new facilities.

 

 

Tuesday, 15:45 - 16:10 h, Room: MA 144, Talk 2

Eugenio Mijangos
An algorithm for nonlinearly-constrained nonlinear two-stage stochastic problems

 

Abstract:
We put forward an algorithm to solve nonlinearly-constrained two-stage stochastic problems with a nonlinear objective function. It is based on the Twin Node Family (TNF) concept involved in the Branch-and-Fix Coordination method. These problems have continuous and binary variables in the first stage and only continuous variables in the second stage. The nonanticipativity constraints are fulfilled by
TNF strategy.
In this work, given that the objective function is nonlinear, we propose to solve each nonlinear subproblem generated in the nodes of the trees associated with this method by solving sequences of quadratic subproblems. If the nonlinear constraints are convex we approximate them by means of outer linear approximations; otherwise, we relax these constraints by using augmented Lagrangian techniques. These methods have been implemented in C++ with the help of Cplex 12.1 to solve only the quadratic approximations. The test problems have been randomly generated by using a C++ code developed by this author. Numerical experiments have been performed and its efficiency has been compared with that of BONMIN (COIN-OR). Results are promising.

 

 

Tuesday, 16:15 - 16:40 h, Room: MA 144, Talk 3

Marcus Poggi
On a class of stochastic programs with endogenous uncertainty: Algorithm and applications

Coauthor: Bruno Flach

 

Abstract:
We study a class of stochastic programming problems with endogenous uncertainty - i.e., those in which the probability distribution of the random parameters is decision-dependent - which is formulated as a Mixed Integer Non-Linear Programming (MINLP) problem. The proposed methodology consists of: (i) a convexification technique for polynomials of binary variables; (ii) an efficient cut-generation algorithm; and (iii) the incorporation of importance sampling concepts into the stochastic programming framework so as to allow the solution of large instances of the problem. We discuss the error tolerance of the approach and its impact on the resulting algorithm efficiency. Computational results are obtained in the context of the humanitarian logistics problem, they demonstrate the effectiveness of the proposed methodology by solving instances significantly larger than those reported in related works. Other applications in this class of stochastic problems are presented.

 

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