## Invited Session Fri.1.MA 041

#### Friday, 10:30 - 12:00 h, Room: MA 041

**Cluster 14: Mixed-integer nonlinear programming** [...]

### Applications of MINLP I

**Chair: RĂ¼diger Schultz**

**Friday, 10:30 - 10:55 h, Room: MA 041, Talk 1**

**Claudia Stangl**

Feasibility testing for transportation orders in real-life gas networks

**Coauthors: Ralf Gollmer, RĂ¼diger Schultz**

**Abstract:**

Checking the feasibility of transportation requests belongs to the key tasks in gas pipeline operation. In its most basic form, the problem is to decide whether a certain quantity of gas can be sent through the network from prescribed entries to prescribed exit points. In the stationary case, the physics of gas flow together with technological and commercial side conditions lead to a pretty big (nonlinear, mixed-integer, finite dimensional) inequality system. We present elimination and approximation techniques so that the remaining system gets within the reach of standard NLP-solvers.

**Friday, 11:00 - 11:25 h, Room: MA 041, Talk 2**

**Francois Margot**

The traveling salesman problem with neighborhoods: MINLP solution

**Coauthors: Iacopo Gentilini, Kenji Shimada**

**Abstract:**

The traveling salesman problem with neighborhoods extends the traveling salesman problem to the case where each vertex of the tour is allowed to move in a given region. This NP-hard optimization problem

has recently received increasing attention in several technical fields such as robotics, unmanned aerial vehicles, or utility management. We formulate the problem as a nonconvex Mixed-Integer

NonLinear Program (MINLP) having the property that fixing all the integer variables to any integer values yields a convex nonlinear program. This property is used to modify the global MINLP optimizer Couenne, improving by orders of magnitude its performance and allowing the exact solution of instances large enough to be useful in applications. Computational results are presented where neighborhoods are either polyhedra or ellipsoids in **R**^{2} or **R**^{3} and with the Euclidean norm as distance metric.

**Friday, 11:30 - 11:55 h, Room: MA 041, Talk 3**

**Jakob Schelbert**

How to route a pipe - Discrete approaches for physically correct routing

**Coauthors: Sonja Mars, Lars Schewe**

**Abstract:**

We consider a real-world problem of routing a pipe through a power plant. This is done with a MISOCP model which is solved to global optimality.

The problem combines discrete aspects and non-linear constraints that model the physics of the pipe. Conventional truss topology optimization methods are not directly applicable. This follows from the discrete constraints that force the pipe to form a path or even a Steiner tree.

The underlying physics of the pipe can be expressed via a SOCP formulation. Additional combinatorial constraints, that are used to force the pipe to a certain design, call for the use of binary variables which renders the problem a MISOCP.

In our real-world application a rough outline of the admissible region, a start and end point are given. In addition to the self-weight of the pipe we are also asked to place hangers that provide support for the pipe. Furthermore we use Timoshenko beams for our pipe to consider a more accurate physical model.

We give some numerical results and show how to speed up the solving process by discrete optimization techniques to obtain global optimality.