Abstract:The development of mathematical simulation and optimization models and algorithms for solving gas transport problems is an active field of research. In order to test and compare these models and algorithms, gas network instances together with demand data are needed. The goal of GasLib is to provide a set of publicly available gas network instances that can be used by researchers in the field of gas transport. The advantages are that researchers save time by using these instances and that different models and algorithms can be compared on the same specified test sets. The library instances are encoded in an XML (extensible markup language) format. In this paper, we explain this format and present the instances that are available in the library.Data Set: http://gaslib.zib.de Data Set License: CC BY 3.0 Keywords: gas transport; networks; problem instances; mixed-integer nonlinear optimization; GasLib MSC: 90-08; 90C90; 90B10 SummaryThe mathematical simulation and optimization of gas transport through pipeline systems is an important field of research with a large practical impact. Over the last decades, many different mathematical models on different levels of accuracy for different components of gas networks have been developed. On the basis of these models, several simulation and optimization algorithms have been proposed. We refer to [1][2][3] and the references therein for more information. With GasLib, we provide a set of network instances that can be used to test and compare such models and the algorithms for solving them.

We consider the time-dependent traveling salesman problem (TDTSP), a generalization of the asymmetric traveling salesman problem (ATSP) to incorporate time-dependent cost functions. In our model, the costs of an arc can change arbitrarily over time (and do not only dependent on the position in the tour). The TDTSP turns out to be structurally more difficult than the TSP. We prove it is NP-hard and APX-hard even if a generalized version of the triangle inequality is satisfied. In particular, we show that even the computation of one-trees becomes intractable in the case of time-dependent costs.We derive two IP formulations of the TDTSP based on time-expansion and propose different pricing algorithms to handle the significantly increased problem size. We introduce multiple families of cutting planes for the TDTSP as well as different LP-based primal heuristics, a propagation method and a branching rule. We conduct computational experiments to evaluate the effectiveness of our approaches on randomly generated instances. We are able to decrease the optimality gap remaining after one hour of computations to about six percent, compared to a gap of more than forty percent obtained by an off-the-shelf IP solver.Finally, we carry out a first attempt to learn strong branching decisions for the TDTSP. At the current state, this method does not improve the running times.

We consider an extended version of the classical Max-$$k$$ k -Cut problem in which we additionally require that the parts of the graph partition are connected. For this problem we study two alternative mixed-integer linear formulations and review existing as well as develop new branch-and-cut techniques like cuts, branching rules, propagation, primal heuristics, and symmetry breaking. The main focus of this paper is an extensive numerical study in which we analyze the impact of the different techniques for various test sets. It turns out that the techniques from the existing literature are not sufficient to solve an adequate fraction of the test sets. However, our novel techniques significantly outperform the existing ones both in terms of running times and the overall number of instances that can be solved.

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