@misc{FujiiKimKojimaetal., author = {Fujii, Koichi and Kim, Sunyoung and Kojima, Masakazu and Mittelmann, Hans D. and Shinano, Yuji}, title = {The Largest Unsolved QAP Instance Tai256c Can Be Converted into A 256-dimensional Simple BQOP with A Single Cardinality Constraint}, issn = {1438-0064}, doi = {10.12752/8808}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-88086}, abstract = {Tai256c is the largest unsolved quadratic assignment problem (QAP) instance in QAPLIB; a 1.48\% gap remains between the best known feasible objective value and lower bound of the unknown optimal value. This paper shows that the instance can be converted into a 256 dimensional binary quadratic optimization problem (BQOP) with a single cardinality constraint which requires the sum of the binary variables to be 92.The converted BQOP is much simpler than the original QAP tai256c and it also inherits some of the symmetry properties. However, it is still very difficult to solve. We present an efficient branch and bound method for improving the lower bound effectively. A new lower bound with 1.36\% gap is also provided.}, language = {en} } @misc{PetkovicZakiyeva, author = {Petkovic, Milena and Zakiyeva, Nazgul}, title = {Mathematical Optimization for Analyzing and Forecasting Nonlinear Network Time Series}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-88037}, abstract = {This work presents an innovative short to mid-term forecasting model that analyzes nonlinear complex spatial and temporal dynamics in energy networks under demand and supply balance constraints using Network Nonlinear Time Series (TS) and Mathematical Programming (MP) approach. We address three challenges simultaneously, namely, the adjacency matrix is unknown; the total amount in the network has to be balanced; dependence is unnecessarily linear. We use a nonparametric approach to handle the nonlinearity and estimate the adjacency matrix under the sparsity assumption. The estimation is conducted with the Mathematical Optimisation method. We illustrate the accuracy and effectiveness of the model on the example of the natural gas transmission network of one of the largest transmission system operators (TSOs) in Germany, Open Grid Europe. The obtained results show that, especially for shorter forecasting horizons, the proposed method outperforms all considered benchmark models, improving the average nMAPE for 5.1\% and average RMSE for 79.6\% compared to the second-best model. The model is capable of capturing the nonlinear dependencies in the complex spatial-temporal network dynamics and benefits from both sparsity assumption and the demand and supply balance constraint.}, language = {en} }