The analytic center of a polytope P fx Ax b ex g is characterized by a saddle point condition min y R max x S g x y max x S min y R g x y on the Lagrangian function

Local search algorithms play an essential role in solving large-scale combinatorial optimization problems. Traditionally, the local search procedure is guided mainly by the objective function of the problem. Hence, the greedy improvement paradigm poses the potential threat of prematurely getting trapped in low quality attraction basins. In this study, we intend to utilize the information extrac...

The Golomb Ruler Problem asks to position n integer marks on a ruler such that all pairwise distances between the marks are distinct and the ruler has minimum total length. It is a very challenging combinatorial problem, and provably optimal rulers are only known for n up to 26. Lower bounds can be obtained using Linear Programming formulations, but these are computationally expensive for large...

Due to irregular operations, the crew cost at the end of a month is typically substantially higher than the projected crew cost in planning. We assume that the fleeting and the aircraft routing decisions have already been made. We present a model and a solution methodology that produces robust crew schedules in planning. Besides the objective of minimizing the crew cost, we introduce the object...

Whereas CP methods are strong with respect to the detection of local infeasibilities, OR approaches have powerful optimization abilities that ground on tight global bounds on the objective. An integration of propagation ideas from CP and Lagrangian relaxation techniques from OR combines the merits of both approaches. We introduce a general way of how linear optimization constraints can strength...

In this work we address the Quadratic Minimum Spanning Tree Problem (QMSTP) known to be NP-hard. Given a complete graph, the QMSTP consists of determining a minimum spanning tree (MST) considering interaction costs between pairs of edges to be modelled. A Lagrangian relaxation procedure is devised and an efficient local search algorithm with tabu thresholding is developed. Computational experim...