90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING
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We introduce a concurrent solver for the periodic event scheduling problem (PESP). It combines mixed integer programming techniques, the modulo network simplex method, satisfiability approaches, and a new heuristic based on maximum cuts. Running these components in parallel speeds up the overall solution process. This enables us to significantly improve the current upper and lower bounds for all benchmark instances of the library PESPlib.
We investigate how the numerical properties of the LP relaxations evolve
throughout the solution procedure in a solver employing the branch-and-cut
algorithm. The long-term goal of this work is to determine whether the effect
on the numerical conditioning of the LP relaxations resulting from the
branching and cutting operations can be effectively predicted
and whether such predictions can be used to make better algorithmic
choices. In a first step towards this goal, we discuss here the numerical
behavior of an existing solver in order to determine whether our
intuitive understanding of this behavior is correct.
This paper describes how we solved 12 previously unsolved mixed-integer program-
ming (MIP) instances from the MIPLIB benchmark sets. To achieve these results we
used an enhanced version of ParaSCIP, setting a new record for the largest scale MIP
computation: up to 80,000 cores in parallel on the Titan supercomputer. In this paper
we describe the basic parallelization mechanism of ParaSCIP, improvements of the
dynamic load balancing and novel techniques to exploit the power of parallelization
for MIP solving. We give a detailed overview of computing times and statistics for
solving open MIPLIB instances.
This thesis represents a game-theoretic investigation of the allocation of inspectors in a transportation network, comparing Nash and Stackelberg equilibrium strategies to a strategy in which inspections are conducted proportionally to the traffic volume. It contains specifications for the integration of space and time dependencies and extensive experimental tests for the application on the transportation network of German motorways using real data. Main results are that - although the formulated spot-checking game is not zero-sum - we are able to compute a Nash equilibrium using linear programming and secondly, that experimental results yield that a Nash equilibrium strategy represents a good trade-off for the Stackelberg equilibrium strategy between efficiency of controls and computation time.
This paper provides a highly integrated solution approach for rolling stock
planning problems in the context of intercity passenger traffic. The main
contributions are a generic hypergraph based mixed integer programming
model and an integrated algorithm for the considered rolling stock rotation
planning problem. The new developed approach is able to handle a very large
set of industrial railway requirements, such as vehicle composition,
maintenance constraints, infrastructure capacity, and regularity aspects.
By the integration of this large bundle of technical railway aspects, we show
that our approach has the power to produce implementable rolling stock
rotations for our industrial cooperation partner DB Fernverkehr.
This is the first time that the rolling stock rotations at DB Fernverkehr
could be optimized by an automated system utilizing advanced mathematical
programming techniques.