On the representation of the search region in multi-objective optimization

Given a finite set $N$ of feasible points of a multi-objective optimization (MOO) problem, the search region corresponds to the part of the objective space containing all the points that are not dominated by any point of $N$, i.e. the part of the objective space which may contain further nondominated points. In this paper, we consider a representation of the search region by a set of tight local upper bounds (in the minimization case) that can be derived from the points of $N$. Local upper bounds play an important role in methods for generating or approximating the nondominated set of an MOO problem, yet few works in the field of MOO address their efficient incremental determination. We relate this issue to the state of the art in computational geometry and provide several equivalent definitions of local upper bounds that are meaningful in MOO. We discuss the complexity of this representation in arbitrary dimension, which yields an improved upper bound on the number of solver calls in epsilon-constraint-like methods to generate the nondominated set of a discrete MOO problem. We analyze and enhance a first incremental approach which operates by eliminating redundancies among local upper bounds. We also study some properties of local upper bounds, especially concerning the issue of redundant local upper bounds, that give rise to a new incremental approach which avoids such redundancies. Finally, the complexities of the incremental approaches are compared from the theoretical and empirical points of view.Comment: 27 pages, to appear in European Journal of Operational Researc

Variabilität der Kopienzahl des TSPY-Gens auf dem Y-Chromosom unter besonderer Berücksichtigung von Hodengewebe und Hodentumoren

Die Genkopienzahl von TSPY (Testis-spezifische Protein des Y-Chromosoms) wird nach Southern Blot-Analyse auf 30 60 geschätzt. In dieser Arbeit erfolgt die Quantifizierung der TSPY-Genkopienzahl N TSPY durch Echtzeit-PCR. An Blut 51 gesunder Männer ergaben sich Werte von 26 - 180 N TSPY (Mittelwert 54). Wegen einer möglichen Rolle von N TSPY für die Prädisposition zu Hodentumoren erfolgten Analysen an Blut von 13 Seminompatienten, dies zeigte 29 60 N TSPY (Mittelwert 46). Die Ergebnisse der beiden Gruppen unterschieden sich nicht signifikant. Die TSPY-Genkopienzahlbestimmung in gesundem Hodengewebe und in Seminomen zeigte keine signifikanten Unterschiede, im Gegensatz zu Blut war allerdings die Kopienzahl im gonadalen Gewebe mit durchschnittlich 179 N TSPY signifikant erhöht. Die genomische N TSPY korreliert offensichtlich nicht mit der Prädisposition für Seminome. Es ergaben sich Hinweise auf eine physiologische somatische Variation der TSPY-Genkopienzahl

Solving the Dynamic Dial-a-Ride Problem Using a Rolling-Horizon Event-Based Graph

In many ridepooling applications transportation requests arrive throughout the day and have to be answered and integrated into the existing (and operated) vehicle routing. To solve this dynamic dial-a-ride problem we present a rolling-horizon algorithm that dynamically updates the current solution by solving an MILP formulation. The MILP model is based on an event-based graph with nodes representing pick-up and drop-off events associated with feasible user allocations in the vehicles. The proposed solution approach is validated on a set of real-word instances with more than 500 requests. In 99.5% of all iterations the rolling-horizon algorithm returned optimal insertion positions w.r.t. the current schedule in a time-limit of 30 seconds. On average, incoming requests are answered within 2.8 seconds

Modular Verification of JML Contracts Using Bounded Model Checking

There are two paradigms for dealing with complex verification targets: Modularization using contract-based specifications and whole-program analysis. In this paper, we present an approach bridging the gap between the two paradigms, introducing concepts from the world of contract-based deductive verification into the domain of software bounded model checking. We present a transformation that takes Java programs annotated with contracts written in the Java Modeling Language and turns them into Java programs that can be read by the bounded model checker JBMC. A central idea of the translation is to make use of nondeterministic value assignments to eliminate JML quantifiers. We have implemented our approach and discuss an evaluation, which shows the advantages of the presented approach