Michael Stiglmayr

Representation of the non-dominated set in biobjective discrete optimization

This paper introduces several algorithms for finding a representative subset of the non-dominated point set of a biobjective discrete optimization problem with respect to uniformity, coverage and the ?-indicator. We consider the representation problem itself as multiobjective, trying to find a good compromise between these quality measures. These representation problems are formulated as particular facility location problems with a special location structure, which allows for polynomial-time algorithms in the biobjective case based on the principles of dynamic programming and threshold approaches. In addition, we show that several multiobjective variants of these representation problems are also solvable in polynomial time. Computational results obtained by these approaches on a wide range of randomly generated point sets are presented and discussed. HighlightsWe formulate the representation problem in two dimensions for three different measures: uniformity, coverage, and ?-indicator.We present algorithms that solve the representation problems for the three measures in polynomial time.We consider multiobjective variants of representation problems, and present polynomial time algorithms to solve them.We present and discuss experimental results for all the problems.

Discrete and geometric Branch and Bound algorithms for medical image registration

Aiming at the development of an exact solution method for registration problems, we present two different Branch & Bound algorithms for a mixed integer programming formulation of the problem. The first B&B algorithm branches on binary assignment variables and makes use of an optimality condition that is derived from a graph matching formulation. The second, geometric B&B algorithm applies a geometric branching strategy on continuous transformation variables. The two approaches are compared for synthetic test examples as well as for 2-dimensional medical data. The results show that medium sized problem instances can be solved to global optimality in a reasonable amount of time.

On the Application of the Monge-Kantorovich Problem to Image Registration

A problem of image registration is considered in the context of optimal mass transportation. The properties and limitations of an optimal image transportation are analyzed. A modified formulation of this approach is proposed in order to overcome the morphing effect. Finally, a fast and simple scale-space approach for the new formulation is introduced, and numerical examples are presented.

A branch & bound algorithm for medical image registration

For a mixed integer programming formulation of the problem of registering two medical images we propose a geometric Branch & Bound algorithm, which applies a geometric branching strategy on the transformation variables. The results show that medium sized problem instances can be solved to global optimality in a reasonable amount of time.

Exact algorithms for handling outliers in center location problems on networks using k-max functions

Abstract In this paper, the identification and exclusion of very distant facilities in center location problems is modeled by k-max functions: One or several new facilities are to be located such that not the largest, but the kth largest weighted distance to the customers is minimized, with k ≥ 1. It is shown that k-max location problems on networks can be solved efficiently by enumerating candidate solutions from a finite dominating set (FDS) that is independent from the particular value of k. As a consequence, k-max locations can be found for all reasonable values of k at little extra cost as compared to a single solver call, for one fixed value of k. The location of several new facilities is naturally more complex. An FDS based recursive algorithm is developed for this case that allows the exact solution of medium size instances.

Personalization of Multicriteria Decision Support Systems

The Dagstuhl Seminar 18031 Personalization in Multiobjective Optimization: An Analytics Perspective carried on a series of five previous Dagstuhl Seminars (04461, 06501, 09041, 12041 and 15031) that were focused on Multiobjective Optimization. The continuing goal of this series is to strengthen the links between the Evolutionary Multiobjective Optimization (EMO) and the Multiple Criteria Decision Making (MCDM) communities, two of the largest communities concerned with multiobjective optimization today. Personalization in Multiobjective Optimization, the topic of this seminar, was motivated by the scientific challenges generated by personalization, mass customization, and mass data, and thus crosslinks application challenges with research domains integrating all aspects of EMO and MCDM. The outcome of the seminar was a new perspective on the opportunities as well as the research requirements for multiobjective optimization in the thriving fields of data analytics and personalization. Several multi-disciplinary research projects and new collaborations were initiated during the seminar, further interlacing the two communities of EMO and MCDM.

On the multicriteria allocation problem

We consider multicriteria allocation problems with linear sum objectives. Despite the fact that the single objective allocation problem is easily solvable, we show that already in the bicriteria case the problem becomes intractable, is NP-hard and has a non-connected efficient set in general. Using the equivalence to appropriately defined multiple criteria multiple-choice knapsack problems, an algorithm is suggested that uses partial dominance conditions to save computational time. Different types of enumeration schemes are discussed, for example, with respect to the number of necessary filtering operations and with regard to possible parallelizations of the procedure.