This manuscript is on the theory and numerical procedures of vector optimization w.r.t. various ordering structures, on recent developments in this area and, most important, on their application to medical engineering. In vector optimization one considers optimization problems with a vectorvalued objective map and thus one has to compare elements in a linear space. If the linear space is the fi...

Looking ahead during search is often useful when solving constraint satisfaction problems. Previous studies have shown that looking ahead helps by causing dead-ends to occur earlier in the search, and by providing information that is useful for dynamic variable ordering. In this paper, we show that another bene t of looking ahead is a useful domain value ordering heuristic, which we call look-a...

A graceful labeling of a graph $G=(V,E)$ with $m$ edges is aninjection $f: V(G) rightarrow {0,1,ldots,m}$ such that the resulting edge labelsobtained by $|f(u)-f(v)|$ on every edge $uv$ are pairwise distinct. For natural numbers $n$ and $k$, where $n > 2k$, a generalized Petersengraph $P(n, k)$ is the graph whose vertex set is ${u_1, u_2, cdots, u_n} cup {v_1, v_2, cdots, v_n}$ and its edge set...

Binary Decision Diagrams (BDDs) have become the data structure of choice for representing discrete functions in some design and verification applications: They are compact and efficient to manipulate with strong theoretical underpinnings. However, and despite many appealing characteristics, BDDs are not a representation commonly considered for evolutionary computation (EC). The inherent difficu...

AND/OR search spaces have recently been introduced as a unifying paradigm for advanced algorithmic schemes for graphical models. The main virtue of this representation is its sensitivity to the structure of the model, which can translate into exponential time savings for search algorithms. Since the variable selection can have a dramatic impact on search performance when solving optimization ta...

The one variable Bernstein-Szegő theory for orthogonal polynomials on the real line is extended to a class of two variable measures. The polynomials orthonormal in the total degree ordering and the lexicographical ordering are constructed and their recurrence coefficients discussed.

This paper describes new metrics for size minimization of the data structure referred to as quantum multiple-valued decision diagrams (QMDD). QMDD are used to represent the matrices describing reversible and quantum gates and circuits. We explore metrics related to the frequency of edges with non-zero weight for the entire QMDD data structure and their histograms with respect to each variable. ...

We present a new exact algorithm for nding the optimal variable ordering for reduced ordered Binary Decision Diagrams (BDDs). The algorithm makes use of a lower bound technique known from VLSI design. Up to now this technique has been used only for theoretical considerations and it is adapted here for our purpose. Furthermore, the algorithm supports symmetry aspects and makes use of a hash-ing ...

It was usually believed that the formation of intragranular ?-carbide in ?-austenite attributed to spinodal decomposition followed by ordering reaction. In this work, near-atomic scale characterization an austenite-based Fe-20Mn-9Al-3Cr-1.2C (wt. %) low-density steel, using (high-resolution) scanning transmission electron microscopy and atomic probe tomography, reveals initially-formed ?-carbid...