Related papers: On a Shape Optimization Problem for Tree Branches
Optimization is an essential component for solving problems in wide-ranging fields. Ideally, the objective function should be designed such that the solution is unique and the optimization problem can be solved stably. However, the…
We consider the problem of optimizing the product of the distances from a given point in a triangle to each vertex. There are two possible cases in general. For isosceles triangles, we explicitly show exactly when both cases occur.
We consider shape optimization problems of the form $$\min\big\{J(\Omega)\ :\ \Omega\subset X,\ m(\Omega)\le c\big\},$$ where $X$ is a metric measure space and $J$ is a suitable shape functional. We adapt the notions of $\gamma$-convergence…
We present a general method for obtaining strong bounds for discrete optimization problems that is based on a concept of branching duality. It can be applied when no useful integer programming model is available, and we illustrate this with…
We study a maximization problem for geometric network design. Given a set of $n$ compact neighborhoods in $\mathbb{R}^d$, select a point in each neighborhood, so that the longest spanning tree on these points (as vertices) has maximum…
In this paper, we present the description of a simplified model of the dynamic of a mono-specific even-aged forest. The model studied is a tree-growth model based on a system of two ordinary differential equations concerning the tree basal…
We model a microchannel cooling system and consider the optimization of its shape by means of shape calculus. A three-dimensional model covering all relevant physical effects and three reduced models are introduced. The latter are derived…
We consider problems in which we are given a rooted tree as input, and must find a subtree with the same root, optimizing some objective function of the nodes in the subtree. When this function is the sum of constant node weights, the…
We consider the problem of \emph{pruning} a classification tree, that is, selecting a suitable subtree that balances bias and variance, in common situations with inhomogeneous training data. Namely, assuming access to mostly data from a…
The paper focuses on a multidimensional optimization problem, which is formulated in terms of tropical mathematics and consists in minimizing a nonlinear objective function subject to linear inequality constraints. To solve the problem, we…
Spaces where each element describes a shape, so-called shape spaces, are of particular interest in shape optimization and its applications. Theory and algorithms in shape optimization are often based on techniques from differential…
Tree-size distribution is one of the most investigated subjects in plant population biology. The forestry literature reports that tree-size distribution trajectories vary across different stands and/or species, while the metabolic scaling…
A fundamental problem in network science is the normalization of the topological or physical distance between vertices, that requires understanding the range of variation of the unnormalized distances. Here we investigate the limits of the…
Linear arrangements of graphs are a well-known type of graph labeling and are found in many important computational problems, such as the Minimum Linear Arrangement Problem ($\texttt{minLA}$). A linear arrangement is usually defined as a…
The cable-trench problem is defined as a linear combination of the shortest path and the minimum spanning tree problem. In particular, the goal is to find a spanning tree that simultaneously minimizes its total length and the total path…
Energy systems optimization problems are complex due to strongly non-linear system behavior and multiple competing objectives, e.g. economic gain vs. environmental impact. Moreover, a large number of input variables and different variable…
Distributing points on a (possibly high-dimensional) sphere with minimal energy is a long-standing problem in and outside the field of mathematics. This paper considers a novel energy function that arises naturally from statistics and…
Tree projections provide a unifying framework to deal with most structural decomposition methods of constraint satisfaction problems (CSPs). Within this framework, a CSP instance is decomposed into a number of sub-problems, called views,…
The optimal power flow (OPF) problem seeks to control power generation/demand to optimize certain objectives such as minimizing the generation cost or power loss in the network. It is becoming increasingly important for distribution…
We study the algorithmic problem of optimally covering a tree with $k$ mobile robots. The tree is known to all robots, and our goal is to assign a walk to each robot in such a way that the union of these walks covers the whole tree. We…