Related papers: Solving Irregular Strip Packing Problems With Free…
Finding nonoverlapping balls with given centers in any metric space, maximizing the sum of radii of the balls, can be expressed as a linear program. Its dual linear program expresses the problem of finding a minimum-weight set of cycles…
We present a model development framework and numerical solution approach to the general problem-class of packing convex objects into optimized convex containers. Specifically, here we discuss the problem of packing ovals (egg-shaped…
We propose two novel algorithms for constructing convex collision-free polytopes in robot configuration space. Finding these polytopes enables the application of stronger motion-planning frameworks such as trajectory optimization with…
Generating time-optimal, collision-free trajectories for autonomous mobile robots involves a fundamental trade-off between guaranteeing safety and managing computational complexity. State-of-the-art approaches formulate spline-based motion…
Graph packing and partitioning problems have been studied in many contexts, including from the algorithmic complexity perspective. Consider the packing problem of determining whether a graph contains a spanning tree and a cycle that do not…
The (unweighted) point-separation problem asks, given a pair of points $s$ and $t$ in the plane, and a set of candidate geometric objects, for the minimum-size subset of objects whose union blocks all paths from $s$ to $t$. Recent work has…
A rectilinear polygon is a polygon whose edges are axis-aligned. Walking counterclockwise on the boundary of such a polygon yields a sequence of left turns and right turns. The number of left turns always equals the number of right turns…
Block-structured integer linear programs (ILPs) play an important role in various application fields. We address $n$-fold ILPs where the matrix $\mathcal{A}$ has a specific structure, i.e., where the blocks in the lower part of…
The obstacle problem is a class of free boundary problems which finds applications in many disciplines such as porous media, financial mathematics and optimal control. In this paper, we propose two operator-splitting methods to solve the…
Nonlinear optimal control problems for trajectory planning with obstacle avoidance present several challenges. While general-purpose optimizers and dynamic programming methods struggle when adopted separately, their combination enabled by a…
We consider the Bin Packing problem with a partition matroid constraint. The input is a set of items of sizes in $(0,1]$, and a partition matroid over the items. The goal is to pack all items in a minimum number of unit-size bins, such that…
Bringing together nonlinear optimization with polyhedral and integrality constraints enables versatile modeling, but poses significant computational challenges. We investigate a method to address these problems based on sequential…
This paper introduces a novel algorithm for Mixed-Integer Nonlinear Programming (MINLP) problems with multilinear interpolations of look-up tables. These problems arise when objective or constraints contain black-box functions only known at…
Near full-null degenerate singular points of analytic vector fields, asymptotic behaviors of orbits are not given by eigenvectors but totally decided by nonlinearities. Especially, in the case of high full-null degeneracy, i.e., the lowest…
The inverse problem of antiplane elasticity on determination of the profiles of $n$ uniformly stressed inclusions is studied. The inclusions are in ideal contact with the surrounding matrix, the stress field inside the inclusions is…
Covering and elimination inequalities are central to combinatorial optimization, yet their role has largely been studied in problem-specific settings or via no-good cuts. This paper introduces a unified perspective that treats these…
We study the two-dimensional hierarchical rectangle packing problem, motivated by applications in analog integrated circuit layout, facility layout, and logistics. Unlike classical strip or bin packing, the dimensions of the container are…
Positive linear programs (LP), also known as packing and covering linear programs, are an important class of problems that bridges computer science, operations research, and optimization. Despite the consistent efforts on this problem, all…
In this paper we present a new algorithm for a layout optimization problem: this concerns the placement of weighted polygons inside a circular container, the two objectives being to minimize imbalance of mass and to minimize the radius of…
Random packing of unoriented regular polygons and star polygons on a two-dimensional flat, continuous surface is studied numerically using random sequential adsorption algorithm. Obtained results are analyzed to determine saturated random…