Related papers: Simulated annealing for weighted polygon packing
We consider the following geometric optimization problem: find a convex polygon of maximum area contained in a given simple polygon $P$ with $n$ vertices. We give a randomized near-linear-time $(1-\varepsilon)$-approximation algorithm for…
Packing problems are in general NP-hard, even for simple cases. Since now there are no highly efficient algorithms available for solving packing problems. The two-dimensional bin packing problem is about packing all given rectangular items,…
We explore the applicability of quantum annealing to the approximation task of curve fitting. To this end, we consider a function that shall approximate a given set of data points and is written as a finite linear combination of…
Given a convex polygon $P$ with $n$ vertices, the two-center problem is to find two congruent closed disks of minimum radius such that they completely cover $P$. We propose an algorithm for this problem in the streaming setup, where the…
In this paper, we show an improved bound and new algorithm for the online square-into-square packing problem. This two-dimensional packing problem involves packing an online sequence of squares into a unit square container without any two…
This paper develops a robust angles-only IROD method based on polynomial optimization for arbitrary nonlinear dynamics. First, the relative motion is approximated by high-order Taylor polynomials within the differential algebra framework,…
Quantum annealing is a method developed to solve combinatorial optimization problems by utilizing quantum bits. Solving such problems corresponds to minimizing a cost function defined over binary variables. However, in many practical cases,…
The problem of rectangle tiling binary arrays is defined as follows. Given an $n \times n$ array $A$ of zeros and ones and a natural number $p$, our task is to partition $A$ into at most $p$ rectangular tiles, so that the maximal weight of…
A wide variety of optimization techniques, both exact and heuristic, tend to be biased samplers. This means that when attempting to find multiple uncorrelated solutions of a degenerate Boolean optimization problem a subset of the solution…
Bin packing is a classic optimization problem with a wide range of applications, from load balancing to supply chain management. In this work, we study the online variant of the problem, in which a sequence of items of various sizes must be…
Earth imaging satellites are a crucial part of our everyday lives that enable global tracking of industrial activities. Use cases span many applications, from weather forecasting to digital maps, carbon footprint tracking, and vegetation…
Many important challenges in science and technology can be cast as optimization problems. When viewed in a statistical physics framework, these can be tackled by simulated annealing, where a gradual cooling procedure helps search for…
In this paper we study the hard sphere packing problem in the Hamming space by the cavity method. We show that both the replica symmetric and the replica symmetry breaking approximations give maximum rates of packing that are asymptotically…
We study a two-dimensional generalization of the classical Bin Packing problem, denoted as 2D Demand Bin Packing. In this context, each bin is a horizontal timeline, and rectangular tasks (representing electric appliances or computational…
We propose a Deep Reinforcement Learning (Deep RL) algorithm for solving the online 3D bin packing problem for an arbitrary number of bins and any bin size. The focus is on producing decisions that can be physically implemented by a robotic…
Optimization is finding the best solution, which mathematically amounts to locating the global minimum of some cost function. Optimization is traditionally automated with digital or quantum computers, each having their limitations and none…
Optimal flight gate assignment is a highly relevant optimization problem from airport management. Among others, an important goal is the minimization of the total transit time of the passengers. The corresponding objective function is…
Finding the global minimum in a rugged potential landscape is a computationally hard task, often equivalent to relevant optimization problems. Simulated annealing is a computational technique which explores the configuration space by…
In information visualization, the position of symbols often encodes associated data values. When visualizing data elements with both a numerical and a categorical dimension, positioning in the categorical axis admits some flexibility. This…
We study the simulated annealing algorithm based on the kinetic Langevin dynamics, in order to find the global minimum of a non-convex potential function. For both the continuous time formulation and a discrete time analogue, we obtain the…