A combinatorial flow-based formulation for temporal bin packing problems

We consider two neighboring generalizations of the classical bin packing problem: the temporal bin packing problem (TBPP) and the temporal bin packing problem with fire-ups (TBPP-FU). In both cases, the task is to arrange a set of given jobs, characterized by a resource consumption and an activity window, on homogeneous servers of limited capacity. To keep operational costs but also energy consumption low, TBPP is concerned with minimizing the number of servers in use, whereas TBPP-FU additionally takes into account the switch-on processes required for their operation. Either way, challenging integer optimization problems are obtained, which can differ significantly from each other despite the seemingly only marginal variation of the problems. In the literature, a branch-and-price method enriched with many preprocessing steps (for TBPP) and compact formulations (for TBPP-FU), benefiting from numerous reduction methods, have emerged as, currently, the most promising solution methods. In this paper, we introduce, in a sense, a unified solution framework for both problems (and, in fact, a wide variety of further interval scheduling applications) based on graph theory. Any scientific contributions in this direction failed so far because of the exponential size of the associated networks. The approach we present in this article does not change the theoretical exponentiality itself, but it can make it controllable by clever construction of the resulting graphs. In particular, for the first time all classical benchmark instances (and even larger ones) for the two problems can be solved – in times that significantly improve those of the previous approaches

Improved flow-based formulations for the skiving stock problem

Thanks to the rapidly advancing development of (commercial) MILP software and hardware components, pseudo-polynomial formulations have been established as a powerful tool for solving cutting and packing problems in recent years. In this paper, we focus on the one-dimensional skiving stock problem (SSP), where a given inventory of small items has to be recomposed to obtain a maximum number of larger objects, each satisfying a minimum threshold length. In the literature, different modeling approaches for the SSP have been proposed, and the standard flow-based formulation has turned out to lead to the best trade-off between efficiency and solution time. However, especially for instances of practically meaningful sizes, the resulting models involve very large numbers of variables and constraints, so that appropriate reduction techniques are required to decrease the numerical efforts. For that reason, this paper introduces two improved flow-based formulations for the skiving stock problem that are able to cope with much larger problem sizes. By means of extensive experiments, these new models are shown to possess significantly fewer variables as well as an average better computational performance compared to the standard arcflow formulation

Object Registration in Semi-cluttered and Partial-occluded Scenes for Augmented Reality

This paper proposes a stable and accurate object registration pipeline for markerless augmented reality applications. We present two novel algorithms for object recognition and matching to improve the registration accuracy from model to scene transformation via point cloud fusion. Whilst the first algorithm effectively deals with simple scenes with few object occlusions, the second algorithm handles cluttered scenes with partial occlusions for robust real-time object recognition and matching. The computational framework includes a locally supported Gaussian weight function to enable repeatable detection of 3D descriptors. We apply a bilateral filtering and outlier removal to preserve edges of point cloud and remove some interference points in order to increase matching accuracy. Extensive experiments have been carried to compare the proposed algorithms with four most used methods. Results show improved performance of the algorithms in terms of computational speed, camera tracking and object matching errors in semi-cluttered and partial-occluded scenes

Variable and constraint reduction techniques for the temporal bin packing problem with fire-ups

The aim of this letter is to design and computationally test several improvements for the compact integer linear programming (ILP) formulations of the temporal bin packing problem with fire-ups (TBPP-FU). This problem is a challenging generalization of the classical bin packing problem in which the items, interpreted as jobs of given weight, are active only during an associated time window. The TBPP-FU objective function asks for the minimization of the weighted sum of the number of bins, viewed as servers of given capacity, to execute all the jobs and the total number of fire-ups. The fire-ups count the number of times the servers are activated due to the presence of assigned active jobs. Our contributions are effective procedures to reduce the number of variables and constraints of the ILP formulations proposed in the literature as well as the introduction of new valid inequalities. By extensive computational tests we show that substantial improvements can be achieved and several instances from the literature can be solved to proven optimality for the first time

A combinatorial flow-based formulation for temporal bin packing problems

For clarity, the instances used in this paper have been gathered together at https://github.com/wotzlaff/tbpp-instances. However, we note that most of these instances were originally designed in Aydin et al. (2020) and Dell’Amico et al. (2020), and some of them were already available online, see https://github.com/sibirbil/TemporalBinPackingWe consider two neighboring generalizations of the classical bin packing problem: the temporal bin pack ing problem (TBPP) and the temporal bin packing problem with fire-ups (TBPP-FU). In both cases, the task is to arrange a set of given jobs, characterized by a resource consumption and an activity window, on ho mogeneous servers of limited capacity. To keep operational costs but also energy consumption low, TBPP is concerned with minimizing the number of servers in use, whereas TBPP-FU additionally takes into ac count the switch-on processes required for their operation. Either way, challenging integer optimization problems are obtained, which can differ significantly from each other despite the seemingly only marginal variation of the problems. In the literature, a branch-and-price method enriched with many preprocessing steps (for TBPP) and compact formulations (for TBPP-FU), benefiting from numerous reduction methods, have emerged as, currently, the most promising solution methods. In this paper, we introduce, in a sense, a unified solution framework for both problems (and, in fact, a wide variety of further interval scheduling applications) based on graph theory. Any scientific contributions in this direction failed so far because of the exponential size of the associated networks. The approach we present in this article does not change the theoretical exponentiality itself, but it can make it controllable by clever construction of the resulting graphs. In particular, for the first time all classical benchmark instances (and even larger ones) for the two problems can be solved – in times that significantly improve those of the previous approaches.This work has been supported by FCT – Fundação para a Ciência e Tecnologia within the R&D Units Project Scope UIDB/00319/2020

How to Localize Humanoids with a Single Camera?

International audienceIn this paper, we propose a real-time vision-based localization approach for humanoid robots using a single camera as the only sensor. In order to obtain an accurate localization of the robot, we first build an accurate 3D map of the environment. In the map computation process, we use stereo visual SLAM techniques based on non-linear least squares optimization methods (bundle adjustment). Once we have computed a 3D reconstruction of the environment, which com- prises of a set of camera poses (keyframes) and a list of 3D points, we learn the visibility of the 3D points by exploiting all the geometric relationships between the camera poses and 3D map points involved in the reconstruction. Finally, we use the prior 3D map and the learned visibility prediction for monocular vision-based localization. Our algorithm is very efficient, easy to implement and more robust and accurate than existing approaches. By means of visibility prediction we predict for a query pose only the highly visible 3D points thus, speeding up tremendously the data association between 3D map points and perceived 2D features in the image. In this way, we can solve very efficiently the Perspective-n-Point (PnP) problem providing ro- bust and fast vision-based localization. We demonstrate the robustness and accuracy of our approach by show- ing several vision-based localization experiments with the HRP-2 humanoid robot