13,419 research outputs found
Solving Irregular Strip Packing Problems With Free Rotations Using Separation Lines
Solving nesting problems or irregular strip packing problems is to position
polygons in a fixed width and unlimited length strip, obeying polygon integrity
containment constraints and non-overlapping constraints, in order to minimize
the used length of the strip. To ensure non-overlapping, we used separation
lines. A straight line is a separation line if given two polygons, all vertices
of one of the polygons are on one side of the line or on the line, and all
vertices of the other polygon are on the other side of the line or on the line.
Since we are considering free rotations of the polygons and separation lines,
the mathematical model of the studied problem is nonlinear. Therefore, we use
the nonlinear programming solver IPOPT (an algorithm of interior points type),
which is part of COIN-OR. Computational tests were run using established
benchmark instances and the results were compared with the ones obtained with
other methodologies in the literature that use free rotation
Efficiently Disassemble-and-Pack for Mechanism
In this paper, we present a disassemble-and-pack approach for a mechanism to
seek a box which contains total mechanical parts with high space utilization.
Its key feature is that mechanism contains not only geometric shapes but also
internal motion structures which can be calculated to adjust geometric shapes
of the mechanical parts. Our system consists of two steps: disassemble
mechanical object into a group set and pack them within a box efficiently. The
first step is to create a hierarchy of possible group set of parts which is
generated by disconnecting the selected joints and adjust motion structures of
parts in groups. The aim of this step is seeking total minimum volume of each
group. The second step is to exploit the hierarchy based on
breadth-first-search to obtain a group set. Every group in the set is inserted
into specified box from maximum volume to minimum based on our packing
strategy. Until an approximated result with satisfied efficiency is accepted,
our approach finish exploiting the hierarchy.Comment: 2 pages, 2 figure
Heuristics with Performance Guarantees for the Minimum Number of Matches Problem in Heat Recovery Network Design
Heat exchanger network synthesis exploits excess heat by integrating process
hot and cold streams and improves energy efficiency by reducing utility usage.
Determining provably good solutions to the minimum number of matches is a
bottleneck of designing a heat recovery network using the sequential method.
This subproblem is an NP-hard mixed-integer linear program exhibiting
combinatorial explosion in the possible hot and cold stream configurations. We
explore this challenging optimization problem from a graph theoretic
perspective and correlate it with other special optimization problems such as
cost flow network and packing problems. In the case of a single temperature
interval, we develop a new optimization formulation without problematic big-M
parameters. We develop heuristic methods with performance guarantees using
three approaches: (i) relaxation rounding, (ii) water filling, and (iii) greedy
packing. Numerical results from a collection of 51 instances substantiate the
strength of the methods
Geometric reasoning via internet crowdsourcing
The ability to interpret and reason about shapes is a peculiarly human capability that has proven difficult to reproduce algorithmically. So despite the fact that geometric modeling technology has made significant advances in the representation, display and modification of shapes, there have only been incremental advances in geometric reasoning. For example, although today's CAD systems can confidently identify isolated cylindrical holes, they struggle with more ambiguous tasks such as the identification of partial symmetries or similarities in arbitrary geometries. Even well defined problems such as 2D shape nesting or 3D packing generally resist elegant solution and rely instead on brute force explorations of a subset of the many possible solutions. Identifying economic ways to solving such problems would result in significant productivity gains across a wide range of industrial applications. The authors hypothesize that Internet Crowdsourcing might provide a pragmatic way of removing many geometric reasoning bottlenecks.This paper reports the results of experiments conducted with Amazon's mTurk site and designed to determine the feasibility of using Internet Crowdsourcing to carry out geometric reasoning tasks as well as establish some benchmark data for the quality, speed and costs of using this approach.After describing the general architecture and terminology of the mTurk Crowdsourcing system, the paper details the implementation and results of the following three investigations; 1) the identification of "Canonical" viewpoints for individual shapes, 2) the quantification of "similarity" relationships with-in collections of 3D models and 3) the efficient packing of 2D Strips into rectangular areas. The paper concludes with a discussion of the possibilities and limitations of the approach
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