Topology optimization of periodically arranged components using shared design domains

Building structures from identical components organized in a periodic pattern is a common design strategy to reduce design effort, structural complexity and cost. However, any periodic pattern will impose certain design restrictions often leading to lower structural efficiency and heavier weight. Much research is available for periodic structures with connected components. This paper addresses minimal compliance design for periodic arrangements of unconnected components. The design problem discussed here is relevant for many applications where a tightly nested, space-saving arrangement of identical components is required. We formulate an optimal design problem for a component being part of a periodic arrangement. The orientation and position of the component relatively to its neighbours are prescribed. The component design is computed by topology optimization on a design domain possibly shared by several neighbouring components. Additional constraints prevent components from overlapping. Constraint aggregation is employed to reduce the computational cost of many local constraints. The effectiveness of the method is demonstrated by a series of 2D and 3D examples with an ever-smaller distance between the components. Moreover, problem-specific ranges with only little to no increase in compliance are reported.

Xeggora: Exploiting Immune-to-Evidence Symmetries with Full Aggregation in Statistical Relational Models (Extended Abstract)

We present improvements in maximum a-posteriori inference for Markov Logic, a widely used SRL formalism. Several approaches, including Cutting Plane Aggregation (CPA), perform inference through translation to Integer Linear Programs. Aggregation exploits context-specific symmetries independently of evidence and reduces the size of the program. We illustrate much more symmetries occurring in long ground clauses that are ignored by CPA and can be exploited by higher-order aggregations. We propose Full-Constraint-Aggregation, a superior algorithm to CPA which exploits the ignored symmetries via a lifted translation method and some constraint relaxations. RDBMS and heuristic techniques are involved to improve the overall performance. We introduce Xeggora as an evolutionary extension of RockIt, the query engine that uses CPA. Xeggora evaluation on real-world benchmarks shows progress in efficiency compared to RockIt especially for models with long formulas.

Xeggora: Exploiting Immune-to-Evidence Symmetries with Full Aggregation in Statistical Relational Models

We present improvements in maximum a-posteriori inference for Markov Logic, a widely used SRL formalism. Inferring the most probable world for Markov Logic is NP-hard in general. Several approaches, including Cutting Plane Aggregation (CPA), perform inference through translation to Integer Linear Programs. Aggregation exploits context-specific symmetries independently of evidence and reduces the size of the program. We illustrate much more symmetries occurring in long ground clauses that are ignored by CPA and can be exploited by higher-order aggregations. We propose Full-Constraint-Aggregation, a superior algorithm to CPA which exploits the ignored symmetries via a lifted translation method and some constraint relaxations. RDBMS and heuristic techniques are involved to improve the overall performance. We introduce Xeggora as an evolutionary extension of RockIt, the query engine that uses CPA. Xeggora evaluation on real-world benchmarks shows progress in efficiency compared to RockIt especially for models with long formulas.

Branch-and-Price-and-Cut for the Periodic Vehicle Routing Problem with Flexible Schedule Structures

This paper addresses the periodic vehicle routing problem with time windows (PVRPTW). Therein, customers require one or several visits during a planning horizon of several periods. The possible visiting patterns (schedules) per customer are limited. In the classical PVRPTW, it is common to assume that each customer requires a specific visit frequency and offers all corresponding schedules with regular intervals between the visits. In this paper, we permit all kinds of schedule structures and the choice of the service frequency. We present an exact branch-and-price-and-cut algorithm for the classical PVRPTW and its variant with flexible schedules. The pricing problems are elementary shortest-path problems with resource constraints. They can be based on one of two new types of networks and solved with a labeling algorithm, which uses several known acceleration techniques, such as the [Formula: see text]-path relaxation and dynamic halfway points within bidirectional labeling. For instances in which schedule sets fulfill a certain symmetry condition, we present specialized improvements of the algorithm, such as constraint aggregation and symmetry breaking. Computational tests on benchmark instances for the PVRPTW show the effectiveness of our algorithm. Furthermore, we analyze the impact of different schedule structures on run times and objective function values. The online appendix is available at https://doi.org/10.1287/trsc.2018.0855 .