Lin-Kernighan Heuristic Adaptations for the Generalized Traveling Salesman Problem

The Lin-Kernighan heuristic is known to be one of the most successful heuristics for the Traveling Salesman Problem (TSP). It has also proven its efficiency in application to some other problems. In this paper we discuss possible adaptations of TSP heuristics for the Generalized Traveling Salesman Problem (GTSP) and focus on the case of the Lin-Kernighan algorithm. At first, we provide an easy-to-understand description of the original Lin-Kernighan heuristic. Then we propose several adaptations, both trivial and complicated. Finally, we conduct a fair competition between all the variations of the Lin-Kernighan adaptation and some other GTSP heuristics. It appears that our adaptation of the Lin-Kernighan algorithm for the GTSP reproduces the success of the original heuristic. Different variations of our adaptation outperform all other heuristics in a wide range of trade-offs between solution quality and running time, making Lin-Kernighan the state-of-the-art GTSP local search.Comment: 25 page

Implementation and Evaluation of Novel Buildstyles in Fused Deposition Modeling (FDM)

Previous investigations have shown that the optimization of extrusion dynamics in .conjunction with the buildstyle pattern is of paramount importance to increase part quality in Fused Deposition Modeling (FDM). Recently domain decomposition and space filling curves have been introduced for slice generation in FDM [1]. The current work focuses on the implementations of fractal-like buildstyle .patterns using. Simulated Annealing [2, 3], Lin-Kernighan algorithms [4] and Construction Procedures based on Nearest Neighbor Heuristics [5]. These computational optimization procedures are able to generate filling patterns that allow the continuous deposition of a single road to fill arbitrary shaped domains. The necessary software modules to produce arbitrary threedimensional artifacts have been developed and are evaluated with respect to part quality and build time.Mechanical Engineerin

Renormalization for Discrete Optimization

The renormalization group has proven to be a very powerful tool in physics for treating systems with many length scales. Here we show how it can be adapted to provide a new class of algorithms for discrete optimization. The heart of our method uses renormalization and recursion, and these processes are embedded in a genetic algorithm. The system is self-consistently optimized on all scales, leading to a high probability of finding the ground state configuration. To demonstrate the generality of such an approach, we perform tests on traveling salesman and spin glass problems. The results show that our ``genetic renormalization algorithm'' is extremely powerful.Comment: 4 pages, no figur