text: In this paper, we propose TauRieL and target Traveling Salesman Problem (TSP) since it has broad applicability in theoretical and applied sciences. TauRieL utilizes an actor-critic inspired architecture that adopts ordinary feedforward nets to obtain a policy update vector @math . Then, we use @math to improve the state transition matrix from which we generate the policy. Also, the state transition matrix allows the solver to initialize from precomputed solutions such as nearest neighbors. In an online learning setting, TauRieL unifies the training and the search where it can generate near-optimal results in seconds. The input to the neural nets in the actor-critic architecture are raw 2-D inputs, and the design idea behind this decision is to keep neural nets relatively smaller than the architectures with wide embeddings with the tradeoff of omitting any distributed representations of the embeddings. Consequently, TauRieL generates TSP solutions two orders of magnitude faster per TSP instance as compared to state-of-the-art offline techniques with a performance impact of 6.1 in the worst case.
  @cite_37: In this paper we present a new approach to solving the Euclidean traveling salesman problem (ETSP) using SOM Kohonen maps with chain topology. The Kohonen learning rule is used with random parameters providing different neuron locations. Any new neuron configuration allows us to obtain a new ETSP solution. This new approach to exploring the solution space of the ETSP is easy to implement and suitable for relatively large ETSP problems. Furthermore, the approach could be combined both with other global optimization methods as genetic algorithms and with simple TSP solving heuristic procedures. The method is illustrated by simulations used for solving some TSPLIB problems.
  @cite_20: Abstract We propose a parallel computation model, called cellular matrix model (CMM), to address large-size Euclidean graph matching problems in the plane. The parallel computation takes place by partitioning the plane into a regular grid of cells, each cell being affected to a single processor. Each processor operates on local data, starting from its cell location and extending its search to the neighborhood cells in a spiral search way. In order to deal with large-size problems, memory size and processor number are fixed as O ( N ), where N is the problem size. Then one key point is that closest point searching in the plane is performed in O (1) expected time for uniform or bounded distribution, for each processor independently. We define a generic loop that models the parallel projection between graphs and their matching, as executed by the many cells at a given level of computation granularity. To illustrate its efficacy and versatility, we apply the CMM, on GPU platforms, to two problems in image processing: superpixel segmentation and stereo matching energy minimization. Firstly, we propose an extended version of the well-known SLIC superpixel segmentation algorithm, which we call SPASM algorithm, by using a parallel 2D self-organizing map instead of k -means algorithm. Secondly, we investigate the idea of distributed variable neighborhood search , and propose a parallel search heuristic, called distributed local search (DLS), for global energy minimization of stereo matching problem. We evaluate the approach with regards to the state-of-the-art graph cut and belief propagation algorithms. For each problem, we argue that the parallel GPU implementation provides new competitive quality time trade-offs, with substantial acceleration factors as the problem size increases.
summary: Previous research has employed neural nets in order to complement local search heuristics @cite_37 @cite_20 . One recent example is that authors in @cite_37 use Kohonen nets and devise a solver. Self organizing nature of Kohononen net iteratively executes and tries to map neurons which are dispersed onto the 2-D euclidean plane to the cities. At each iteration neurons attempt to decrease the distance between the cities in the neighborhood region which is a parametric set that consists of the nearby cities. The learning rate and the neighborhood function are the hyperparameters. Due to the fact that the number of neurons are higher than the cities, the algorithm presents an ordering mechanism for selecting the best fit neurons that represent the cities.