An new self-organizing maps strategy for solving the traveling salesman problem

Genetic operators for combinatorial optimization in TSP and microarray gene ordering

“…As a consequence, the time required to execute one iteration, on an average, becomes almost equal for both FRAG GA and OX SIM. Similar observations are also made when the proposed method is compared with other GAs [1,6] and other methods like Self Organizing Map (SOM) [10].…”

“…FRAG GA is implemented in C on Pentium-4 (1.2 GHz) and the results are compared with those obtained using SWAP GATSP [6], MMGA [4], IGA [5], OX SIM, (standard GA with order crossover and simple inversion mutation) [1] MOC SIM (Modified order crossover and SIM), and self organizing map (SOM) [10] for solving TSP. For fair comparison with the above mentioned methods Lin-Kernighan (LK) heuristic is not used with FRAG GA, whereas, for comparison with HeSEA [16] and other LK based methods each chromosome in FRAG GALK is updated probabilistically with 20 runs of consecutive chained LK and mutation (as recommended in [16]).…”

“…The systematic process of determining frag is described later in this section. As an example, let us consider a string P that is sliced into three random fragments (1-8), (9)(10)(11)(12)(13)(14) and (15)(16)(17)(18)(19)(20) for a 20-city problem. P = 1 2 3 4 5 6 7 8 |9 10 11 12 13 14| 15 16 17 18 19 20 For tour construction the first fragment (9-14) is chosen randomly.…”

“…Over decades, researchers have suggested a multitude of heuristic algorithms, such as genetic algorithms (GAs) [3][4][5][6], tabu search [7,8], neural networks [9,10], and ant colonies [11] for solving TSP. Of particular interest are the GAs, due to the effectiveness achieved by this class of techniques in finding near optimal solutions in short computational time for large combinatorial optimization problems.…”

Recurrent Neural Networks with the Soft 'Winner Takes All' Principle Applied to the Traveling Salesman Problem

“…4 shows that from the 36 problems tested, 14 have the worst results with higher costs with the Soft WTA technique than with the Hard WTA: rd100, a280, ch130, bier127, kroA100, kroC100, kroE100, brazil58, pr107, eil51, gil262, lin318, fl417 and rat575. (Jin et al, 2003); • the Co-Adaptive Network (CAN), which uses the idea of cooperation among neighboring neurons and uses a number of neurons that is higher than the number of cities in the problem (Cochrane & Beasley, 2003); • the Real-Valued Antibody Network (RABNET), which uses a mechanism to stabilize the winning neurons and the centroids of the groups of cities for growth and pruning of the network (Massutti & Castro, 2009); • the Modified Growing Ring Self-Organizing Network (MGSOM) incorporates other initialization methods for the weights in the network, with other adaptation parameters proposed for the SOM network and other indexing forms for the order of cities (Bai et al, 2006); • the MSOM, which consists in a hybrid technique with Self-Organizing Maps (SOM) and evolutionary algorithms to solve the TSP, called Memetic Neural Network (Créput & Kouka, 2007); and • the technique of building a decision tree with minimum amplitude to choose the candidate cities for path exchange with the Lin-Kernighan of 2 up to 5-opt techniques (Kelsgaun, 2000). The comparisons are shown in Table 3, where 16 of the 24 problems tested have better results with the technique proposed using the 2-opt route improving technique.…”