A Novel Constructive-Optimizer Neural Network for the Traveling Salesman Problem

Abstract

In this paper, a novel constructive-optimizer neural network (CONN) is proposed for the traveling salesman problem (TSP). CONN uses a feedback structure similar to Hopfield-type neural networks and a competitive training algorithm similar to the Kohonen-type self-organizing maps (K-SOMs). Consequently, CONN is composed of a constructive part, which grows the tour and an optimizer part to optimize it. In the training algorithm, an initial tour is created first and introduced to CONN. Then, it is trained in the constructive phase for adding a number of cities to the tour. Next, the training algorithm switches to the optimizer phase for optimizing the current tour by displacing the tour cities. After convergence in this phase, the training algorithm switches to the constructive phase anew and is continued until all cities are added to the tour. Furthermore, we investigate a relationship between the number of TSP cities and the number of cities to be added in each constructive phase. CONN was tested on nine sets of benchmark TSPs from TSPLIB to demonstrate its performance and efficiency. It performed better than several typical Neural networks (NNs), including KNIES_TSP_Local, KNIES_TSP_Global, Budinich's SOM, Co-Adaptive Net, and multivalued Hopfield network as wall as computationally comparable variants of the simulated annealing algorithm, in terms of both CPU time and accuracy. Furthermore, CONN converged considerably faster than expanding SOM and evolved integrated SOM and generated shorter tours compared to KNIES_DECOMPOSE. Although CONN is not yet comparable in terms of accuracy with some sophisticated computationally intensive algorithms, it converges significantly faster than they do. Generally speaking, CONN provides the best compromise between CPU time and accuracy among currently reported NNs for TSP.

Solving the traveling salesman problem based on an adaptive simulated annealing algorithm with greedy search

“…As a rule, the hot t initial , low t end , and slow t cool are necessary for finding a good solution at the cost of a lot of computation time. Hence, in order to speed Table 6 Comparison ASA-GS with RABNET-TSP [23], Memetic-SOM [6], and CONN [29], respectively.…”

“…Comparison ASA-GS with RABNET-TSP [23], Memetic-SOM [6], and CONN [29] up the convergence rate of the ASA-GS, greedy search technique is considered and designed in this paper. In this paper, our algorithm is carried out with a two-stage adaptive local search strategy based on the four parameters t initial , t cool , t greedy and t end , and the two-stage adaptive local search strategy is described in Fig.…”

“…The methods include branch-and-bound [9], particle swarm optimization [21,22,32], neural network [6,23,29], tabu search [11], ant colony optimization [5,10,20,34], genetic algorithms [3,13,36], selforganizing maps [1], simulated annealing [18,19,24,33], elastic net [7,8,37], and Lagrangean relaxation [38].…”

Importance of the Initial Conditions and the Time Schedule in the Simulated Annealing

“…The first method chosen for comparison is the Constructive Optimizing Neural Network (CONN) proposed in [24], for which it is claimed that all runs has led to the same results, so that the best, the worst and the average of the solutions are the same. The second one is a Kohonen-Like decomposition method [25], in its three different versions abbreviated by KD, KL and KG.…”

An efficient solving of the traveling salesman problem: the ant colony system having parameters optimized by the Taguchi method

“…Yi et al [19] presented a fast elastic net method for solving the TSP. Saadatmand-Tarzjan et al [20] presented a novel constructive-optimizer neural network for solving the TSP. Sauer and Coelho [21] presented a discrete differential evolution with a local search method to solve the TSP.…”