ELUCIDATION OF TSP WITH SAMAN-NET

Various problems of combinatorial optimization and permutation can be solved with neural network optimization. Traveling salesman problem is an important example of this category, which is characterized by its large number of iterating degree of freedom. There are various solutions of this problem has been given. These solutions are exact and heuristic methods, but all the exact approaches may be considered for theoretical interest. In this paper, we propose the Simulated Annealing of mean field approximation for choosing the possible minimum distance path that satisfies all the necessary constraints. A new energy function with mean field approximation is proposed. And the annealing schedule is also defined dynamically which changes with the distance on each iteration of the process. The algorithm shows that this approach generates optimal solution for the aforesaid problem. Keywords: TSP, MFA, SA, and Optimization. I. INTRODUCTION Most of the traditional problems of combinatorial permutation can be solved with the help of ANN(1), as it is well known that ANN consists of various non-linear processing units (2). These processing units may be interconnected through various topologies (3). One form of the topology is, feed back manner. In this form, a set of processing units, connected to each processing unit except to itself. The output of each unit is feed as input to all other units. With each link connecting between two units, a weight is associated, which determines the amount of output, a unit output provided as an input to the other units. The function of a feedback network with nonlinear units can be described in terms of the trajectory of the state of a network with time. By associating an energy function with each state, the trajectory describes a traversal along the energy landscape. The minima of the energy landscape correspond to the stable states, which can be used to store the given input patterns. The numbers of patterns that can be stored in the network depends upon the number of units and the strength of the connecting links. The state of the network at successive instants of time i.e. the trajectory of the states is determined by the activation dynamics (4), for the network. Any pattern can be stored and recalled from such type of network (5). During the process of the recalling the pattern, the network reaches to an equilibrium state (6), with the activation and synaptic dynamics. Associated with each output state is an energy (7), which depends on the network parameters like the weights and bias, besides the state of the network. The energy as a function of the state of the network corresponds to an energy landscape. One of the most prevalent uses of Neural Network is neural optimization which is a technique for solving a problem by casting it into a mathematical equation that, when either maximized or minimized, solves the problem without going into detailed dynamics of the concerned physical system. In other words, one of the most successful applications of the neural network principles is in solving optimization problem (8, 9). There are many situations where a problem may be formulated as Minimization or Maximization of some cost function or objective function subject to constraints. It is possible to map such problem onto a feedback network, where the units and connection strengths are identified by comparing the cost function of the problem with the energy function of the network expressed in terms of the states values of the units and the connection strength. It has been demonstrated (10) that how highly interconnected