Consideration of Lagrange multiplier of annealing method in Traveling Salesman Problem

Abstract

In order to conduct the efficient replacement of water pipe, it is required the non-destructive pipe inspection technology. Furthermore, optimal planning of inspection pass and replacement pass using inspection result is more important. In this research, we consider the optimal method based on the annealing method for inspection pass planning. The planning problem is formulated by the traveling salesman problem. However, the problem has not established the determination method of Lagrange multiplier for constraint. In this paper, we proposed the determination method of Lagrange multiplier based on the Hamiltonian decomposition. First, the analysis of Lagrange multiplier dependency in terms of probability in two-level system is conducted. Furthermore, determination method of Lagrange multiplier is proposed. Moreover, the numerical verification of proposed algorithm is conducted using SDK (Software Development Kit) of D-Wave.