In a Wavelength Division Multiplexing (WDM) network, the performance of the virtual topology designed for a pre-specified traffic pattern can be improved by performing virtual topology reconfiguration. Simultaneously, the provision of survivability of WDM networks is important, because the transmission of huge data should be protected when a fiber fails. Thus, the combination of survivability and reconfiguration is an important issue in WDM networks. In this paper, the Virtual Topology Reconfiguration Problem (VTRP) on WDM networks with a reconfiguration constraint is studied. Given the physical topology, dedicated path-protection virtual topology and a new traffic demand matrix, the goal of VTRP is to reconfigure current virtual topology under the pre-specified reconfiguration constraint (r, a positive integer) so that the objective value can be minimized. The objective cost of VTRP is the average weighted propagation delay (AWPD). Because designing a polynomial time algorithm to find the optimal solution of VTRP is impractical when the reconfiguration constraint r is larger, two heuristic algorithms are proposed to solve this problem. They are Positive Reconfiguration Heuristic Algorithm (PRHA) and Conservative Reconfiguration Heuristic Algorithm (CRHA). Experimental results of these algorithms are also given.