We consider a path planning problem wherein an agent needs to swiftly navigate from a source to a destination through an arrangement of obstacles in the plane. We suppose the agent has a limited neutralization capability in the sense that it can safely pass through an obstacle upon neutralization at a cost added to the traversal length. The agent's goal is to find the sequence of obstacles to be neutralized en route that minimizes the overall traversal length subject to the neutralization limit. We call this problem the obstacle neutralization problem (ONP), which is essentially a variant of the intractable weight-constrained shortest path problem in the literature. In this study, we propose a simple, yet efficient and effective suboptimal algorithm for ONP based on the idea of penalty search and we present special cases where our algorithm is provably optimal. Computational experiments involving both real and synthetic naval minefield data are also presented. (C) 2014 Elsevier Ltd. All rights reserved.