A penalty search algorithm for the obstacle neutralization problem

Abstract

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.

An optimal algorithm for the obstacle neutralization problem

“…However, number of allowed neutralizations is limited, say by K, due to a particular reason such as the payload capacity of the agent or vehicle and the central issue is how to direct the agent to optimally utilize this neutralization capability. This problem, called obstacle neutralization problem (ONP), is a recently introduced NP-Hard problem [7]. Note that, if the number of allowed neutralizations is infinite, then the problem turns out to be the classical (unconstrained) shortest path problem and can be easily solved.…”

“…There are two studies directly related with the ONP where heuristic methods are proposed and used for solving it. In [7], the authors propose a penalty based algorithm to find suboptimal solutions for the ONP. On the other hand, in [4], an ant system algorithm is adapted to solve the ONP.…”

“…In the first phase, a suboptimal algorithm, named Penalty Search Algorithm (PSA) is called. PSA is explained in more detail in [7] but here a basic explanation of it is provided for the sake of completeness. If the path returned by PSA has exactly K neutralizations, then the algorithm returns this path since it is proven that when PSA dictates exactly K neutralizations, then the path returned by PSA is indeed optimal [7].…”

“…PSA is explained in more detail in [7] but here a basic explanation of it is provided for the sake of completeness. If the path returned by PSA has exactly K neutralizations, then the algorithm returns this path since it is proven that when PSA dictates exactly K neutralizations, then the path returned by PSA is indeed optimal [7]. However, PSA cannot always find a path with exactly K neutralizations and returns a path with less number of neutralizations than available (thus an upper bound solution).…”

“…This is the path returned by PSA and it clearly satisfies the neutralization limit constraint. The search for the penalty term is found by a straightforward bisection method [7]. The correctness of the PSA algorithm resides on the fact that as α is increased, the number of neutralizations dictated by PSA decreases and the total cost increases monotonically.…”