  Incremental graph search algorithms such as D* Lite reuse previous, and
perhaps partial, searches to expedite subsequent path planning tasks. In this
article, we are interested in developing incremental graph search algorithms
for path finding problems to simultaneously optimize multiple objectives such
as travel risk, arrival time, etc. This is challenging because in a
multi-objective setting, the number of "Pareto-optimal" solutions can grow
exponentially with respect to the size of the graph. This article presents a
new multi-objective incremental search algorithm called Multi-Objective
Path-Based D* Lite (MOPBD*) which leverages a path-based expansion strategy to
prune dominated solutions. Additionally, we introduce a sub-optimal variant of
MOPBD* to improve search efficiency while approximating the Pareto-optimal
front. We numerically evaluate the performance of MOPBD* and its variants in
various maps with two and three objectives. Results show that our approach is
more efficient than search from scratch, and runs up to an order of magnitude
faster than the existing incremental method for multi-objective path planning.
