Incremental graph search algorithms, such as D* Lite, reuse previous search efforts to speed up subsequent similar path planning tasks. These algorithms have demonstrated their efficiency in comparison with search from scratch, and have been leveraged in many applications such as navigation in unknown terrain. On the other hand, path planning typically involves optimizing multiple conflicting objectives simultaneously, such as travel risk, arrival time, etc. Multi-objective path planning is challenging as the number of Pareto-optimal solutions can grow exponentially with respect to the size of the graph, which makes it computationally burdensome to plan from scratch each time when similar planning tasks needs to be solved. This article presents a new multi-objective incremental search algorithm called Multi-Objective Path-Based D* Lite (MOPBD*) which reuses previous search efforts to speed up subsequent planning tasks while optimizing multiple objectives. Numerical results show that MOPBD* is more efficient than search from scratch and runs an order of magnitude faster than existing incremental method for multi-objective path planning.
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