Dealing with numerical information is practically important in many real-world planning domains where the executability of an action can depend on certain numerical conditions, and the action effects can consume or renew some critical continuous resources, which in PDDL can be represented by numerical fluents. When a planning problem involves numerical fluents, the quality of the solutions can be expressed by an objective function that can take different plan quality criteria into account. We propose an incremental approach to automated planning with numerical fluents and multi-criteria objective functions for PDDL numerical planning problems. The techniques in this paper significantly extend the framework of planning with action graphs and local search implemented in the LPG planner. We define the numerical action graph (NA-graph) representation for numerical plans and we propose some new local search techniques using this representation, including a heuristic search neighborhood for...