Query plans offer diverse tradeoffs between conflicting cost metrics such as execution time, energy consumption, or execution fees in a multi-objective scenario. It is convenient for users to choose the desired cost tradeoff in an interactive process, dynamically adding constraints and finally selecting the best plan based on a continuously refined visualization of optimal cost tradeoffs. Multi-objective query optimization (MOQO) algorithms must possess specific properties to support such an interactive process: First, they must be anytime algorithms, generating multiple result plan sets of increasing quality with low latency between consecutive results. Second, they must be incremental, meaning that they avoid regenerating query plans when being invoked several times for the same query but with slightly different user constraints. We present an incremental anytime algorithm for MOQO, analyze its complexity and show that it offers an attractive tradeoff between result update frequency, single invocation time complexity, and amortized time over multiple invocations. Those properties make it suitable to be used within an interactive query optimization process. We evaluate the algorithm in comparison with prior work on TPC-H queries; our implementation is based on the Postgres database management system.