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This paper presents a new stochastic algorithm for solving hierarchical multiobjective optimization problems. The algorithm is based on the simulated annealing concept and returns a single solution that corresponds to the lexicographic ordering approach. The algorithm optimizes simultaneously the multiple objectives by assigning a different initial temperature to each one, according to its position in the hierarchy. A major advantage of the proposed method is its low computational cost. This is very critical, particularly, for online applications, where the time that is available for decision making is limited. The method is tested in a number of benchmark problems, which illustrate its ability to find near-optimal solutions even in nonconvex multiobjective optimization problems. The results are comparable with those that are produced by state-of-the-art multiobjective evolutionary algorithms, such as the nondominated sorting genetic algorithm II. The algorithm is further applied to the solution of a large-scale problem that is formulated online, when a multiobjective adaptive model predictive control (MPC) configuration is adopted. This particular control scheme involves an adaptive discrete-time model of the system, which is developed using the radial-basis-function neural-network architecture. A key issue in the success of the adaptation strategy is the introduction of a persistent excitation constraint, which is transformed to a top-priority objective. The overall methodology is applied to the control problem of a pH reactor and proves to be superior to conventional MPC configurations.