Simulated annealing algorithm for prioritized multiobjective optimization-implementation in an adaptive model predictive control configuration

Abstract

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.