Multiobjective Dynamic Optimization of Nonlinear Systems With Path Constraints

In this article, two algorithms are proposed to solve multiobjective path-constrained dynamic optimization problems. In each algorithm, an adaptive $\varepsilon $ -constraint method is employed to solve the multiobjective dynamic optimization problems (MODOPs) with path constraints in two iterative loops. In the outer loop, the adaptive $\varepsilon $ -constraint method adaptively adjusts the choice of the parameters $\varepsilon $ , which transfers MODOP into a sequence of single-objective dynamic optimization problems (SODOPs) with extra inequality constraints. In the inner loop, two different algorithms are used to solve the single-objective optimization problems. The first algorithm guarantees that the path constraints can be satisfied with any finite prescribed tolerance by replacing path constraints with a finite number of point constraints. Furthermore, the second algorithm guarantees that the path constraints are rigorously satisfied by enforcing the path constraints at a limited number of time points and by restricting the right-hand side of the path constraints. The proposed algorithms are proven to converge within finite iterations. The effectiveness of the algorithms is verified via numerical studies, along with a comparison to a state-of-the-art algorithm.