An image set-oriented method for the numerical treatment of bi-level multi-objective optimization problems. (English) Zbl 1477.65092
Junge, Oliver (ed.) et al., Advances in dynamics, optimization and computation. A volume dedicated to Michael Dellnitz on the occasion of his 60th birthday. Cham: Springer. Stud. Syst. Decis. Control 304, 337-354 (2020).
Summary: In this chapter, we consider equality constrained bi-level multi-objective optimization problems, where the lower level problem is convex. Based on a suitable reformulation of the Kuhn-Tucker equations, we present an image set-oriented algorithm of reference point type for the approximation of the solution set, the Pareto set respectively its image, the Pareto front, of such a problem. The algorithm is designed such that the generated representation of the Pareto front is well-distributed with respect to the higher level image space. We first prove convergence for this algorithm and further on indicate its efficiency on two academic test problems.
For the entire collection see [Zbl 1445.37003].
For the entire collection see [Zbl 1445.37003].
MSC:
| 65K05 | Numerical mathematical programming methods |
| 90C29 | Multi-objective and goal programming |
| 90C30 | Nonlinear programming |
| 94A08 | Image processing (compression, reconstruction, etc.) in information and communication theory |
Keywords:
bi-level multi-objective optimization; bi-level optimization; multi-objective optimization; hierarchical optimization; image set-oriented methods; reference point methodsSoftware:
NBIReferences:
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