Dynamic programming bi-criteria combinatorial optimization

Mankowski, Michal; Moshkov, Mikhail

Dynamic programming bi-criteria combinatorial optimization

Files

M_C_O_3.pdf (2.15 MB)

Embargo End Date

2022-04-29

Type

Article

Authors

Mankowski, Michal

Moshkov, Mikhail

KAUST Department

Applied Mathematics and Computational Science Program
Computer Science Program
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Extensions of Dynamic Programming, Machine Learning and Discrete Optimization Research Group

Online Publication Date

2020-04-29

Print Publication Date

2020-09

Date

2020-04-29

Submitted Date

2019-10-02

Abstract

We introduce a model for combinatorial optimization problems based on the notion of a circuit. This circuit builds a set of elements for optimization from one-element sets attached to input nodes. It uses the operation of union of sets and functional operations on elements extended to sets of elements. We design a dynamic programming algorithm based on this circuit which constructs the set of Pareto optimal points for the problem of bi-criteria optimization of elements described by the circuit relative to two cost functions. We tested this approach on nine known combinatorial optimization problems. The problems related to the matrix chain multiplication, optimal paths in directed graphs, and binary search trees are considered in detail.

Citation

Mankowski, M., & Moshkov, M. (2020). Dynamic programming bi-criteria combinatorial optimization. Discrete Applied Mathematics. doi:10.1016/j.dam.2020.04.016

Acknowledgements

Research reported in this publication was supported by King Abdullah University of Science and Technology (KAUST), Kingdom of Saudi Arabia . We are greatly indebted to the anonymous reviewers for useful comments and suggestions.