KAUST DepartmentApplied 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 Date2020-04-29
Print Publication Date2020-09
Embargo End Date2022-04-29
Permanent link to this recordhttp://hdl.handle.net/10754/662698
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AbstractWe 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.
CitationMankowski, M., & Moshkov, M. (2020). Dynamic programming bi-criteria combinatorial optimization. Discrete Applied Mathematics. doi:10.1016/j.dam.2020.04.016
SponsorsResearch 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.
JournalDiscrete Applied Mathematics