Stability of lexicographical multicommodity flow problem
We consider the following lexicographical multicommodity network flow problem which generalizes the feasibility problem. Let {theta}{sub 1} = max (x, z) E X(d) {theta} z{sub i} {>=} {theta}f{sub i}, i = 1, ..., M where X(d) is the set of all admissible multicommodity flows x; z E R{sub +}{sup M} is the vector of flow values; parameters d and f are the vectors of edge capacities and flow requirements, respectively. Assuming that the problem is solved and letting z{sub i} = {theta}f{sub i} for all i such that there is no optimal solution (x*, z*) with z* > {theta}{sub 1}f{sub i} (denote the set of all such i by M{sub i}), we come to the next problem {theta}{sub 2} = max (x, z) E X(d) {theta} z{sub i} = {theta}{sub 1}f{sub i}, i E M{sub 1}, z{sub i}, {>=} {theta}f{sub i}, i M{sub 1}. Let us continue solving the sequence of such problems until {union}M{sub i} = M, thus obtaining the Pareto-optimal vector z{sup 0} closest to the vector f. We prove that the procedure and the Pareto-optimal solution z{sup 0} are stable with respectable to perturbations in d and f.
- OSTI ID:
- 35933
- Report Number(s):
- CONF-9408161-; TRN: 94:009753-0199
- Resource Relation:
- Conference: 15. international symposium on mathematical programming, Ann Arbor, MI (United States), 15-19 Aug 1994; Other Information: PBD: 1994; Related Information: Is Part Of Mathematical programming: State of the art 1994; Birge, J.R.; Murty, K.G. [eds.]; PB: 312 p.
- Country of Publication:
- United States
- Language:
- English
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