On nonlinear replicated networks
- Autores: Laureano Fernando Escudero Bueno
- Localización: Questiió: Quaderns d'Estadística, Sistemes, Informatica i Investigació Operativa, ISSN 0210-8054, Vol. 9, Nº. 1, 1985, págs. 55-74
- Idioma: inglés
- Títulos paralelos:
- Sobre redes no lineales reiteradas
- Enlaces
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Resumen
In this paper we describe a new type of network flow problem that basically consists of the classical transshipment problem with the following extensions: (1) The replication of a network by producing subnetworks with identical structure, such that they are linked by so-called linking arcs; (2) The objective function terms related to the linking arcs are nondifferentiable nonlinear functions. We also describe an implementation of a linearly constrained nonlinear programming algorithm which is fast and can solve large-scale replicated network flow problems; the major ideas incorporated are: (i) The sparsity and the structure of the constraints system is used to reduce the time and computer storage requirements; (ii) The new concept of independent superbasic sets is introduced, so that it allows to obtain in parallel independent pieces of the solution at each iteration; (iii) The predecessor, depth, transverse and reverse structures are specialized for the case of replicated networks; (iv) A bending, backtracking linesearch that allows to activate more than one basic-superbasic arc at each iteration; (v) A procedure for pricing nonbasic arcs in the presence of non-differentiable terms in the objective function
