OPTIMIZAREA COSTULUI INSTALATIILOR ARBORESCENTE DE TRANSPORT

Autor/autori: Ing. drd. Vlad ENACHE, Prof. dr. ing. Stoian PETRESCU

Rezumat: Considerand niste functii-cost generice, neprecizate, demonstram ca minimizarea costului unei instalatii (pompa + conducte) ce transporta un fluid generic printr-un arbore Steiner catre niste consumatori avand cerinte de debit si presiune oarecare conduce la respectarea a doua legi generale: 1) costul per bar al conductelor si al pompei se conserva in noduri (similar cu debitul); 2) in orice nod Steiner, gradientii costurilor conductelor se afla in echilibru vectorial. Reteaua cu aceste proprietati este optima si sub alte aspecte: dintre toate retelele cu acelasi cost, aceasta disipa putere minima si cere presiune/putere minima de pompare pentru a satisface toti consumatorii. Bazandu-ne pe aceste rezultate, propunem un algoritm de optimizare a costului total in care fiecare element se modifica tinand cont numai de informatia accesibila local, tinand cont si de eventuala neomogenitate a mediului. Nefiind necesara o coordonare centralizata, acest mecanism ar putea sta la baza auto-optimizarii unor retele de transport biologice (vase de sange, vase capilare etc.).

Cuvinte cheie: instalatie de transport fluide, retea arborescenta, algoritm de optimizare a costului.

Abstract: Considering generic cost functions, we show that minimizing the cost (pump + pipes) of tree-like installations transporting a generic fluid to sinks with given flows and pressures follows two general laws: 1) the pump’s and pipes’ “cost per bar” is conserved in nodes (similarly to the flow); 2) in each Steiner node, the pipes’ cost gradients are in equilibrium. The resulting configuration is also optimal in another sense: among all the networks with the same cost, this has minimum power dissipation and requires minimum pump pressure/power. Based on these results, we propose a local optimization algorithm which may be responsible for how biological networks (of blood vessels, capillary vessels etc.) minimize their cost. The algorithm takes into account the possible non-homogenous environment.

Keywords: fluid-transporting installation, tree-like network, cost-optimization algorithm

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