Optimization Models and Algorithms for Network Problems of Resours’ Distribution

The efficient algorithms for nonlinear programming problems for calculating networks have been offered, as well as the new network models to determine the optimal flows and distribution of resources have been constructed. The problems with nonlinear objective functions of general form and network structure of restrictions, which allow reaching quite a wide range of networks using common approach, were considered. For calculations the modifications of well-known methods of nonlinear programming were applied. The proposed methods of the first order is comparable by convergence rate with the methods of sequential quadratic programming through an efficient algorithm for the solution of the auxiliary quadratic problems and convenient procedure of step factor calculation. A series of models of resource distribution problems, taking into account the customers’ orders, the variable performance of sources and temporary storage of the product, was analyzed and numerically tested. The comparison of calculation results of applied problems using a standard package Solver and a specially designed computer program by the method of linearization of B.M. Pshenichniy demonstrated the possibility of reducing the number of iterations in the procedures of the same order by several times. The constructed models and algorithms of optimization of flow distribution allow creating effective information-analytical system for optimum control of functioning of the network distribution systems.
Keywords: problems of flow distribution, network models, methods of nonlinear programming, optimization algorithms.

Publication year: 
2014
Issue: 
5
УДК: 
519.8
С. 39–45., Іл. 5. Бібліогр.: 8 назв.
References: 

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References [transliteration]: 

1. M.C. Biggs, “Constrained Minimization Using Recursive Quadratic Programming”, Towards Global Optimization, L.C.W. Dixon and G.P. Szergo, Eds. North-Holland, 1975, pp. 341–349.
2. S.P. Han, “A Globally Convergent Method for Nonlinear Programming”, J. Optimization Theory and Applications, vol. 22, p. 297, 1977.
3. M.J.D. Powell, Variable Metric Methods for Constrained Optimization. Mathematical Programming: The State of the Art, A. Bachem et al., Eds. Springer Verlag, 1983, pp. 288–311.
4. Pshenichnyĭ B.N. Metod linearizat͡sii. – M.: Nauka, 1983. – 136 s.
5. Kirik O.I͡e. Alhorytmy linearyzat͡siï ta spri͡az͡henykh hradii͡entiv dli͡a neliniĭnykh zadach rozpodilu potokiv // Naukovi visti NTUU “KPI”. – 2007. – # 3. – S. 67–73.
6. D. Goldfarb and A. Idnani, “A numerically stable dual method for solving strictly convex quadratic problem”, Math. Progr., vol. 27, no. 1, pp. 1–33, 1983.
7. Aleksandrova V.M., Sobolenko L.A. Ėffektivnai͡a realizat͡sii͡a uskorennogo metoda reshenii͡a variat͡sionnykh neravenstv // Systemni doslidz͡henni͡a ta inform. tekhnolohiï. – 2014. – # 3. – S. 119–129.
8. Kirik O.I͡e. Neliniĭni zadachi rozpodilu potokiv u merez͡hakh z fiksovanymy ta vil′nymy vuzlovymy parametramy // Tam z͡he. – 2002. – # 4. – S. 106–119.

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