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TWO-WAY ITERATIVE PROCESS FOR DETERMINING AN APPROXIMATE OPTIMAL SOLUTION TO A LIMITED-CAPACITY PLACEMENT PROBLEM
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TWO-WAY ITERATIVE PROCESS FOR DETERMINING AN APPROXIMATE OPTIMAL SOLUTION TO A LIMITED-CAPACITY PLACEMENT PROBLEM
Annotation
PII
S042473880000616-6-1
Publication type
Article
Status
Published
Authors
Bayrambek Alibekov 
Edition
Issue №2
Pages
111-117
Abstract
We consider a multi-extreme placement problem with a nonlinear goal function and linear constraints. The upwardly convex original goal function is replaced by a piecewise linear function, and the original problem is reduced to a partial-integer approximate problem. To solve the approximate problem, we propose a two-way iterative method for determining the plan that is close to the optimal plan. At each iteration, transport problems are solved and the locally optimal solution of the original problem is determined. Using the obtained locally optimal solution of the approximate problem, it is possible to implement a two-way coordinate narrowing of the area of acceptable solutions to the original problem. Using the optimal solution to the problem of placement with limited capacities, the range of acceptable solutions to the problem of placement with capacity restrictions in the variant formulation is narrowed. We define a plan that belonged to a new domain obtained by excluding some non-optimal plans from the set of acceptable solutions, which provides a minimum of the objective function of the original problem. The value of the objective function corresponding to the obtained solution is evaluated from below. The article describes the algorithm for solving the placement problem and analyzes the effectiveness of the method based on experimental calculations.
Date of publication
01.04.2007
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708
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Alibekov B.I. (1975): O zadache na razmeschenie s ogranichennymi moschnostyami // Ehkonomika i mat. metody. T. XI. Vyp. 3.
 
 Alibekov B.I. (1979): Dvukhstoronnij iteratsionnyj protsess opredeleniya priblizhennogo optimal'nogo resheniya mnogoehkstremal'noj zadachi tipa razmescheniya. V “Avtomatizatsiya proektirovaniya sistem upravleniya zhelezny dorog”. Mezhvuzovskij tematicheskij sbornik. Vyp. 154. Rostov-na-Donu: RIIZhT. Alibekov B.I. (2002): Dvukhstoronnij iteratsionnyj protsess opredeleniya priblizhennogo optimal'nogo resheniya zadachi razmescheniya. Materialy tret'ej regional'noj nauchno-prakticheskoj konferentsii. Makhachkala: Dagestanskij gosudarstvennyj universitet.
 
 Alibekov B.I., Zhukov V.P. (1990): Sistema modelej transportnogo kompleksa regiona // Transport. Nauka, tekhnika, upravlenie. № 5.
 
 Belov D.K., Minkin V.B., Alibekov B.I. (1983): Optimizatsiya transportno-ehkonomicheskikh svyazej perevozok gruzov v regione na primere sakharnoj svekly. V sb.: “Izvestiya Severo-Kavkazskogo nauchnogo tsentra vysshej shkoly”. Ser. “Tekhnicheskie nauki”. № 3.
 
 Khachaturov V.R. (1967): Algoritm i programma resheniya zadachi razmescheniya predpriyatij s neogranichennymi ob'emami proizvodstva // Ehkonomika i mat. metody. T. III. Vyp. 2.

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