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1 ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes
1 Zeszyty Naukowe Politechniki Rzeszowskiej. Budownictwo i Inżynieria Środowiska

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Optimization of linear functions on a cyclic permutation. Based on the random search

Grebennik I., Baranov O., Chorna A., Gorbacheva E.

ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes

2016

Vol. 5, No 3

211--216

For creating adequate mathematical models of combinatorial problems of constructing optimal cyclic routes, mathematical modeling and solving a number of planning and control tasks solutions of optimization problems on the set of cyclic permutations are required. Review of the publications on combinatorial optimization demonstrates that the optimization problem on the cyclic permutations have not been studied sufficiently. This paper is devoted to solving optimization problem of a linear function with linear constraints on the set of cyclic permutations. For solving problems of this class using of known methods, taking into account the properties of a combinatorial set of cyclic permutations, is proposed. For this purpose we propose a method based on the ideology of random search. Heuristic method based on the strategy of the branch and bound algorithm is proposed to solve auxiliary optimization problem of a linear function without constraints on the set of cyclic permutations. Since application of the branch and bound algorithm immediately leads to an exponential growth of the complexity with increasing the dimension of the problem a number of modifications are suggested. Modifications allow reducing computational expenses for solving higher dimension problems. The effectiveness of the proposed improvements is demonstrated by computational experiments.

Ekologihchnih aspekti problemi utilihzacihji produktihv ochistki vodojjmishh

Gihmbarzhevs'kijj V., Chorna A.

Zeszyty Naukowe Politechniki Rzeszowskiej. Budownictwo i Inżynieria Środowiska

1998

z. 29 [166], T.1

121-124