Abstract
In this paper we consider a generalization of the One–Dimensional Space Allocation Problem (ODSAP). It is a well–known optimization problem. The classical formulation of the problem is as follows. It is required to place rectangular connected objects (linear segments) on a line with the minimal total cost of connections between them. The generalization of the problem is that there are fixed objects (forbidden zones) on the line and between the objects a partial order of their placement on the line is given. It is impossible to place the objects in the forbidden zones. The area in which the placement is allowed consists of disjoint segments (blocks). Centers of the placed objects are connected among themselves and with centers of the zones. The structure of connections between the objects is defined using a graph. A review of the formulations and methods for solving the classical ODSAP is given. We propose a polynomial–time algorithm for finding a local optimum for a fixed partition of the objects into the blocks when the graph of connections between the objects is a composition of rooted trees and parallel–serial graphs.
G.G. Zabudsky—The work was supported by the program of fundamental scientific research of the SB RAS No. I.5.1., project No. 0314-2019-0019.
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Zabudsky, G.G., Veremchuk, N.S. (2019). On the One–Dimensional Space Allocation Problem with Partial Order and Forbidden Zones. In: Bykadorov, I., Strusevich, V., Tchemisova, T. (eds) Mathematical Optimization Theory and Operations Research. MOTOR 2019. Communications in Computer and Information Science, vol 1090. Springer, Cham. https://doi.org/10.1007/978-3-030-33394-2_11
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