Models and methods for One-Dimensional Space Allocation Problem with forbidden zones

Abstract

We consider an extension of the well–known optimization placement problem. The problem is One–Dimensional Space Allocation Problem (ODSAP). The classical formulation of the problem is to place rectangular connected objects on a line with the minimum total cost of connections between them. The extension of the problem is that there are fixed objects (forbidden zones) on the line. The objects are impossible to place in forbidden zones. The placed objects are connected among themselves and with the zones. The configuration of connections between objects is defined by a network. A similar situation arises, for example, when designing the location of technological equipment of petrochemical enterprise. It is necessary to place units of equipment so that the total cost of the pipeline ties was minimal. In this article a review of the models and methods to solve of the classical ODSAP is given. The properties of the problem with the forbidden zones are noted. Models of combinatorial optimization and integer programming for the problem are constructed. Algorithms for finding an approximate solution and branch and bounds are described. Results of computational experiments are reported.