Article ID: | iaor20061925 |
Country: | Netherlands |
Volume: | 33 |
Issue: | 1 |
Start Page Number: | 7 |
End Page Number: | 49 |
Publication Date: | Jan 2006 |
Journal: | Computational Optimization and Applications |
Authors: | Murray Walter, Shanbhag Uday V. |
Keywords: | programming: integer, programming: quadratic, energy |
The siting and sizing of electrical substations on a rectangular electrical grid can be formulated as an integer programming problem with a quadratic objective and linear constraints. We propose a novel approach that is based on solving a sequence of local relaxations of the problem for a given number of substations. Two methods are discussed for determining a new location from the solution of the relaxed problem. Each leads to a sequence of strictly improving feasible integer solutions. The number of substations is then modified to seek a further reduction in cost. Lower bounds for the solution are also provided by solving a sequence of mixed-integer linear programs. Results are provided for a variety of uniform and Gaussian load distributions as well as some real examples from an electric utility. The results of GAMS/DICOPT, GAMS/SBB, GAMS/BARON and CPLEX applied to these problems are also reported. Our algorithm shows slow growth in computational effort with the number of integer variables.