Decomposition methods for solving discrete-continuous facility location models with nonlinear objective cost functions
Two classes of nonlinear facility location problems are formulated as nonlinear mixed-integer programming problems. These problems are characterized by the discrete-continuous structure in the objective function and constraint sets which are modeled in many large-scale optimization systems. This work focuses on the understanding and application of decomposition solution procedures to optimize these mixed-integer models that arise in facility location optimizing systems. For solving these two location models, Lagrangean methods (relaxation and decomposition) are used to decompose the primal problem, such as for a separable objective function with a linear integer part and a continuous nonlinear part and for a partitioning of constraint sets in which the integer variables are decoupled from the nonlinear part of the programming problem. Aggregation and non-aggregation approaches in Lagrangean decomposition are suggested in the study, and the number of multiplier variables relative to the dualized constraints are significantly reduced to a manageable size which may lead to some flexibility and potential application in Lagrangean decomposition for other applications. By applying both convergence decomposition methods, such as the generalized Benders' decomposition and the generalized cross decomposition, the problem decomposes into a continuous quadratic programming problem and a linear mixed-integer master programming problem. The other convergent decomposition method known as the generalized cross algorithm combined the advantage of feasible solution in generalized Benders' subproblem and the special structured Lagrangean subproblems. The results indicate that when exact convergent solution is required, this method proves to be a competitive solution technique for this class of nonlinear mixed-integer programming problems.
Mak, Yiu Tsan, "Decomposition methods for solving discrete-continuous facility location models with nonlinear objective cost functions" (1993). Dissertations available from ProQuest. AAI9331869.