Real-world problems may require large-scale systems with particular features.
Thus, water resource systems (WRS) can be described by large-size multi-objective
optimization systems. The main characteristics of such systems are notably their large
scale with mixed-integer decision variables and the multiplicity of objectives. Adapted
methods for solving such systems are required. The generalized Benders decomposition
and branch-and-bound techniques are such efficient methods. Suppose a MOO problem
for which we can have an equivalent parametric pMINLP. A decomposition-based
algorithm describes an iterative process where subproblems interact with a master
problem. Suppose a SOO programming problem. Using a GBD algorithm will generate
an upper bound and a lower bound of the solution at each iteration step. A primal NLP
subproblem provides information about the upper bounds and Lagrange multipliers. Next,
the master ILP problem calculates the new set of lower bounds. In this study, the Benders
decomposition method is used for solving single objective and multi-objective MINLP
problems.
Keywords: Benders decomposition, Branch-and-bound, Cutting-plane method,
Discrete variable, GBD algorithm, Duality theory, Generalized cross decomposition,
Inner approximation, Integrality constraint, Lagrangian relaxation, Lagrange
decomposition, Lagrange multipliers, Master problem, MINLP problem, Mixed-
Integer linear programming, NLP problem, Outer approximation, Parametric
MINLP, Primal problem, Separable function.
