J.F. Benders devised an approach for exploiting the structure of mathematical programming problems with complicating
variables (variables which, when temporarily fixed, render the remaining optimization problem considerably more
tractable).The algorithm he proposed for finding the optimal value of this vector employs a cutting-plane approach for
building up adequate representations of...
The organization of general design problems into programming models allows for the defining and finding of their
(global) optimal solution. MINLP models represent problems as a sets of continuous variables with binary integer
variables. The continuous variables are restricted to defined constraints, and the binary variables represent whether
or not...
The Branch and Bound (BB or B&B) algorithm is first proposed by A. H. Land and A. G. Doig in 1960 for
discrete programming. It is a general algorithm for finding optimal solutions of various optimization problems,
especially in discrete and combinatorial optimization. A branch and bound algorithm consists of...
General disjunctive programming, GDP, is an alternative approach to represent the formulation of traditional
Mixed-Integer Nonlinear Programming, solving discrete/continuous optimization problems. By using algebraic
constraints, disjunctions and logic propositions, Boolean and continuous variables are involved in the GDP
formulation. The formulation process of GDP problem are more intuitive, and the...
The generalized disjunctive programming (GDP) was first introduced by Raman and Grossman (1994). The GDP extends
the use of (linear) disjunctive programming (Balas, 1985) into mixed-integer nonlinear programming (MINLP) problems,
and hence the name. The GDP enables programmers to solve the MINLP/MILP optimization problems by applying a
combination of algebraic...
Mixed-integer linear fractional programming (MILFP) is a category of mixed-integer linear programming (MILP). It is similar to MILP in that it uses the branch and bound
approach. It is widely used in process engineering for optimizing a wide variety of production processes ranging from petroleum refinery to polymerization processses and...
Sigmoid problems are a class of optimization problems with the objective of maximizing the sum of multiple
sigmoid functions. They are defined by their limits at negative and positive infinity. Similar to the unit step
function the function approaches 1 as it approaches infinity and approaches -1 as it approaches...
Branch and cut method is a very successful algorithm for solving a variety of integer programming problems, and
it also can provide a guarantee of optimality. Many problems involve variables which are not continuous but
instead have integer values, and they can be solved by branch-and cut method. This method...
A heuristic algorithm is one that is designed to solve a problem in a faster and more efficient fashion than
traditional methods by sacrificing optimality, accuracy, precision, or completeness for speed. Heuristic algorithms
often times used to solve NP-complete problems, a class of decision problems. In these problems, there is...
Column generation algorithms are used for MILP problems. The formulation was initially proposed by Ford and
Fulkerson in 1958 . The main advantage of column generation is that not all possibilities need to be enumerated.
Instead, the problem is first formulated as a restricted master problem (RMP). This RMP has...