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...
Lagrangian duality theory refers to a way to find a bound or solve an optimization problem (the primal problem) by
looking at a different optimization problem (the dual problem). More specifically, the solution to the dual problem
can provide a bound to the primal problem or the same optimal solution...
A disjunctive inequality is a type of constraint that exists in mixed integer linear programming (MILP) and mixed
integer nonlinear programming (MINLP) problems. It involves constraining a solution space with multiple
inequalities or sets of inequalities related by an OR statement. This "OR" statement must then be reformulated
using one...
Mixed-integer cuts or Cutting-plane methods is an iterative approach used to simplify the solution of a mixed
integer linear programming (MILP) problem. Cutting-plane methods work by first relaxing the MILP to a
complementary linear programming problem and cutting the feasible region to narrow down the solution search
space to only...
The traveling salesman problem (TSP) is a widely studied combinatorial optimization problem, which, given a set of cities and a cost to travel from one city to another, seeks to identify the tour that will allow a salesman to visit each city only once, starting and ending in the same...
Facility location problems deal with selecting the placement of a facility (often from a list of integer possibilities)
to best meet the demanded constraints. The problem often consists of selecting a factory location that minimizes
total weighted distances from suppliers and customers, where weights are representative of the difficulty of...
Optimization with absolute values is a special case of linear programming in which a problem made nonlinear due
to the presence of absolute values is solved using linear programming methods.
Absolute value functions themselves are very difficult to perform standard optimization procedures on. They are
not continuously differentiable functions, are...
Interior point methods are a type of algorithm that are used in
solving both linear and nonlinear convex optimization
problems that contain inequalities as constraints. The LP
Interior-Point method relies on having a linear programming
model with the objective function and all constraints being
continuous and twice continuously differentiable. In...