Tag: Operations Research (2): Optimization Algorithms

The objectives for any research is that we want to build a mathematical model to formulate the given problem. The heart of operations research is a mathematical model. That model is going to precisely describe the problem, but the model may be too complicated to get an optimal solution. We need heuristic algorithms, and the model could be…

Non-Linear Programs When visualizing a linear program, its feasible region looks like a polygon. Because the objective function is also linear, the optimal solution is on the boundary or corner of the region. But a non-linear program is quite different, its feasible region may be in any shape, moreover the optimal solution may not exist…

In some cases, variables must take integer values, or binary values. Formulating and solving the models with integer variables is integer programming. There are mainly 2 methods to solve it: The branch-and-bound algorithm finds an optimal solution for an integer program. Essentially, it decomposes the integer program into multiple linear programs, then solves all of…

The simplex method is the most fundamental tool in linear programming, it is a single algorithm that is able to solve any kinds of linear program regardless of its format, number of variables and constraints. We firstly transform the linear program to a standard form, then we focus on the standard form. The idea of…

There are 2 perspectives to look at linear equation systems, row view and column view. Both are equivalent, sometimes row view is more intuitive, sometimes column view is easier to understand. Linear Equations (n = 2) By row Each equation represents a straight line on the x-y plane.The intersection is the only point on both…