The purpose of the application is to provide convenient tools for creating and solving models of objects for linear optimization.
Linear optimization, also called linear programming (LP), is a method to achieve the best outcome (such as maximum( minimum) profit or lowest cost) in a mathematical model whose requirements and objective are represented by linear relationships. Linear programming is a special case of mathematical programming (also known as mathematical optimization).
Linear programs( models in sense of this app) are problems that can be expressed in standard formas(Wikipedia):- find vector x; - that maximizes(minimizes) Z = cx; - subject to Ax<=b – in maximizes( Ax>=b – in minimizes );- and x>=0.
Find a vectorxthat maximizescTxsubject toAx≤bandx≥0.
Here the components of x
x
are the variables to be determined, c and b are given vectors, and A is a given matrix.
From the initial activity of the application – App Linear Optimization, the functions for creating, editing, solving and deleting models are included. The models are stored in SQLite data base with name linearProgramming.db. The application has functions for storing and restoring the database in the directory Download of the device.
When creating an optimization model, two parameters are entered(Linear Model activity) - the number of vector x variables and the number of constraints (this does not include the constraints for variables) – i.e. the rows of the matrix A . After entering these data and pressing the button – Linear Model, you proceed to enter the model data – from activity Linear Model Creation.
The vector x coefficients c are entered in the line with a label Z= in front of the labels *Xi+.
The elements of the matrix А are entered in the table named Constraints in front of the fields label *Xi+. In the last field of each row of the matrix after the label <= , the bounds b of the constraints is also entered. After entering these data and pressing the OK button, it returns to the activity - Linear Model activity , where a mandatory field for the model name and a button for saving appears.
When a model is saved, its name appears in the list of models displayed in the initial activity of the application. Selected model from the list can be edited( button Edit) or solved(button Calculate). After editing and saving, the edited version is stored as a new model, and the old one remains unchanged in the database. This is so that both models can be solved and the results can be compared. If some of them are not needed, it can be deleted.
When solving a model, the result shows the maximization and minimization of the target function Z and at what values of the elements of the vector x at which this occurs and also constraints.
Industries that use linear programming models include transportation, energy, telecommunications, and manufacturing. It has proven useful in modeling diverse types of problems in planning, routing, scheduling, assignment, and design.
The application uses for optimization class SimplexSolver from the standard library org.apache.commons:commons-math:3.6.1.
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