Constraint Satisfaction: Methodology

When working with constraint satisfactions, you can apply constraints with values of the same order of magnitude as the objective function. It prevents a constraint from being over-considered by the optimization process.

This page discusses:

About the Use of Precision and Solution Distance in Constraint Satisfactions

This section gives you more information about the use of precision and solution in constraint satisfactions.

The solution distance option used in constraint satisfaction results takes its meaning if and only if at least 2 solutions are sought. This option ensures that the distance (Maxi (xi-yi)) between the two solutions is not less than the value specified by the option. In the case of more than two solutions, the distance considered is the distance between the current solution and all previously found solutions. The distance between two solutions you want to compare is the MAX of the absolute value of the difference between the parameters computed by the Constraint Satisfaction.max (|x1-x2|, |y1-y2|, |fxy1-fxy2|)

Note: To have meaningful results regarding solution distances, it is recommended that you formulate the problem you want to solve using parameters having same dimensions. The solution distance must be formulated in MKS unit for this dimension.

Example of solution distance impact on the results:

Problem setup

Formula.1: fxy = x*x + y*y

CST.1: 

fxy == 25;
x > -100; x < 100;
y > -100; y < 100

First trial for options

This section gives you more information about the first trial for options.

Results options: Number of solutions: 100, distance between solutions: 0.02.

Options: Precision: 0.001

Solutions found: around 50000 (due to precision) among which 100 satisfy the distance specified.

Second trial for options

This section gives you more information about the second trial for options.

If the precision and the distance between solutions are increased, the span of the solutions increases (due to a larger distance between solutions) and the computation time decreases (due to less precision).

Results options: Number of solutions: 100, distance between solutions: 0.15.

Options: Precision: 0.1

Solutions found: Around 1700 (due to precision) among which 100 satisfy the distance specified.