About the Computations Results Tab

Algorithms Description

Simulated Annealing (global search):

All constraints are introduced at once in the algorithm. Priorities are handled by assigning weights corresponding to priorities to each constraint. A global function which regroups the objective and the modified constraints constitute the new objective function of the optimization.

Gradient Based Methods (Local search):

All the constraints must be differentiable as well as the objective function. The optimizer takes each constraint modified by its weight into account during the optimization process. The weights impact the search direction of the gradient.
Thus in both cases modifying the weights might lead to different solutions for the same problem definition.

Exploiting Results: Filtering and Handling Weights

Priorities are handled at 2 levels:

Lexicographic order

Priorities are all different
Constraints C1 C2 C3 Index # Class #
Priorities 2 3 1    
Values 10 20 30 1 5
  10 3 2 2 2*
  3 7 9 3 4
  7 3 8 4 1*
  3 6 8 5 3
In the table opposite, to know which row is the best, we first compare the values of c2 (highest Priority: 3). If they are equal, we compare the values of c1 (example of Class # 2* and 1*) and so on in case of equality.

 

Constraints C1 C2 C3 Index # Class #
Priorities 2 1 3   2
Values 10 20 30 1 5
  10 3 2 2 1 (based on c1)
  3 7 9 3 4
  7 3 8 4 3* (based on c1 because c3 values are equal)
  6 3 8 5 2*
In the table opposite, the C1 values must be taken into account because C2 and C1 values are equal.
  • When priorities are all equal, the only equivalence of 2 solutions occurs when all constraint values are equal between the 2 different solutions.
  • Changing priorities changes the ranking of the solutions (Class #)
Some Priorities are equal
Constraints C1 C2 C3 Index # Class #
Priorities 1 2 2    
Values 10 20 30 1 4
  7 2 3 2 1*
  3 7 9 3 3
  7 3 2 4 1*
  3 6 9 5 2
In the table opposite, if you consider only C1 and C2 values,  3 solutions are identical: 5, 4 and 2. Solution 3 is the intermediate solution and 1 is the worst
If you consider, all constraints, you get the following order, going from the best to the worst: 2, 4, 5, 3, 1.

* Both solutions are equivalent: When c2 increases, c3 decreases and conversely. Furthermore c1 is equal in both cases.

All Priorities are equal
Constraints C1 C2 C3 Index # Class #
Priorities 1 1 1    
Values 10 20 30 1 2*
  10 3 2 2 1
  3 7 8 3 1
  7 3 8 4 1
  3 6 9   1
In the table opposite, all solutions are strictly equivalent except 2.

* All values are worse.

Analyzing Results

  • The results of the optimization are displayed in the Computations Results tab of the Optimization dialog box (2).
  • Note that priorities are displayed in this tab and can be changed (1). Modifying a constraint priority in this tab will only impact the Lexicographic sort and not the algorithm.
  • Several constraints can have the same priorities, results can be multiple (i.e. equivalent solutions). Those solutions are presented in decreasing order of significance.
  • The #Class column is the quality of the solution(3). Solutions belonging to the same class are equivalent.
  • Adjust priorities from weights: Allows to sort the constraints in the order dictated by the weights assigned for each constraint in the Constraints tab page.

 

Filtering Results

The results list can be filtered to restrict the number of solutions displayed and to re-order solutions:

Filters can also be applied to constraints values. A combo list enables you to select the desired filter:

All: All solutions will be displayed.

All constraints satisfied only: Only solutions with satisfied constraints will be displayed.

User defined: Only the items you selected will be displayed in the sorted list.

 Selecting a Solution

It is possible to select a solution by clicking the and to apply it to the parameters.