Optimization Settings

Applying a LP-optimization model in forest management planning, integer solutions are sometimes of interest. A stand is usually regarded as a treatment unit to be completely treated according to a certain treatment in a certain period. This might be of certain interest when it comes to short term-planning, i.e. what to do now and in the next year - couple of years.

The most straightforward way to obtain integer solutions is to allow only integer values of the decision variable, i.e. constrain the range type of x_{i, j} to "Binary". However, this might lead to infeasible solutions. Another way is to round off to closest integer value (0 or 1), hence forcing the results to be a set of complete treatment programmes for each stand in the analysis area. In menu "Optimization" > "Settings...":

1. The General-tab allows the user to, e.g., selecting "Round to integer solution". Do observe that this is done after solving the optimization problem. Any results shown in the output window will not be rounded off (except the decision variable, with its actual values within parentheses). Results derived from the result database will however be of integer solutions, if this was selected. Optimization results are saved to the database by pressing the "Save"-button in the optimization model builder-window. As an alternative to rounding off, the "Mip Gap" gives an opportunity to accept a solution not certainly optimal. A relative gap of 1% imply that the solution might be one percentage from the optimum. An absolute gap in defined in the same unit as the objective function. The "Time Limit" defines the time, in seconds, for the optimization model to search for a feasible solution.

• • Relative mip gap: Relative optimization tolerance. The optimization algorithm stops when an integer solution is quaranteed to be within this percentage of the true optimal solution.
  • Absolute mip gap: Absolute optimization tolerance (not available in Lp_Solve). The optimization algorithm stops when an integer solution is proven to be within this absolute difference of the optimal solution.
  • Time limit: The maximum time for the solving a problem. If the time limit has been passed but an optimal solutions has not been found, the best solution found is returned. For difficult problems it is possible that no feasible solutions is found.

1. The Lpsolve Settings-tab allows the user to select default settings in presolving.
2. The Cplex Settings-tab allows the user to set and test the validity of the licence file.

• Note

Values, in SEK/ha, can obviously be less than zero (negative) for stands and analysis areas in one or several periods. Make sure that this variable has a "RangeType" set to "All" (and not "Default" that only allows for positive values).