MOLA

I. Map the cells in the decision space

The Multi-Objective Land Allocation (MOLA) procedure was introduced by (1993). MOLA is a hierarchical extension of the multi-criteria evaluation process: A set of suitability maps, each derived as a single objective multi-criteria evaluation, serve as factors for a new evaluation in which the objectives are themselves weighted and combined. For reasons of simplicity we start with the normalized maps showing "suitability for sheep pasture" and "suitability for wolf habitat". Our task is now to balance the needs of the different objectives.

The map panel (left) shows the 64 km² available land of St. Gittal in a raster model, each cell representing 1 km². Blue colour tones represent the suitability "wolf habitat", green tones indicate the suitability "sheep meadow". In the decision panel (right) the suitability for a purpose may be thought of as an axis of a two-dimensional diagram, the decision space. Every raster cell in the map panel can be located within the decision space according to its suitability level according to each of the two objectives. You can verify this by clicking on the raster cells and checking their corresponding position in the decision space, and vice versa. Note that the location of a point in the decision space is solely dependent on the two suitabilities of its correspondent raster cell.

II. First allocation

Finding the best 20 km² of land for "wolf habitat" you simply move a perpendicular decision line down from the position of maximum suitability until enough cells are captured to fulfil the areal goal. Use the +/- arrows until the counter shows the required number of cells. Holding the shift key, increases the step size. Finding the best 16 km² of land for "sheep pasture" you proceed in an equal way with a decision line perpendicular to the second axis. Doing so, you divided the decision space in four rectangular sub-areas holding pixels…

• not suitable at all,
• suitable for wolf, but not suited for sheep (blue cells, respectively blue points in decision space)
• suitable for sheep, but not suited for wolf (green cells, respectively green points in decision space), and
• suitable for wolf and suitable for sheep, i.e. conflicting cells (red cells, respectively red points in decision space).

III. Iterative resolution of conflicts

The red cells lying in the top right area are judged suitable for both purposes. To resolve these conflicts, a simple partitioning of the affected cells is used. For every cell we check for which use it is more suited, i.e. which suitability measure is higher and assign it to this land use. Click "solve conflicts" to show the red dividing line. Having divided the conflict cells between the two objectives, it is clear that both will be short on meeting their area goals, the counters decreased. As a result, the decision lines have to be lowered for both objectives to gain more territory. This process of resolving conflicts and lowering decision lines is repeated until the exact area targets are achieved.

IV. Weighting the objectives

Another useful feature of the MOLA approach is that unequal weighting of the two objectives is possible and very intuitive. If two objectives are equally weighted, the red dividing line has a gradient of 45°. For an unequal weighting we can simply change the gradient of the dividing line, such that the angle’s tangent represents the ratio of the new unequal weights. Use the blue arrow to increase the weight of the purpose "wolf habitat", use the green arrow to increase the weight of the purpose "sheep" pasture. Again the shift key lets you increase the step size. Move the dividing line and note the change of the allocation in decision and real space.

What makes this procedure a heuristic? (Click here for more information)