# Statistical Analysis of the Crosswalk Lighting Design Correctness
## 2 State of the Art
### Robust Approach to Roadway Illumination Planning  
For many years, lighting designers were only supported by systems, such as DIALux or AGi32 [8, 9], verifying correctness of the photometric projects. A project was created relying on the expert's intuition which allowed a designer to match a considered lighting situation to one of the existing patterns/templates. In this approach, lamp spacing 27, 28 or 29 m, for instance, is rounded up (intentionally overestimated) to 30 m. That guarantees meeting standard requirements also in the case of factual distances (27, 28, 29 m); nevertheless. the resultant energy efficiency of this project gets worse, i.e., lighting installation power will be overestimated accordingly. Analogously, other parameters are also rounded up in such a \"pessimistic\" manner to satisfy the CEN 13201-2 [2] standard requirements. Lighting engineers can overestimate values of other parameters as well, such as road width, pole setback, etc. Thanks to this, multiple similar lighting situations can be covered in a single project. The serious drawback of this approach, however, is reduced energy efficiency implied by the conservative assumptions on road and lighting installation layout.  
The second simplification made by designers is going a step further, beyond a simple averaging of a scene geometry. Values of particular geometric parameters are grouped to certain \"buckets\" with some tolerance. For example, road width is assumed to be 2 m, 3 m, 4 m, etc. Thus one obtains a set of predefined calculation templates which can be widely applied to multiple lighting situations.  
The third simplification made by designers concerns lighting classes being assigned to particular roads. The classifications should be made according to the standard CEN/TR 13201-1 [1] which specifies criteria of such an assignment: traffic flow intensity, number of road junctions per kilometer, typical road users and others. In spite of that, designers often omit those criteria and use their intuition and expertise which may affect lighting conditions of roads.  
Despite the above simplifications, a typical human-made design process is extremely time-consuming. For example, the retrofit project for 3700 streetlights, made in the city of Cracow, Poland, took seven weeks of a designer's work.  
The crucial factor in a lighting project preparation, especially when preparing offers in a tender for public lighting retrofit, is the computation time required for finding an optimal solution. In most cases, _optimal_ means implying the lowest power usage (future exploitation costs) and investment outlays. The time overhead is related to the huge search space size. Finding optimal solutions in outdoor lighting design has been the subject to intensive research whose results have been published in multiple works. The research was concentrated in the three main areas: graph-based representations of computational problems [19], application of multi-agent systems [20, 21] and distributed processing [22]. In fact, all developed solutions which were successfully applied in real-life large-scale optimization problems have combined the above approaches.  
The projects made by an AI system are made quickly, and they are optimal. A calculation for a large-scale optimization (e.g., Tbilisi, Georgia, for 100,000 or Washington D.C.,  
Figure 3: Calculation grids in pedestrian crossing lighting design: (a) horizontal grid for calculating \(E_{h}\); (b) two orthogonal grids for calculating \(E_{v}\).  
for 54,000 lamps) takes a few hours. Smaller projects take a few minutes. Moreover, resultant installations are not only more effective (from 20% to 30%, in terms of power usage), but also cheaper, what reduces a retrofit cost up to 10%.