Optimal Data-Driven Strategies for Efficient Demining Operations
Alireza Soroudi, PhD
Lead Data Scientist @ bluecrux || SMIEEE || Optimization expert in Supply chain management|| Healthcare management || Lab Digitalization || Power and Energy systems || Developer || Author / Speaker || (views are mine)
Demining involves removing landmines to ensure safety. In military contexts, the goal is to quickly clear paths using devices like mine plows and blast waves. Humanitarian demining aims to completely remove mines for safe land use, employing trained dogs, mechanical devices, and various detection methods.
Time and human resources are limited, so the goal is to identify and prioritize the most efficient areas for rapid search and demining.
Let's skip to the good part !
Consider some points scattered on a surface. Each point has a value (+ or -)Find the coordinates of a rectangle which contains the max sum of the values. This rectangle indicates the search area. The ORtools Package is used for solving this problem.
Data
Positive values indicate a high likelihood of finding mines, while negative values suggest a low chance, meaning searching these areas would likely be a waste of time for the team.
Math Model
The idea is to make sure if a point is inside the rectangle or not (inside the search area)?
For each node iii, we need 4 binary variables to compare its position with the edges of the rectangle, which is determined by two nodes (top right and bottom left). Additionally, an extra binary variable, pi, is required. This variable is defined as the product of the four binary variables.
This multiplication can be also linearized:
Here is the whole python code:
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Results:
no limitation on the dimentions of rectangle:
OF = 26866
The horizontal expantion <= 150
In this case, the search and demining team cannot conduct searches along the horizontal axis for distances exceeding 150 meters due to terrain issues.
We should add this constraint to the model
Xu-Xd <= 150
OF = 14100
The horizontal and vertical expantion <= 150
Xu-Xd <= 150
Yu-Yd <= 150
OF = 8697
The search procedure continues until the whole area is fully discovered.
Some observations:
The code is available on my github , feel free to give it a star
#Demining #DataScience #optimization #EfficientResourceAllocation #RiskAssessment #LandRehabilitation #CommunityResettlement #AI #BigData
More With Less (MWL)
3 个月Alireza, thank you for this interesting problem. I always read your posts with a lot of interest. Thanks a lot. I reimplemented it in my own modeling language LPL and solved it with Gurobi. See https://matmod.ch/lpl/HTML/box.html
Dipl.Math., Data Scientist at Garmin Würzburg GmbH, Germany
3 个月Very interesting problem again; finding the optimal solution without mathematical programming is possible in O(n^4) and I also have an algorithm for the problem that has that complexity. For practical reasons, i.e. for very large problems, there may be the need to reduce the number of candidate rectangles via restricting their north-west and south-east corners to be chosen from a randomly chosen set of points.