1. Area Coverage Problem Optimization by (local) Search
By Shachar Mossek
Artificial Intelligence Project Presentation

2. Optimization by (local) Search
Area Coverage Problem
Optimization by (local) Search
Definitions
Given an area with obstacles and set of cameras what is the best coverage?
Area – Space of interest
Obstacles – Static, non-movable view obstructing objects
Camera – Means to uncover the area
Coverage – Positioning of cameras in an area with obstacles

3. Optimization by (local) Search
Area Coverage Problem
Optimization by (local) Search
Is it even interesting?
Coverage vs best coverage?
Cost factors
Resources
Redundancies
Optimization
Real world problems

4. Optimization by (local) Search
Area Coverage Problem
Optimization by (local) Search
Objectives
Complete Coverage (max)
Least cost (min)
More Redundancies (max)
Asymmetry - solving all at one
Order of importance

5. Optimization by (local) Search
Area Coverage Problem
Optimization by (local) Search
Relaxations
Discrete 2D reduced Area
Cell can be either free, camera or obstacle
No resource restrictions
Camera FOV and angle are constant

6. Objectives refinement
Area Coverage Problem
Optimization by (local) Search
Objectives refinement
Visibility testing in 2D space
Coverage is number of cells covered by at least one camera
Cost is sum of placed cameras
Redundancies is number of cells covered more than once

7. Optimization by (local) Search
Area Coverage Problem
Optimization by (local) Search
Approaches
Complexity
Convergence
State of the Art – CSP, LP, Logic and More
Local search – Simple, naïve and fast
This project

8. Optimization by (local) Search
Area Coverage Problem
Optimization by (local) Search
Local Search
Implemented algorithms
Basic: BFS, DFS, A*
Hill Climbing: Deterministic, Stochastic, First Choice, Random Restart
Simulated Annealing
Local beam: Regular and Stochastic
Genetic
Particle Swarm
Project research objectives
Theory to practice
Effectiveness
Dominance

9. Optimization by (local) Search
Area Coverage Problem
Optimization by (local) Search
Software Suite
Graphical User Application
Plan mode
Play mode: Manual and Algorithm
Compare Application
Main research tool
Overnight runs
Output: Log and incremental results
Single area/algorithm vs Multiple algorithms and areas

10. Optimization by (local) Search
Area Coverage Problem
Optimization by (local) Search

11. Optimization by (local) Search
Area Coverage Problem
Optimization by (local) Search
Results and Analysis
Focusing on three test areas
Many runs on different computers and configurations
Results are of a single run
Analysis is based on combining all runs and extracting each algorithm best, median and worst solutions

12. Optimization by (local) Search
Area Coverage Problem
Optimization by (local) Search
Results and Analysis
Corridor area
Considered as a “few obstacles” area
Approximation is known
Single run results
Run time: 1.5 hours
Winner: Random restart
Coverage: 2.04 seconds
Cost: 3 minutes
Redundancies: 38 minutes
Cumulative analysis
Random Restart by knockout
Varies on redundancies

13. Optimization by (local) Search
Area Coverage Problem
Optimization by (local) Search
Results and Analysis
Office area
Considered as “many obstacles” area
Simulates well a real world structure
Single run results
Run time: 1.5 hours
Winner: Stochastic best Hill Climbing
Coverage: 9.12 seconds
Cost and Redundancies: 17 minutes
Cumulative analysis
Stochastic Hill Climbing is best
Hill Climbing “family” work well

14. Optimization by (local) Search
Area Coverage Problem
Optimization by (local) Search
Results and Analysis
Clear area
No obstacles area
Larger space than other areas (20x20 vs. 10x10)
Optimum is known
Single run results
Run time: 2 hours
Winner: Hill Climbing
All objectives: 14 seconds
Falling far behind: Every one else
Cumulative analysis
Hill Climbing by a mile
Results vary on time (deterministic)
Random Restart and Stochastic Hill Climbing achieve optimal on few runs while other algorithms don’t come close

15. Optimization by (local) Search
Area Coverage Problem
Optimization by (local) Search
Analysis

16. Optimization by (local) Search
Area Coverage Problem
Optimization by (local) Search
Analysis

17. Optimization by (local) Search
Area Coverage Problem
Optimization by (local) Search
Analysis

18. Optimization by (local) Search
Area Coverage Problem
Optimization by (local) Search
Conclusions
The problem mostly non-intuitive
Try solving by yourselves
Hard enough with the relaxations
Random Restart Hill Climbing, Stochastic Hill Climbing and Hill Climbing itself are the clear choice. Also, all reach good approximation/results in a small amount of time, even intermediate “fast” results can be good enough for a consumer
Advanced algorithms fail due to their complexity and time restriction – ultimately explore less of the space than the algorithms above
Stochastic algorithms are less effective on a more “open” area due to the size of the solutions space and impossibility of same path avoidance (hardware limitations)
Genetic and Particle Swarm should be refined to achieve better results

19. Optimization by (local) Search
Area Coverage Problem
Optimization by (local) Search
Future Work (I)
Refinement of Genetic and Particle Swarm algorithms
Adding thresholds – When solution is "good enough“
Different camera types, costs, ranges, angles and sectors
Modifying and Testing in 3D continuous space
Divide and conquer by Applying computer vision/graph/link analysis
Adding priority areas and minimum required redundancies per cell

20. Optimization by (local) Search
Area Coverage Problem
Optimization by (local) Search
Future Work (II)
Tradeoff between cost and redundancies
Applying state of the art techniques and preform local search on their solutions
Pruning of the successors tree by heuristic (reduction of solution space states)
Reverse analysis – What cover each cell and search only on complete solutions, i.e. states with best coverage parameter at minimum
Compression and marking of explored solutions to allow implementation of same path avoidance
Information sharing between concurrently running algorithms, e.g. each algorithm can be a particle in a swarm like approach