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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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