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Optimisation
Published on Feb 25, 20074735 Views
It has been a century and a half since Darwin provided the first mechanistic explanation for the complexity of the living things we see around us. Only in the last 30 years or so have computational sy
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Chapter list
Optimisation00:01
Outline01:20
Evolution and Optimisation01:56
Unintended Consequences03:29
Optimisation05:32
Combinatorial Optimisation Problems08:56
Outline10:18
Travelling Salesperson Problem10:34
Example of Distance Table11:01
Example Tour11:13
Brute Force11:28
How Many Possible Tours Are There?12:24
Counting Tours12:53
Counting Tours12:59
Counting Tours13:13
Counting Tours13:20
How Long Does It Take?13:29
How Big is 99 Factorial?14:02
How Long Does It Take?14:45
Answer15:48
Record TSP Solved—15 112 and 24 978 Cities16:14
Can We Parallelise the Search17:18
Variety of Life18:47
Outline20:36
The Nature of Optimisation Problems20:46
Continuous Search Spaces22:10
Discrete Search Spaces24:23
Shortest Path: Dijkstra’s Algorithm24:45
Polynomial Time Algorithms25:56
NP-Hard Problems26:27
Decision Problems28:33
Class NP30:10
Class NP-complete31:32
Other Examples of NP-complete38:21
Structure of Decision Problems39:04
NP-Hard40:42
Not All Hard Problems are NP-Hard42:04
Not All NP-Hard Problems are Hard43:35
Outline46:48
Heuristic Methods46:54
Heuristics47:59
General Purpose Heuristic Algorithms49:21
Hill-Climbing 50:28
Why is Optimisation Hard?51:19
Local Optima52:55
Multi-Start Hill-Climbers53:52
Simulated Annealing55:10
Stochastic Descent55:40
Simulated Annealing56:22
Cooling Schedule56:54
Convergence Theorem57:34
Conclusions59:30