On the efficiency of bionic optimisation procedures

Transcription

1 Gekeler, S.,, R., Widmann, C. Reutlingen Research Institute,, Germany Content 1. Motivation 2. Bionic Optimisation 3. Efficiency of Optimisation Strategies 4. Test Examples 5. Conclusions Title Sheet 1

2 1. Motivation : - 10 years of bionic optimisation research - projects with industry and federal support - earthquakes, brake squeal, casting - lot of experience - never enough computing power Consequences: - compare different approaches - find rules of applicability - propose efficient strategy - reduce computing requirements Motivation Sheet 2

3 1. Motivation Optimisation: Definitions goal z free parameters p 1, p 2,... p n boundary conditions constraints a priory defined (no politics) all you may modify limits to parameters relations between parameters maximum = minimum of z(p 1, p 2,... p n ) goal parameters boundary conditions constraint mass, prize, number thickness, radii, length, material, handling non-negative, deliverable, max cost fits, slender, stability, feasibility Motivation Sheet 3

4 1. Motivation Optimisation: Definitions Many local optima: Difficult to jump from hill to hill => Gradient approaches not suitable Curse of dimension High # of dims=> small probability to find optimum But small driving gradient as well Many trials required: darts with closed eyes Motivation Sheet 4

5 2. Bionic Optimisation Bionic engineering: - all the ideas to learn from natural processes - ISBE founded in 2010 in China - many national branches, BIOKON in Germany Bionic Optimisation: We look at - optimisation is a natural process - evolution: adapt better to environment => EVOOPT - populations interact to succeed => PSO - brains are learning => ANN - individuals search safe spots => RS - evolutionary optimisation (including ferns) - particle swarm optimisation - gradient and response surfaces - neural nets Bionic Optimisation Sheet 5

6 2. Bionic Optimisation Evolutionary optimisation basic idea: 1. Select initial parents (µ) 2. Produce λ kids (cross over, mutation) 3. Select the best: new parents 4. New cycle Example: 2 parent 4 kids Bionic Optimisation Sheet 6

7 2. Bionic Optimisation Evolutionary optimisation Typical result: The objective of the parents tends after some generations to an optimum. If we are lucky, it is the absolute optimum goal of 3 best + worst parent 4.4 x 106 goal vs. generation generation Bionic Optimisation Sheet 7

8 2. Bionic Optimisation Ferns: no crossing, only mutation, spores basic idea: 1. Select initial parents (µ) 2. Produce λ kids by mutation 3. Select the best: new parents 4. New cycle Example: 1 parent 4 kids Bionic Optimisation Sheet 8

9 2. Bionic Optimisation Ferns Accelerate fern optimisation: Remove slow tribes from process Process faster goal But: good approaches removed? Individuals offspring goals during a study best after slow start removed, too slow removed, too slow best fast enough generation Bionic Optimisation Sheet 9

10 2. Bionic Optimisation Particle Swarm Optimisation PSO swarms best position of some individuals goal individuals best new velocity social cognitive inertia v = c v + c r d + c new v old cog cog cog soc r soc d soc Bionic Optimisation Sheet 10

11 2. Bionic Optimisation Particle Swarm Optimisation 1.3 x 105 goal of parts After some generations, 1.2 swarms tend to converge to a local optimum 1.1 goals generation Bionic Optimisation Sheet 11

12 2. Bionic Optimisation Particle Swarm Optimisation Weighting factorsnot appropriate => Sticking to local optimum, Not finding global optimum v = c v + c r d + c new v old cog cog cog soc r soc d soc Bionic Optimisation Limit velocity => stable but slow Sheet 12

13 3. Efficiency of Optimisation Strategies Optimisation: Time + CPU consuming. Tends to fail. Sticks to local optima. => Measure efficiency and reliability. Possible measures: Time to find best solution? => when starting, when accepting a solution? Total computing power? => which computer, how many processors +++? # of individuals to best? => pre-testing included, parameters fixed? Efficiency of Optimisation Strategies Sheet 13

14 3. Efficiency of Optimisation Strategies Real optimisation: Large numbers Task needs optimisation. Gradient approaches fail. Are initial designs good? Is there enough time for a bionic optimisation? # of free params * number of reruns FE-jobs is not very much Curse of dimension Good solutions: Hidden needles in param spaces Efficiency of Optimisation Strategies Sheet 14

15 4. Test Examples Simple frames with increasing # of rods F1 F2 F3 F= 5kN F free params F= 1kN F= 100 kip F= kn Free params: 58 Optimisation: Minimize mass of rods Constraints on - stress and - displacement F5 F= 1kN Free params: 193 F= 1kN Test Examples Sheet 15

16 4. Test Examples For smaller # of params: - no significant difference Number of runs to best For larger # of params: fern slow, not reliable - PSO,EVO comparable But: - params after many prejobs - total time essentially larger - experience governs success of optimisation - good initial designs: main acceleration component # of individuals to best ES Fern PSO # of free parameters Test Examples Sheet 16

17 4. Test Example Impact of initial design 4.4 x 106 goal vs. generation goal of 3 best + worst parent Good initial designs Fast to goal random initial designs save unnecessary variants Save 50% of job! good initial design generation Test Examples Sheet 17

18 5. Conclusions From a long series of studies we may conclude: - Optimisation is a time and power consuming process. - Bionic approaches preferable if many local optima. - Much experience needed to fix parameters. - Total optimisation time essentially longer than final optimisation. - Switch to gradient / Response Surface if close to optimum? - Good initial designs are most important. Conclusions Sheet 18