Seminar: Black-Box Challenge Michael Gla Faramarz Khosravi Moritz - PowerPoint PPT Presentation

Seminar: Black-Box Challenge Michael Glaß Faramarz Khosravi Moritz Mühlenthaler Tobias Schwarzer Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Germany 26.10.2015

Outline Black-Box Optimization Algorithms Particle Swarm Optimization Evolutionary Algorithm Differential Evolution Local Search 26.10.2015 | | Friedrich-Alexander-Universität Erlangen-Nürnberg | Black-Box Challenge 2

Black-Box Optimization

Black-Box Optimization Definition (Black-Box Optimization Problem (BBOP)) • domain D • objective function f : D → R • goal ∈ { min , max } Task: Find x ∈ D such that f ( x ) = goal { f ( y ) | y ∈ D} No further assumptions about the problem structure! f ( x ) x ∈ D f : D → R 26.10.2015 | | Friedrich-Alexander-Universität Erlangen-Nürnberg | Black-Box Challenge 4

Algorithms

Particle Swarm Optimization (PSO) Inspiration: cooperative behaviour of animals, “swarm intelligence” 26.10.2015 | | Friedrich-Alexander-Universität Erlangen-Nürnberg | Black-Box Challenge 6

PSO (1) • D ⊆ R n • a swarm of particles cooperatively explores the domain • particle i is. . . • a position x i ∈ R n (candidate solution) • a velocity v i ∈ R n • a local guide ℓ i ∈ D (best solution found by this particle) • global guide g ∈ D : best solution found by the swarm so far 26.10.2015 | | Friedrich-Alexander-Universität Erlangen-Nürnberg | Black-Box Challenge 7

PSO (2) particles move according to equations v i ← ω v i + U [ 0 , c 1 ] ⊙ ( p i − x i ) + U [ 0 , c 2 ] ⊙ ( ℓ i − x i ) (1) x i ← x i + v i (2) x ′ g i g − x i v i x i ℓ i − x i ℓ i 26.10.2015 | | Friedrich-Alexander-Universität Erlangen-Nürnberg | Black-Box Challenge 8

Evolutionary Algorithm (EA) Inspiration: natural selection 26.10.2015 | | Friedrich-Alexander-Universität Erlangen-Nürnberg | Black-Box Challenge 9

The Evolutionary Cycle initialization n o termination? i t c e l e s r o v parent selection i v r u s parent population crossover offspring population mutation mutated offsprings variety of mutation, crossover, and selection methods; may include problem dependent knowledge 26.10.2015 | | Friedrich-Alexander-Universität Erlangen-Nürnberg | Black-Box Challenge 10

Differential Evolution (DE) Inspiration: Evolutionary Algorithms � 26.10.2015 | | Friedrich-Alexander-Universität Erlangen-Nürnberg | Black-Box Challenge 11

DE Algorithm • similar to evolutionary cycle • population of k candidate solutions (individuals), domain R n • create mutant for each individual x i : • pick distinct r 1 , r 2 , r 3 ∈ { 1 , . . . , k } , F u.a.r. ∈ [ 0 , 2 ] , • let the mutant m i := x r 1 + F ( x r 2 − x r 3 ) • crossover : create new solution c i from m i and x i • pick index j and set c j i = m j i • roll the dice for all other entries of c i • selection : replace x i with c i if f ( c i ) < f ( x i ) 26.10.2015 | | Friedrich-Alexander-Universität Erlangen-Nürnberg | Black-Box Challenge 12

Local Search Ridiculously simple, but apparently effective. . . Example: Late-acceptance Hill Climbing Algorithm 1: L ATE A CCEPTANC H ILL C LIMBING input : s ❝✉r : initial solution, ▲ : history size output : s ❜❡st : best solution found so far initialize history: ∀ i ∈ { 0 , . . . , ▲ − 1 } : ❈ [ i ] = f ( s ❝✉r ) while stopping criterion not met do s ♥❡①t ← ♥❡✐❣❤❜♦r✭ s ❝✉r ✮ ❈ next ← f ( s ♥❡①t ) if ❈ next ≤ ❈ [ ✐ mod ▲ ] then s ❝✉r ← s ♥❡①t , update ❈ [ ✐ mod ▲ ] return s ❜❡st 26.10.2015 | | Friedrich-Alexander-Universität Erlangen-Nürnberg | Black-Box Challenge 13

Black Box Challenge Meta-heuristic Optimization for Arbitrary Problems Michael Glaß, Moritz Mühlenthaler, Faramarz Khosravi, Tobias Schwarzer, Rolf Wanka

Organizational Matters ● Credit criteria (5 ECTS): ● Implementation of the algorithm in the Black Box Challenge / O PT 4J environment ● Submission of documented source code at the end of the seminar ● A talk of 45 minutes including 15 minutes for Q&A ● A 4-to-6-page paper documenting your algorithm concepts and implementation ● Talks will be given en bloc at the end of the semester ● Date and time to be decided ● Meetings: ● After 3 weeks: Questions? Problems? ● After 6 weeks: Show committed reference implementation ● Two weeks before the talks: Show committed extensions and variations Black Box Challenge | Introduction | October 2015 3

Contact ● Michael Glaß ● glass@cs.fau.de ● Moritz Mühlenthaler ● moritz.muehlenthaler@cs.fau.de ● Faramarz Khosravi ● faramarz.khosravi@cs.fau.de ● Tobias Schwarzer ● tobias.schwarzer@cs.fau.de ● Rolf Wanka ● rwanka@cs.fau.de Black Box Challenge | Introduction | October 2015 4

Multi-Objective Optimization costs multiple, often conflicting design objectives energy consumption dominance convergence diversity Black Box Challenge | Introduction | October 2015 5

This Semester: Single-Objective Optimization Black Box Challenge | Introduction | October 2015 6

Complex Search Problems Black Box Challenge | Introduction | October 2015 7

Optimization based on Evolutionary Algorithms synthesis evaluation Black Box Challenge | Introduction | October 2015 8

Distinction between Genotype and Phenotype Black Box Challenge | Introduction | October 2015 9

Distinction between Genotype and Phenotype g y p create decode evaluate rng random search solution objective number space space space generator g – genotype p – phenotype y – objectives Black Box Challenge | Introduction | October 2015 10

Choose the Genotype according to your Problem ● For continuous problems Real Genotype ● e.g., (0.3 , 0.44 , 0.7) ● For discrete problems Integer Genotype ● e.g., knapsack problem (27 , 3 , -2 , 8 , 10) Boolean Genotype (1 , 0 , 0 , 1 , 1) ● For sequences Permutation ● e.g., travelling salesman problem Genotype (a < d < c < b) Black Box Challenge | Introduction | October 2015 11

Composite Genotypes for Complex Problems Composite Genotype Composite Boolean Genotype (1 , 0 , 0 , 1 , 1) Genotype Real Genotype Boolean Genotype (0 , 1 , 1 , 1 , 0 , 1 , 1) (0.3 , 0.44 , 0.7) Black Box Challenge | Introduction | October 2015 12

Eclipse Project ● MOEAD07.java Implementation of the optimizer ● ● MOEAD07Module.java Configuration ● ● See Opt4J tutorial ● bhc.jar ● The jar file to submit ● blackholecompetition.launch ● Eclipse run configuration ● export.jardesc ● Creates the jar file ● Moead07.xml ● Configuration for MOEAD and WFG problem ● Submit optimizer-specific part Black Box Challenge | Introduction | October 2015 13

Accessing SVN code repository ● Generate SSH key: ssh-keygen ● 2 files in /home/YOU/.ssh id_rsa id_rsa.pub <- public key ● Send public key to ● faramarz.khosravi@cs.fau.de ● tobias.schwarzer@cs.fau.de Black Box Challenge | Introduction | October 2015 14

Optimizer Submission ● Web-based submission system ● Comparison of your optimizer to other optimizers (Opt4J implementations) ● A number of benchmarks already available ● Daily update of results ● Task 1: ● Submit exact implementation of previous work ● Task 2: ● Try to enhance previous work to achieve better results Black Box Challenge | Introduction | October 2015 15

Topics ● Online Black-Box Algorithm Portfolios for Continuous Optimization ● P. Baudiš and P. Pošík 2014 [doi>10.1007/978-3-319-10762-2_4] ● It’s Fate: A Self -organising Evolutionary Algorithm ● J. Bim et al. 2012 [doi>10.1007/978-3-642-32964-7_19] ● A Local Genetic Algorithm for Binary-Coded Problems ● T. Runarsson et al. 2006 [doi>10.1007/11844297_20] ● A Compass to Guide Genetic Algorithms ● G. Rudolph 2008 [doi>10.1007/978-3-540-87700-4_26] ● Threshold accepting: A general purpose optimization algorithm appearing superior to simulated annealing ● G. Dueck and T. Scheuer 1990 [doi>10.1016/0021-9991(90)90201-B] Black Box Challenge | Introduction | October 2015 16