Aging Beyond Restarts Thomas Jansen University College Cork joint - - PowerPoint PPT Presentation

▶
aging beyond restarts
SMART_READER_LITE
LIVE PREVIEW

Aging Beyond Restarts Thomas Jansen University College Cork joint - - PowerPoint PPT Presentation

Mar 25, 2023 133 likes •1.23k views

Introduction Aging Beyond Restarts: Ideas Results Conclusions Aging Beyond Restarts Thomas Jansen University College Cork joint work with Christine Zarges Technische Universitt Dortmund J./Zarges: Aging beyond restarts. In GECCO 2010.

slide-1
SLIDE 1

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Aging Beyond Restarts

Thomas Jansen

University College Cork joint work with

Christine Zarges

Technische Universität Dortmund

J./Zarges: Aging beyond restarts. In GECCO 2010.

slide-2
SLIDE 2

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Aging Beyond Restarts

Thomas Jansen

University College Cork joint work with

Christine Zarges

Technische Universität Dortmund

J./Zarges: Aging beyond restarts. In GECCO 2010.

A Talk on Artificial Immune Systems, actually

1/13

slide-3
SLIDE 3

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Artificial Immune Systems

2/13

slide-4
SLIDE 4

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Artificial Immune Systems

  • (yet another) nature-inspired randomized search heuristic

2/13

slide-5
SLIDE 5

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Artificial Immune Systems

  • (yet another) nature-inspired randomized search heuristic
  • different from evolutionary algorithms

2/13

slide-6
SLIDE 6

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Artificial Immune Systems

  • (yet another) nature-inspired randomized search heuristic
  • different from evolutionary algorithms, ant-colony
  • ptimization

2/13

slide-7
SLIDE 7

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Artificial Immune Systems

  • (yet another) nature-inspired randomized search heuristic
  • different from evolutionary algorithms, ant-colony
  • ptimization, . . .

2/13

slide-8
SLIDE 8

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Artificial Immune Systems

  • (yet another) nature-inspired randomized search heuristic
  • different from evolutionary algorithms, ant-colony
  • ptimization, . . .
  • based on the immune-system of vertebrates (and various

theories about it)

2/13

slide-9
SLIDE 9

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Artificial Immune Systems

  • (yet another) nature-inspired randomized search heuristic
  • different from evolutionary algorithms, ant-colony
  • ptimization, . . .
  • based on the immune-system of vertebrates (and various

theories about it)

  • different aspects: clonal selection, specific mutations

(contiguous hypermutations, inverse fitness-proportional mutation, . . . ), aging, . . .

2/13

slide-10
SLIDE 10

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Artificial Immune Systems

  • (yet another) nature-inspired randomized search heuristic
  • different from evolutionary algorithms, ant-colony
  • ptimization, . . .
  • based on the immune-system of vertebrates (and various

theories about it)

  • different aspects: clonal selection, specific mutations

(contiguous hypermutations, inverse fitness-proportional mutation, . . . ), aging, . . .

  • a randomized search heuristic

2/13

slide-11
SLIDE 11

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Artificial Immune Systems

  • (yet another) nature-inspired randomized search heuristic
  • different from evolutionary algorithms, ant-colony
  • ptimization, . . .
  • based on the immune-system of vertebrates (and various

theories about it)

  • different aspects: clonal selection, specific mutations

(contiguous hypermutations, inverse fitness-proportional mutation, . . . ), aging, . . .

  • a randomized search heuristic

Overview

1 Introduction to Aging: known results and open problems 2 Aging beyond restarts: main ideas 3 Aging beyond restarts: results 4 Aging beyond restarts: open problems

2/13

slide-12
SLIDE 12

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Aging

3/13

slide-13
SLIDE 13

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Aging

  • Main Idea
  • equip each search point with an individual age

3/13

slide-14
SLIDE 14

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Aging

  • Main Idea
  • equip each search point with an individual age
  • each search point’s age increases in each round of the RSH

3/13

slide-15
SLIDE 15

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Aging

  • Main Idea
  • equip each search point with an individual age
  • each search point’s age increases in each round of the RSH
  • too old search points are removed

3/13

slide-16
SLIDE 16

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Aging

  • Main Idea
  • equip each search point with an individual age
  • each search point’s age increases in each round of the RSH
  • too old search points are removed
  • simple implementations
  • fixed maximal lifespan τ

3/13

slide-17
SLIDE 17

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Aging

  • Main Idea
  • equip each search point with an individual age
  • each search point’s age increases in each round of the RSH
  • too old search points are removed
  • simple implementations
  • fixed maximal lifespan τ
  • evolutionary aging each new search point gets age 0

3/13

slide-18
SLIDE 18

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Aging

  • Main Idea
  • equip each search point with an individual age
  • each search point’s age increases in each round of the RSH
  • too old search points are removed
  • simple implementations
  • fixed maximal lifespan τ
  • evolutionary aging each new search point gets age 0

(extremes: plus-selection (τ = ∞), comma-selection (τ = 0))

3/13

slide-19
SLIDE 19

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Aging

  • Main Idea
  • equip each search point with an individual age
  • each search point’s age increases in each round of the RSH
  • too old search points are removed
  • simple implementations
  • fixed maximal lifespan τ
  • evolutionary aging each new search point gets age 0

(extremes: plus-selection (τ = ∞), comma-selection (τ = 0))

  • static pure aging each new search point gets age 0

if it is an improvement, otherwise it inherits its age

3/13

slide-20
SLIDE 20

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Aging

  • Main Idea
  • equip each search point with an individual age
  • each search point’s age increases in each round of the RSH
  • too old search points are removed
  • simple implementations
  • fixed maximal lifespan τ
  • evolutionary aging each new search point gets age 0

(extremes: plus-selection (τ = ∞), comma-selection (τ = 0))

  • static pure aging each new search point gets age 0

if it is an improvement, otherwise it inherits its age

  • motivation
  • increase diversity
  • cope with more difficult (multi-modal?) problems

3/13

slide-21
SLIDE 21

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Known Results

4/13

slide-22
SLIDE 22

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Known Results

  • on the maximal lifespan τ

(Horoba/J./Zarges (GECCO 2009)) 4/13

slide-23
SLIDE 23

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Known Results

  • on the maximal lifespan τ

(Horoba/J./Zarges (GECCO 2009))

  • if τ is too large, static pure aging is ineffective

4/13

slide-24
SLIDE 24

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Known Results

  • on the maximal lifespan τ

(Horoba/J./Zarges (GECCO 2009))

  • if τ is too large, static pure aging is ineffective
  • if τ is too small, the RSH becomes unsuccessful

4/13

slide-25
SLIDE 25

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Known Results

  • on the maximal lifespan τ

(Horoba/J./Zarges (GECCO 2009))

  • if τ is too large, static pure aging is ineffective
  • if τ is too small, the RSH becomes unsuccessful
  • the ‘correct’ lifespan depends on the optimization problem

4/13

slide-26
SLIDE 26

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Known Results

  • on the maximal lifespan τ

(Horoba/J./Zarges (GECCO 2009))

  • if τ is too large, static pure aging is ineffective
  • if τ is too small, the RSH becomes unsuccessful
  • the ‘correct’ lifespan depends on the optimization problem
  • the range of ‘correct’ lifespans can be extremely small

4/13

slide-27
SLIDE 27

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Known Results

  • on the maximal lifespan τ

(Horoba/J./Zarges (GECCO 2009))

  • if τ is too large, static pure aging is ineffective
  • if τ is too small, the RSH becomes unsuccessful
  • the ‘correct’ lifespan depends on the optimization problem
  • the range of ‘correct’ lifespans can be extremely small
  • on different aging strategies (J./Zarges (ICARIS 2009, TCS))

4/13

slide-28
SLIDE 28

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Known Results

  • on the maximal lifespan τ

(Horoba/J./Zarges (GECCO 2009))

  • if τ is too large, static pure aging is ineffective
  • if τ is too small, the RSH becomes unsuccessful
  • the ‘correct’ lifespan depends on the optimization problem
  • the range of ‘correct’ lifespans can be extremely small
  • on different aging strategies (J./Zarges (ICARIS 2009, TCS))
  • static pure aging more effective than evolutionary aging in

escaping local optima

4/13

slide-29
SLIDE 29

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Known Results

  • on the maximal lifespan τ

(Horoba/J./Zarges (GECCO 2009))

  • if τ is too large, static pure aging is ineffective
  • if τ is too small, the RSH becomes unsuccessful
  • the ‘correct’ lifespan depends on the optimization problem
  • the range of ‘correct’ lifespans can be extremely small
  • on different aging strategies (J./Zarges (ICARIS 2009, TCS))
  • static pure aging more effective than evolutionary aging in

escaping local optima

  • evolutionary aging more robust than static pure aging on

plateaus

4/13

slide-30
SLIDE 30

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Known Results

  • on the maximal lifespan τ

(Horoba/J./Zarges (GECCO 2009))

  • if τ is too large, static pure aging is ineffective
  • if τ is too small, the RSH becomes unsuccessful
  • the ‘correct’ lifespan depends on the optimization problem
  • the range of ‘correct’ lifespans can be extremely small
  • on different aging strategies (J./Zarges (ICARIS 2009, TCS))
  • static pure aging more effective than evolutionary aging in

escaping local optima

  • evolutionary aging more robust than static pure aging on

plateaus

  • advantages of both can be combined in phenotypic aging

4/13

slide-31
SLIDE 31

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Known Results

  • on the maximal lifespan τ

(Horoba/J./Zarges (GECCO 2009))

  • if τ is too large, static pure aging is ineffective
  • if τ is too small, the RSH becomes unsuccessful
  • the ‘correct’ lifespan depends on the optimization problem
  • the range of ‘correct’ lifespans can be extremely small
  • on different aging strategies (J./Zarges (ICARIS 2009, TCS))
  • static pure aging more effective than evolutionary aging in

escaping local optima

  • evolutionary aging more robust than static pure aging on

plateaus

  • advantages of both can be combined in phenotypic aging
  • general observation
  • in all published cases: restarts can replace aging

4/13

slide-32
SLIDE 32

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Known Results

  • on the maximal lifespan τ

(Horoba/J./Zarges (GECCO 2009))

  • if τ is too large, static pure aging is ineffective
  • if τ is too small, the RSH becomes unsuccessful
  • the ‘correct’ lifespan depends on the optimization problem
  • the range of ‘correct’ lifespans can be extremely small
  • on different aging strategies (J./Zarges (ICARIS 2009, TCS))
  • static pure aging more effective than evolutionary aging in

escaping local optima

  • evolutionary aging more robust than static pure aging on

plateaus

  • advantages of both can be combined in phenotypic aging
  • general observation
  • in all published cases: restarts can replace aging
  • restarts conceptually simpler, easier to implement,

computationally cheaper

4/13

slide-33
SLIDE 33

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Known Results

  • on the maximal lifespan τ

(Horoba/J./Zarges (GECCO 2009))

  • if τ is too large, static pure aging is ineffective
  • if τ is too small, the RSH becomes unsuccessful
  • the ‘correct’ lifespan depends on the optimization problem
  • the range of ‘correct’ lifespans can be extremely small
  • on different aging strategies (J./Zarges (ICARIS 2009, TCS))
  • static pure aging more effective than evolutionary aging in

escaping local optima

  • evolutionary aging more robust than static pure aging on

plateaus

  • advantages of both can be combined in phenotypic aging
  • general observation
  • in all published cases: restarts can replace aging
  • restarts conceptually simpler, easier to implement,

computationally cheaper

Open Question What can aging do beyond restarts?

4/13

slide-34
SLIDE 34

Introduction Aging Beyond Restarts: Ideas Results Conclusions

The Randomized Search Heuristic

5/13

slide-35
SLIDE 35

Introduction Aging Beyond Restarts: Ideas Results Conclusions

The Randomized Search Heuristic

Parameters population size µ ∈ N \ {1}, µ = nO(1), lifespan τ ∈ N0 crossover probability pc ∈ (0, 1), constant number of crossover points k ∈ N, k = O(1)

5/13

slide-36
SLIDE 36

Introduction Aging Beyond Restarts: Ideas Results Conclusions

The Randomized Search Heuristic

Parameters population size µ ∈ N \ {1}, µ = nO(1), lifespan τ ∈ N0 crossover probability pc ∈ (0, 1), constant number of crossover points k ∈ N, k = O(1) 1. Initialization: Select collection C of µ points x ∈ {0, 1}n u. a. r., set x.age = 0 for all.

5/13

slide-37
SLIDE 37

Introduction Aging Beyond Restarts: Ideas Results Conclusions

The Randomized Search Heuristic

Parameters population size µ ∈ N \ {1}, µ = nO(1), lifespan τ ∈ N0 crossover probability pc ∈ (0, 1), constant number of crossover points k ∈ N, k = O(1) 1. Initialization: Select collection C of µ points x ∈ {0, 1}n u. a. r., set x.age = 0 for all. 2. Growing older: Increase x.age by 1 for all x ∈ C.

5/13

slide-38
SLIDE 38

Introduction Aging Beyond Restarts: Ideas Results Conclusions

The Randomized Search Heuristic

Parameters population size µ ∈ N \ {1}, µ = nO(1), lifespan τ ∈ N0 crossover probability pc ∈ (0, 1), constant number of crossover points k ∈ N, k = O(1) 1. Initialization: Select collection C of µ points x ∈ {0, 1}n u. a. r., set x.age = 0 for all. 2. Growing older: Increase x.age by 1 for all x ∈ C. 3. Variation: With prob. pc select x, y ∈ C u. a. r., z := mutate(k-pt-cross(x, y)) else (with prob. 1 − pc) select x ∈ C u. a. r., y := x, z := mutate(x).

5/13

slide-39
SLIDE 39

Introduction Aging Beyond Restarts: Ideas Results Conclusions

The Randomized Search Heuristic

Parameters population size µ ∈ N \ {1}, µ = nO(1), lifespan τ ∈ N0 crossover probability pc ∈ (0, 1), constant number of crossover points k ∈ N, k = O(1) 1. Initialization: Select collection C of µ points x ∈ {0, 1}n u. a. r., set x.age = 0 for all. 2. Growing older: Increase x.age by 1 for all x ∈ C. 3. Variation: With prob. pc select x, y ∈ C u. a. r., z := mutate(k-pt-cross(x, y)) else (with prob. 1 − pc) select x ∈ C u. a. r., y := x, z := mutate(x). 4. Determine age: If f(z) > max{f(x), f(y)} then z.age = 0, else z.age = max{x.age, y.age}.

5/13

slide-40
SLIDE 40

Introduction Aging Beyond Restarts: Ideas Results Conclusions

The Randomized Search Heuristic

Parameters population size µ ∈ N \ {1}, µ = nO(1), lifespan τ ∈ N0 crossover probability pc ∈ (0, 1), constant number of crossover points k ∈ N, k = O(1) 1. Initialization: Select collection C of µ points x ∈ {0, 1}n u. a. r., set x.age = 0 for all. 2. Growing older: Increase x.age by 1 for all x ∈ C. 3. Variation: With prob. pc select x, y ∈ C u. a. r., z := mutate(k-pt-cross(x, y)) else (with prob. 1 − pc) select x ∈ C u. a. r., y := x, z := mutate(x). 4. Determine age: If f(z) > max{f(x), f(y)} then z.age = 0, else z.age = max{x.age, y.age}. 5. Dying of age: Remove all x ∈ C with x.age > τ.

5/13

slide-41
SLIDE 41

Introduction Aging Beyond Restarts: Ideas Results Conclusions

The Randomized Search Heuristic

Parameters population size µ ∈ N \ {1}, µ = nO(1), lifespan τ ∈ N0 crossover probability pc ∈ (0, 1), constant number of crossover points k ∈ N, k = O(1) 1. Initialization: Select collection C of µ points x ∈ {0, 1}n u. a. r., set x.age = 0 for all. 2. Growing older: Increase x.age by 1 for all x ∈ C. 3. Variation: With prob. pc select x, y ∈ C u. a. r., z := mutate(k-pt-cross(x, y)) else (with prob. 1 − pc) select x ∈ C u. a. r., y := x, z := mutate(x). 4. Determine age: If f(z) > max{f(x), f(y)} then z.age = 0, else z.age = max{x.age, y.age}. 5. Dying of age: Remove all x ∈ C with x.age > τ. 6. Selection: If |C| < µ If z.age ≤ τ then C := C ∪ {z}. While |C| < µ select x ∈ {0, 1}n u. a. r., x.age = 0, C := C ∪ {x}.

5/13

slide-42
SLIDE 42

Introduction Aging Beyond Restarts: Ideas Results Conclusions

The Randomized Search Heuristic

Parameters population size µ ∈ N \ {1}, µ = nO(1), lifespan τ ∈ N0 crossover probability pc ∈ (0, 1), constant number of crossover points k ∈ N, k = O(1) 1. Initialization: Select collection C of µ points x ∈ {0, 1}n u. a. r., set x.age = 0 for all. 2. Growing older: Increase x.age by 1 for all x ∈ C. 3. Variation: With prob. pc select x, y ∈ C u. a. r., z := mutate(k-pt-cross(x, y)) else (with prob. 1 − pc) select x ∈ C u. a. r., y := x, z := mutate(x). 4. Determine age: If f(z) > max{f(x), f(y)} then z.age = 0, else z.age = max{x.age, y.age}. 5. Dying of age: Remove all x ∈ C with x.age > τ. 6. Selection: If |C| < µ If z.age ≤ τ then C := C ∪ {z}. While |C| < µ select x ∈ {0, 1}n u. a. r., x.age = 0, C := C ∪ {x}. Else

5/13

slide-43
SLIDE 43

Introduction Aging Beyond Restarts: Ideas Results Conclusions

The Randomized Search Heuristic

Parameters population size µ ∈ N \ {1}, µ = nO(1), lifespan τ ∈ N0 crossover probability pc ∈ (0, 1), constant number of crossover points k ∈ N, k = O(1) 1. Initialization: Select collection C of µ points x ∈ {0, 1}n u. a. r., set x.age = 0 for all. 2. Growing older: Increase x.age by 1 for all x ∈ C. 3. Variation: With prob. pc select x, y ∈ C u. a. r., z := mutate(k-pt-cross(x, y)) else (with prob. 1 − pc) select x ∈ C u. a. r., y := x, z := mutate(x). 4. Determine age: If f(z) > max{f(x), f(y)} then z.age = 0, else z.age = max{x.age, y.age}. 5. Dying of age: Remove all x ∈ C with x.age > τ. 6. Selection: If |C| < µ If z.age ≤ τ then C := C ∪ {z}. While |C| < µ select x ∈ {0, 1}n u. a. r., x.age = 0, C := C ∪ {x}. Else If z.age ≤ τ and f(z) ≥ min{f(x) | x ∈ C} then

5/13

slide-44
SLIDE 44

Introduction Aging Beyond Restarts: Ideas Results Conclusions

The Randomized Search Heuristic

Parameters population size µ ∈ N \ {1}, µ = nO(1), lifespan τ ∈ N0 crossover probability pc ∈ (0, 1), constant number of crossover points k ∈ N, k = O(1) 1. Initialization: Select collection C of µ points x ∈ {0, 1}n u. a. r., set x.age = 0 for all. 2. Growing older: Increase x.age by 1 for all x ∈ C. 3. Variation: With prob. pc select x, y ∈ C u. a. r., z := mutate(k-pt-cross(x, y)) else (with prob. 1 − pc) select x ∈ C u. a. r., y := x, z := mutate(x). 4. Determine age: If f(z) > max{f(x), f(y)} then z.age = 0, else z.age = max{x.age, y.age}. 5. Dying of age: Remove all x ∈ C with x.age > τ. 6. Selection: If |C| < µ If z.age ≤ τ then C := C ∪ {z}. While |C| < µ select x ∈ {0, 1}n u. a. r., x.age = 0, C := C ∪ {x}. Else If z.age ≤ τ and f(z) ≥ min{f(x) | x ∈ C} then D := {x ∈ C | f(x) = min{f(x′) | x′ ∈ C}}

5/13

slide-45
SLIDE 45

Introduction Aging Beyond Restarts: Ideas Results Conclusions

The Randomized Search Heuristic

Parameters population size µ ∈ N \ {1}, µ = nO(1), lifespan τ ∈ N0 crossover probability pc ∈ (0, 1), constant number of crossover points k ∈ N, k = O(1) 1. Initialization: Select collection C of µ points x ∈ {0, 1}n u. a. r., set x.age = 0 for all. 2. Growing older: Increase x.age by 1 for all x ∈ C. 3. Variation: With prob. pc select x, y ∈ C u. a. r., z := mutate(k-pt-cross(x, y)) else (with prob. 1 − pc) select x ∈ C u. a. r., y := x, z := mutate(x). 4. Determine age: If f(z) > max{f(x), f(y)} then z.age = 0, else z.age = max{x.age, y.age}. 5. Dying of age: Remove all x ∈ C with x.age > τ. 6. Selection: If |C| < µ If z.age ≤ τ then C := C ∪ {z}. While |C| < µ select x ∈ {0, 1}n u. a. r., x.age = 0, C := C ∪ {x}. Else If z.age ≤ τ and f(z) ≥ min{f(x) | x ∈ C} then D := {x ∈ C | f(x) = min{f(x′) | x′ ∈ C}} If f(z) = min{f(x′) | x′ ∈ C} then D := {x ∈ D | |x.age − z.age| = min{|x′.age − z.age| | x′ ∈ D}}

5/13

slide-46
SLIDE 46

Introduction Aging Beyond Restarts: Ideas Results Conclusions

The Randomized Search Heuristic

Parameters population size µ ∈ N \ {1}, µ = nO(1), lifespan τ ∈ N0 crossover probability pc ∈ (0, 1), constant number of crossover points k ∈ N, k = O(1) 1. Initialization: Select collection C of µ points x ∈ {0, 1}n u. a. r., set x.age = 0 for all. 2. Growing older: Increase x.age by 1 for all x ∈ C. 3. Variation: With prob. pc select x, y ∈ C u. a. r., z := mutate(k-pt-cross(x, y)) else (with prob. 1 − pc) select x ∈ C u. a. r., y := x, z := mutate(x). 4. Determine age: If f(z) > max{f(x), f(y)} then z.age = 0, else z.age = max{x.age, y.age}. 5. Dying of age: Remove all x ∈ C with x.age > τ. 6. Selection: If |C| < µ If z.age ≤ τ then C := C ∪ {z}. While |C| < µ select x ∈ {0, 1}n u. a. r., x.age = 0, C := C ∪ {x}. Else If z.age ≤ τ and f(z) ≥ min{f(x) | x ∈ C} then D := {x ∈ C | f(x) = min{f(x′) | x′ ∈ C}} If f(z) = min{f(x′) | x′ ∈ C} then D := {x ∈ D | |x.age − z.age| = min{|x′.age − z.age| | x′ ∈ D}} Select x ∈ D u. a. r., C := (C \ {x}) ∪ {z}.

5/13

slide-47
SLIDE 47

Introduction Aging Beyond Restarts: Ideas Results Conclusions

The Randomized Search Heuristic

Parameters population size µ ∈ N \ {1}, µ = nO(1), lifespan τ ∈ N0 crossover probability pc ∈ (0, 1), constant number of crossover points k ∈ N, k = O(1) 1. Initialization: Select collection C of µ points x ∈ {0, 1}n u. a. r., set x.age = 0 for all. 2. Growing older: Increase x.age by 1 for all x ∈ C. 3. Variation: With prob. pc select x, y ∈ C u. a. r., z := mutate(k-pt-cross(x, y)) else (with prob. 1 − pc) select x ∈ C u. a. r., y := x, z := mutate(x). 4. Determine age: If f(z) > max{f(x), f(y)} then z.age = 0, else z.age = max{x.age, y.age}. 5. Dying of age: Remove all x ∈ C with x.age > τ. 6. Selection: If |C| < µ If z.age ≤ τ then C := C ∪ {z}. While |C| < µ select x ∈ {0, 1}n u. a. r., x.age = 0, C := C ∪ {x}. Else If z.age ≤ τ and f(z) ≥ min{f(x) | x ∈ C} then D := {x ∈ C | f(x) = min{f(x′) | x′ ∈ C}} If f(z) = min{f(x′) | x′ ∈ C} then D := {x ∈ D | |x.age − z.age| = min{|x′.age − z.age| | x′ ∈ D}} Select x ∈ D u. a. r., C := (C \ {x}) ∪ {z}. 7. Continue at line 2.

5/13

slide-48
SLIDE 48

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Aging Beyond Restarts: Main Idea

6/13

slide-49
SLIDE 49

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Aging Beyond Restarts: Main Idea

Observation

  • Aging can perform restarts.

restart =empty C completely due to age

6/13

slide-50
SLIDE 50

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Aging Beyond Restarts: Main Idea

Observations

  • Aging can perform restarts.

restart =empty C completely due to age

  • Aging can perform partial restarts.

partial restart =remove some x from C due to age and insert new random points

6/13

slide-51
SLIDE 51

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Aging Beyond Restarts: Main Idea

Observations

  • Aging can perform restarts.

restart =empty C completely due to age

  • Aging can perform partial restarts.

partial restart =remove some x from C due to age and insert new random points

  • new random points probably no good quickly removed

6/13

slide-52
SLIDE 52

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Aging Beyond Restarts: Main Idea

Observations

  • Aging can perform restarts.

restart =empty C completely due to age

  • Aging can perform partial restarts.

partial restart =remove some x from C due to age and insert new random points

  • new random points probably no good quickly removed
  • only a few generations where new points can actually do

something

6/13

slide-53
SLIDE 53

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Aging Beyond Restarts: Main Idea

Observations

  • Aging can perform restarts.

restart =empty C completely due to age

  • Aging can perform partial restarts.

partial restart =remove some x from C due to age and insert new random points

  • new random points probably no good quickly removed
  • only a few generations where new points can actually do

something

  • “There’s hardly anything less random than some x ∈ {0, 1}n

selected uniformly at random.”

6/13

slide-54
SLIDE 54

Introduction Aging Beyond Restarts: Ideas Results Conclusions

An Example Problem

7/13

slide-55
SLIDE 55

Introduction Aging Beyond Restarts: Ideas Results Conclusions

An Example Problem

0n 1n f : {0, 1}n → R

7/13

slide-56
SLIDE 56

Introduction Aging Beyond Restarts: Ideas Results Conclusions

An Example Problem

0n 1n f : {0, 1}n → R f(x) =

            n − OneMax(x)

  • therwise

7/13

slide-57
SLIDE 57

Introduction Aging Beyond Restarts: Ideas Results Conclusions

An Example Problem

0n 1n n/4 1n/403n/4 f : {0, 1}n → R f(x) =

            

n + i if x = 1i0n−i, i ≤ n/4 n − OneMax(x)

  • therwise

7/13

slide-58
SLIDE 58

Introduction Aging Beyond Restarts: Ideas Results Conclusions

An Example Problem

0n 1n n/4 1n/403n/4 3n/4 n/2 n/3 1n/40n/41n/2 1n/40n/4q f : {0, 1}n → R f(x) =

            

2n if x = 1n/40n/4q, q ∈ {0, 1}n/2, OneMax(q) ≥ n/12 n + i if x = 1i0n−i, i ≤ n/4 n − OneMax(x)

  • therwise

7/13

slide-59
SLIDE 59

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Static Pure Aging on f

0n 1n n/4 1n/403n/4 3n/4 n/2 n/3 1n/40n/41n/2 1n/40n/4q

8/13

slide-60
SLIDE 60

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Static Pure Aging on f

0n 1n n/4 1n/403n/4 3n/4 n/2 n/3 1n/40n/41n/2 1n/40n/4q

  • pt. n − OneMax(x)

8/13

slide-61
SLIDE 61

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Static Pure Aging on f

0n 1n n/4 1n/403n/4 3n/4 n/2 n/3 1n/40n/41n/2 1n/40n/4q

  • pt. n − OneMax(x)

O(µn + n log n)

  • w. high prob.

8/13

slide-62
SLIDE 62

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Static Pure Aging on f

0n 1n n/4 1n/403n/4 3n/4 n/2 n/3 1n/40n/41n/2 1n/40n/4q

  • pt. n − OneMax(x)

O(µn + n log n)

  • w. high prob.
  • pt. 1i0n−4

8/13

slide-63
SLIDE 63

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Static Pure Aging on f

0n 1n n/4 1n/403n/4 3n/4 n/2 n/3 1n/40n/41n/2 1n/40n/4q

  • pt. n − OneMax(x)

O(µn + n log n)

  • w. high prob.
  • pt. 1i0n−4

Θ

n2 + µn log n

  • w. high prob.

8/13

slide-64
SLIDE 64

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Static Pure Aging on f

0n 1n n/4 1n/403n/4 3n/4 n/2 n/3 1n/40n/41n/2 1n/40n/4q

  • pt. n − OneMax(x)

O(µn + n log n)

  • w. high prob.
  • pt. 1i0n−4

Θ

n2 + µn log n

  • w. high prob.

perform partial restart

8/13

slide-65
SLIDE 65

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Static Pure Aging on f

0n 1n n/4 1n/403n/4 3n/4 n/2 n/3 1n/40n/41n/2 1n/40n/4q

  • pt. n − OneMax(x)

O(µn + n log n)

  • w. high prob.
  • pt. 1i0n−4

Θ

n2 + µn log n

  • w. high prob.

perform partial restart Θ(τ)

  • w. prob. p

8/13

slide-66
SLIDE 66

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Static Pure Aging on f

0n 1n n/4 1n/403n/4 3n/4 n/2 n/3 1n/40n/41n/2 1n/40n/4q

  • pt. n − OneMax(x)

O(µn + n log n)

  • w. high prob.
  • pt. 1i0n−4

Θ

n2 + µn log n

  • w. high prob.

perform partial restart Θ(τ)

  • w. prob. p

find opt. with XO

8/13

slide-67
SLIDE 67

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Static Pure Aging on f

0n 1n n/4 1n/403n/4 3n/4 n/2 n/3 1n/40n/41n/2 1n/40n/4q

  • pt. n − OneMax(x)

O(µn + n log n)

  • w. high prob.
  • pt. 1i0n−4

Θ

n2 + µn log n

  • w. high prob.

perform partial restart Θ(τ)

  • w. prob. p

find opt. with XO 1

  • w. prob. q

8/13

slide-68
SLIDE 68

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Static Pure Aging on f

0n 1n n/4 1n/403n/4 3n/4 n/2 n/3 1n/40n/41n/2 1n/40n/4q

  • pt. n − OneMax(x)

O(µn + n log n)

  • w. high prob.
  • pt. 1i0n−4

Θ

n2 + µn log n

  • w. high prob.

perform partial restart Θ(τ)

  • w. prob. p

find opt. with XO 1

  • w. prob. q

Adding things up upper bound O

p−1 · q−1 · τ + n2 + µn log n

  • lower bound

Ω

p−1 · q−1 · τ + n2 + µn log n

  • 8/13
slide-69
SLIDE 69

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Creating an Optimum with Crossover

9/13

slide-70
SLIDE 70

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Creating an Optimum with Crossover

local optimum x 11· · · 11 n/4 00000000· · · 0000000

9/13

slide-71
SLIDE 71

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Creating an Optimum with Crossover

local optimum x 11· · · 11 n/4 00000000· · · 0000000 new random search point y

9/13

slide-72
SLIDE 72

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Creating an Optimum with Crossover

n/4 n/2 n/2 7n/12 7n/12 3n/4 3n/4 5n/6 5n/6 yA yB yC yD yE yF local optimum x 11· · · 11 n/4 00000000· · · 0000000 new random search point y

9/13

slide-73
SLIDE 73

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Creating an Optimum with Crossover

n/4 n/2 n/2 7n/12 7n/12 3n/4 3n/4 5n/6 5n/6 yA yB yC yD yE yF local optimum x 11· · · 11 n/4 00000000· · · 0000000 new random search point y We need k crossover points c1 < c2 < · · · < ck with c1 > n/2 and ≥ n/12 1-bits in used y-parts

9/13

slide-74
SLIDE 74

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Creating an Optimum with Crossover

n/4 n/2 n/2 7n/12 7n/12 3n/4 3n/4 5n/6 5n/6 yA yB yC yD yE yF local optimum x 11· · · 11 n/4 00000000· · · 0000000 new random search point y We need k crossover points c1 < c2 < · · · < ck with c1 > n/2 and ≥ n/12 1-bits in used y-parts Observation

  • Prob (n/2 ≤ c1 < 7n/12) = Ω(1)

9/13

slide-75
SLIDE 75

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Creating an Optimum with Crossover

n/4 n/2 n/2 7n/12 7n/12 3n/4 3n/4 5n/6 5n/6 yA yB yC yD yE yF local optimum x 11· · · 11 n/4 00000000· · · 0000000 new random search point y We need k crossover points c1 < c2 < · · · < ck with c1 > n/2 and ≥ n/12 1-bits in used y-parts Observations

  • Prob (n/2 ≤ c1 < 7n/12) = Ω(1)
  • Prob (3n/4 ≤ c2 < 5n/6) = Ω(1)

9/13

slide-76
SLIDE 76

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Creating an Optimum with Crossover

n/4 n/2 n/2 7n/12 7n/12 3n/4 3n/4 5n/6 5n/6 yA yB yC yD yE yF local optimum x 11· · · 11 n/4 00000000· · · 0000000 new random search point y We need k crossover points c1 < c2 < · · · < ck with c1 > n/2 and ≥ n/12 1-bits in used y-parts Observations

  • Prob (n/2 ≤ c1 < 7n/12) = Ω(1)
  • Prob (3n/4 ≤ c2 < 5n/6) = Ω(1)
  • ∀i > 2: Prob (ci > 5n/6) = Ω(1)

9/13

slide-77
SLIDE 77

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Creating an Optimum with Crossover

n/4 n/2 n/2 7n/12 7n/12 3n/4 3n/4 5n/6 5n/6 yA yB yC yD yE yF local optimum x 11· · · 11 n/4 00000000· · · 0000000 new random search point y We need k crossover points c1 < c2 < · · · < ck with c1 > n/2 and ≥ n/12 1-bits in used y-parts Observations

  • Prob (n/2 ≤ c1 < 7n/12) = Ω(1)
  • Prob (3n/4 ≤ c2 < 5n/6) = Ω(1)
  • ∀i > 2: Prob (ci > 5n/6) = Ω(1)
  • Prob (OneMax(yD) ≥ n/12) ≥ 1/2

9/13

slide-78
SLIDE 78

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Creating an Optimum with Crossover

n/4 n/2 n/2 7n/12 7n/12 3n/4 3n/4 5n/6 5n/6 yA yB yC yD yE yF local optimum x 11· · · 11 n/4 00000000· · · 0000000 new random search point y We need k crossover points c1 < c2 < · · · < ck with c1 > n/2 and ≥ n/12 1-bits in used y-parts Observations

  • Prob (n/2 ≤ c1 < 7n/12) = Ω(1)
  • Prob (3n/4 ≤ c2 < 5n/6) = Ω(1)
  • ∀i > 2: Prob (ci > 5n/6) = Ω(1)
  • Prob (OneMax(yD) ≥ n/12) ≥ 1/2

Result Prob (k-pt-crossover(x, y) ∈ OPT) = q = Θ(1)

9/13

slide-79
SLIDE 79

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Results

We have

10/13

slide-80
SLIDE 80

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Results

We have

  • pt. n − OneMax(x)

O(µn + n log n)

  • w. high prob.
  • pt. 1i0n−4

Θ

n2 + µn log n

  • w. high prob.

perform partial restart Θ(τ)

  • w. prob. p

find opt. with XO 1

  • w. prob. Θ(1)

10/13

slide-81
SLIDE 81

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Results

We have

  • pt. n − OneMax(x)

O(µn + n log n)

  • w. high prob.
  • pt. 1i0n−4

Θ

n2 + µn log n

  • w. high prob.

perform partial restart Θ(τ)

  • w. prob. p

find opt. with XO 1

  • w. prob. Θ(1)

Adding things up upper bound O

p−1 · τ + n2 + µn log n

  • lower bound

Ω

p−1 · τ + n2 + µn log n

  • 10/13
slide-82
SLIDE 82

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Results

We have

  • pt. n − OneMax(x)

O(µn + n log n)

  • w. high prob.
  • pt. 1i0n−4

Θ

n2 + µn log n

  • w. high prob.

perform partial restart Θ(τ)

  • w. prob. p

find opt. with XO 1

  • w. prob. Θ(1)

Adding things up upper bound O

p−1 · τ + n2 + µn log n

  • lower bound

Ω

p−1 · τ + n2 + µn log n

  • Theorem

upper bound O

µ · τ + n2 + µn log n

  • for any poly. µ, const. pc, const. k, any τ = ω(µn log µ)

lower bound Ω

τ + n2 + µn log n

  • for any poly. µ, const. pc, const. k, any τ (2O(n))

10/13

slide-83
SLIDE 83

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Experimental Setup

Theorem upper bound O

µ · τ + n2 + µn log n

  • for any poly. µ, const. pc, const. k, any τ = ω(µn log µ)

lower bound Ω

τ + n2 + µn log n

  • for any poly. µ, const. pc, const. k, any τ (2O(n))

Perform Experiments with

11/13

slide-84
SLIDE 84

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Experimental Setup

Theorem upper bound O

µ · τ + n2 + µn log n

  • for any poly. µ, const. pc, const. k, any τ = ω(µn log µ)

lower bound Ω

τ + n2 + µn log n

  • for any poly. µ, const. pc, const. k, any τ (2O(n))

Perform Experiments with

  • crossover probability pc = .5

11/13

slide-85
SLIDE 85

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Experimental Setup

Theorem upper bound O

µ · τ + n2 + µn log n

  • for any poly. µ, const. pc, const. k, any τ = ω(µn log µ)

lower bound Ω

τ + n2 + µn log n

  • for any poly. µ, const. pc, const. k, any τ (2O(n))

Perform Experiments with

  • crossover probability pc = .5
  • 1-point crossover (k = 1)

11/13

slide-86
SLIDE 86

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Experimental Setup

Theorem upper bound O

µ · τ + n2 + µn log n

  • for any poly. µ, const. pc, const. k, any τ = ω(µn log µ)

lower bound Ω

τ + n2 + µn log n

  • for any poly. µ, const. pc, const. k, any τ (2O(n))

Perform Experiments with

  • crossover probability pc = .5
  • 1-point crossover (k = 1)
  • lifespan τ = 6µn ⌊log µ⌋ ⌊log n⌋

11/13

slide-87
SLIDE 87

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Experimental Setup

Theorem upper bound O

µ · τ + n2 + µn log n

  • for any poly. µ, const. pc, const. k, any τ = ω(µn log µ)

lower bound Ω

τ + n2 + µn log n

  • for any poly. µ, const. pc, const. k, any τ (2O(n))

Perform Experiments with

  • crossover probability pc = .5
  • 1-point crossover (k = 1)
  • lifespan τ = 6µn ⌊log µ⌋ ⌊log n⌋
  • problem size n ∈ {10, 20, 30, . . . , 1000}

11/13

slide-88
SLIDE 88

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Experimental Setup

Theorem upper bound O

µ · τ + n2 + µn log n

  • for any poly. µ, const. pc, const. k, any τ = ω(µn log µ)

lower bound Ω

τ + n2 + µn log n

  • for any poly. µ, const. pc, const. k, any τ (2O(n))

Perform Experiments with

  • crossover probability pc = .5
  • 1-point crossover (k = 1)
  • lifespan τ = 6µn ⌊log µ⌋ ⌊log n⌋
  • problem size n ∈ {10, 20, 30, . . . , 1000}
  • population size µ ∈ {2, ⌊√n⌋ , ⌊n/ ⌊log n⌋⌋ , n, n ⌊log n⌋}

11/13

slide-89
SLIDE 89

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Experimental Setup

Theorem upper bound O

µ · τ + n2 + µn log n

  • for any poly. µ, const. pc, const. k, any τ = ω(µn log µ)

lower bound Ω

τ + n2 + µn log n

  • for any poly. µ, const. pc, const. k, any τ (2O(n))

Perform Experiments with

  • crossover probability pc = .5
  • 1-point crossover (k = 1)
  • lifespan τ = 6µn ⌊log µ⌋ ⌊log n⌋
  • problem size n ∈ {10, 20, 30, . . . , 1000}
  • population size µ ∈ {2, ⌊√n⌋ , ⌊n/ ⌊log n⌋⌋ , n, n ⌊log n⌋}
  • 100 independent runs per setting

11/13

slide-90
SLIDE 90

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Experimental Results

n #f-evals 100 200 300 400 500 600 700 800 900 1000 107 2 · 107 3 · 107 4 · 107 5 · 107 6 · 107 7 · 107

12/13

slide-91
SLIDE 91

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Experimental Results

n #f-evals 100 200 300 400 500 600 700 800 900 1000 107 2 · 107 3 · 107 4 · 107 5 · 107 6 · 107 7 · 107 µ = n ⌊log n⌋

12/13

slide-92
SLIDE 92

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Experimental Results

n #f-evals 100 200 300 400 500 600 700 800 900 1000 107 2 · 107 3 · 107 4 · 107 5 · 107 6 · 107 7 · 107 µ = n ⌊log n⌋ µ = n

12/13

slide-93
SLIDE 93

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Experimental Results

n #f-evals 100 200 300 400 500 600 700 800 900 1000 107 2 · 107 3 · 107 4 · 107 5 · 107 6 · 107 7 · 107 µ = n ⌊log n⌋ µ = n µ = n/ ⌊log n⌋

12/13

slide-94
SLIDE 94

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Experimental Results

n #f-evals 100 200 300 400 500 600 700 800 900 1000 107 2 · 107 3 · 107 4 · 107 5 · 107 6 · 107 7 · 107 µ = n ⌊log n⌋ µ = n µ = n/ ⌊log n⌋ µ = √n

12/13

slide-95
SLIDE 95

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Experimental Results

n #f-evals 100 200 300 400 500 600 700 800 900 1000 107 2 · 107 3 · 107 4 · 107 5 · 107 6 · 107 7 · 107 µ = n ⌊log n⌋ µ = n µ = n/ ⌊log n⌋ µ = √n µ = 2

12/13

slide-96
SLIDE 96

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Experimental Results

n #f-evals 100 200 300 400 500 600 700 800 900 1000 107 2 · 107 3 · 107 4 · 107 5 · 107 6 · 107 7 · 107 µ = n ⌊log n⌋ µ = n µ = n/ ⌊log n⌋ µ = √n µ = 2

12/13

slide-97
SLIDE 97

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Experimental Results

n #f-evals 100 200 300 400 500 600 700 800 900 1000 107 2 · 107 3 · 107 4 · 107 5 · 107 6 · 107 7 · 107 µ = n ⌊log n⌋ µ = n µ = n/ ⌊log n⌋ µ = √n µ = 2

12/13

slide-98
SLIDE 98

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Experimental Results

n #f-evals 100 200 300 400 500 600 700 800 900 1000 107 2 · 107 3 · 107 4 · 107 5 · 107 6 · 107 7 · 107 µ = n ⌊log n⌋ µ = n µ = n/ ⌊log n⌋ µ = √n µ = 2

12/13

slide-99
SLIDE 99

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Experimental Results

n #f-evals 100 200 300 400 500 600 700 800 900 1000 107 2 · 107 3 · 107 4 · 107 5 · 107 6 · 107 7 · 107 µ = n ⌊log n⌋ µ = n µ = n/ ⌊log n⌋ µ = √n µ = 2

12/13

slide-100
SLIDE 100

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Experimental Results

n #f-evals 100 200 300 400 500 600 700 800 900 1000 107 2 · 107 3 · 107 4 · 107 5 · 107 6 · 107 7 · 107 µ = n ⌊log n⌋ µ = n µ = n/ ⌊log n⌋ µ = √n µ = 2

12/13

slide-101
SLIDE 101

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Open Problems

13/13

slide-102
SLIDE 102

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Open Problems

  • True expected optimization time on f?

13/13

slide-103
SLIDE 103

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Open Problems

  • True expected optimization time on f?
  • Improving the upper bounds?

13/13

slide-104
SLIDE 104

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Open Problems

  • True expected optimization time on f?
  • Improving the upper bounds?
  • Other problems where aging helps and restarts don’t?

13/13

slide-105
SLIDE 105

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Open Problems

  • True expected optimization time on f?
  • Improving the upper bounds?
  • Other problems where aging helps and restarts don’t?
  • Natural problems where aging helps and restarts don’t?

13/13

slide-106
SLIDE 106

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Open Problems

  • True expected optimization time on f?
  • Improving the upper bounds?
  • Other problems where aging helps and restarts don’t?
  • Natural problems where aging helps and restarts don’t?
  • Relevant problems where aging helps and restarts don’t?

13/13

slide-107
SLIDE 107

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Open Problems

  • True expected optimization time on f?
  • Improving the upper bounds?
  • Other problems where aging helps and restarts don’t?
  • Natural problems where aging helps and restarts don’t?
  • Relevant problems where aging helps and restarts don’t?
  • Other aging variants?

13/13

slide-108
SLIDE 108

Introduction Aging Beyond Restarts: Ideas Results Conclusions

Open Problems

  • True expected optimization time on f?
  • Improving the upper bounds?
  • Other problems where aging helps and restarts don’t?
  • Natural problems where aging helps and restarts don’t?
  • Relevant problems where aging helps and restarts don’t?
  • Other aging variants?
  • Do you have any questions?

13/13