Adaptive Terrain-Based Memetic Algorithms

Adaptive Terrain-Based Memetic Algorithms – GECCO 2009 – Carlos R. B. Azevedo1 and V. Scott Gordon2 1

UFPE, Brazil

Universidade Federal de Pernambuco, Centro de Informática (Brazil) 2 California State University Sacramento, Computer Science Department (U.S.)

CSUS, U.S.

Agenda • • • • • • • •

Motivation Objectives Background The models Experimental methodology Results and discussion Conclusion Ongoing works Adaptive Terrain-Based Memetic Algorithms, Azevedo and Gordon – GECCO’09

Motivation • Memetic Algorithms (MA) can greatly benefit from the adaptation of Local Search (memes) – Few adaptive diffusion MAs are available in the literature – The Terrain-Based Genetic Algorithm (TBGA) by Gordon et al. (1999) provided a good starting point from where simple adaptation mechanisms for diffusion MAs could be derived Adaptive Terrain-Based Memetic Algorithms, Azevedo and Gordon – GECCO’09

Motivation A term coined by R. Dawkins • Memetic Algorithms (MA) can greatly benefit designating an unit of (memes) from thefor adaptation of Local Search memes cultural transmission – Few adaptive diffusion MAs are available in the literature – The Terrain-Based Genetic Algorithm (TBGA) by Gordon et al. (1999) provided a good starting point from where simple adaptation mechanisms for diffusion MAs can be derived Adaptive Terrain-Based Memetic Algorithms, Azevedo and Gordon – GECCO’09

Objectives • General – To investigate the auto-adaptation of memes in diffusion Memetic Algorithms (MA)

• Specific – To investigate the adaptation capabilities of the Terrain-Based Memetic Algorithm (TBMA) for an Image Vector Quantization problem – Which one is better: following more effective memes or trasmitting sucessful memes to nearby cells? Adaptive Terrain-Based Memetic Algorithms, Azevedo and Gordon – GECCO’09

PART I

BACKGROUND

Cellular Genetic Algorithm (cGA) • Main concepts – Locality – Isolation-by-distance – Periodic interaction – Diffusion of genes

Cellular Genetic Algorithm (cGA) • Main concepts – Locality – Isolation-by-distance – Periodic interaction – Diffusion of genes

Individual

Neighbors

Terrain-Based GA (TBGA) [Gordon et al., 1999] • Extends cGA by distributing GAs’ parameter values along the axes; – Neighbors evolve according to similar parameters settings. Individual

Neighbors

Terrain-Based GA (TBGA) [Gordon et al., 1999] • A starting point to adaptation – The simultaneous usage of different parameter values combinations implies that near-optimal parameters can be explored at different stages of the optimization process Individual

Neighbors

TB Patchwork Model (TBPM) [Krink and Ursem, 2000] • In TBPM, individuals are mobile intelligent agents whose behavior is modeled by a motivation network.

TB Patchwork Model (TBPM) [Krink and Ursem, 2000] • The TBPM presents characteristics of both island and diffusion models



Isolated Agents


Isolated Agents

PART II

ADAPTIVE MEMETIC ALGORITHMS

Adaptive Memetic Algorithms • Inheritance of memes – Krasnogor and Smith (2001) proposed an inheritance mechanism for learning which localsearch procedure to use at different stages of the evolutionary search

Adaptive Terrain-Based Memetic Algorithms, Azevedo and Gordon – GECCO’09

Adaptive Memetic Algorithms


Meta-Lamarckian Learning [Ong and Keane, 2004] • A framework for selecting best local search – The local methods which leads to higher fitness improvements are rewarded with greater chances of being chosen for subsequent chromosome optimizations


Diffusion Memetic Algorithm (DMA) [Nguyen, Ong and Lee, 2008] • DMA follows the Meta-Lamarckian approach – Individual may be associated or tagged with a meme that will be used to perform local improvement on it – In the first generation, the meme attached with each individual is randomly initialized


PART III

THE ADAPTIVE TERRAIN-BASED MEMETIC ALGORITHMS (TBMA)

Terrain-Based MA (TBMA) • Slight cultural differences are often observed in sparse populations • Individual behavior gradually changes with geographic distance within a population – In the proposed TBMAs, such behaviors are modeled as adjustable Local Search step sizes values spread over the terrain


Terrain-Based MA (TBMA) • Four different proposals – Stationary TBMA (sTBMA) – Local-Adaptive Stationary TBMA (LA-sTBMA) – Hierarchical Adaptive TBMA (HA-TBMA) – Motioner TBMA (mTBMA)


Terrain-Based MA (TBMA) • Four different proposals – Stationary TBMA (sTBMA) – Local-Adaptive Stationary TBMA (LA-sTBMA) – Hierarchical Adaptive TBMA (HA-TBMA) – Motioner TBMA (mTBMA) Algorithm

Meme transmission

Allows movements

Individuals per cell

sTBMA

No

No

One

LA-sTBMA

Yes

No

One

HA-TBMA

Yes

Yes

One

mTBMA

No

Yes

Multiple


Terrain-Based MA (TBMA) • Four different proposals

Adaptive MAs

– Stationary TBMA (sTBMA) – Local-Adaptive Stationary TBMA (LA-sTBMA) – Hierarchical Adaptive TBMA (HA-TBMA) – Motioner TBMA (mTBMA) Algorithm

Meme transmission

Allows movements

Individuals per cell

sTBMA

No

No

One

LA-sTBMA

Yes

No

One

HA-TBMA

Yes

Yes

One

mTBMA

No

Yes

Multiple


Stationary TBMA (sTBMA) [Azevedo et al. 2009 (in press)] • The simplest of the TBMAs – No meme transmission, no allowed movements – One individual per cell

• Local steps values are spread over both axes – Each cell C(i, j) has a pair (1, 2) of values attached to it, composing the parameter space of the algorithm. • 1 – value utilized on the first local search iteration • 2 – value utilized on the second local search iteration Adaptive Terrain-Based Memetic Algorithms, Azevedo and Gordon – GECCO’09

Stationary TBMA (sTBMA) [Azevedo et al. 2009 (in press)]

Local Adaptive-sTBMA (LA-sTBMA) • A self-tuning version of sTBMA – No allowed movements, BUT meme transmission – One individual per cell

• Self-tuning mechanism (every k generations) • Lef F(⋅,⋅) be the sum of fitnesses of all offspring being generated at cell C(x, y) from generation 1 to current generation G:


Local Adaptive-sTBMA (LA-sTBMA) • Self-tuning mechanism (every k generations) • Lef F(⋅,⋅) be the sum of fitnesses of all offspring being generated at cell C(x, y) from generation 1 to current generation G:


Local Adaptive-sTBMA (LA-sTBMA) • Self-tuning mechanism (every k generations) • Lef F(⋅,⋅) be the sum of fitnesses of all offspring being generated at cell C(x, y) from generation 1 to current generation G:

• Compute the adjustment factor i for each cell C(xi, yi):


Local Adaptive-sTBMA (LA-sTBMA) • Self-tuning mechanism (every k generations) • Compute the adjustment factor i for each cell C(xi, yi):



Best neighbor’s coordinates

Coordinates for the i-th individual in the population



• Update the terrain-variables at cell C(xi, yi):




Value of terrain-variable for the i-th individual In the population Adaptive Terrain-Based Memetic Algorithms, Azevedo and Gordon – GECCO’09



Value of terrain-variable for the best neighbor of the i-th individual Adaptive Terrain-Based Memetic Algorithms, Azevedo and Gordon – GECCO’09

Hierarchical Adaptive-TBMA (HA-TBMA) • A self-tuning TBMA with movements – Movements AND meme transmission – One individual per cell

• Swap operator – On each generation, individuals are ranked, compete for locations near the best individual (leader) – Switch positions • if there is a neighbor of lower rank on the shortest path to the leader Adaptive Terrain-Based Memetic Algorithms, Azevedo and Gordon – GECCO’09

Hierarchical Adaptive-TBMA (HA-TBMA) • Swap operator – On each generation, individuals are ranked, compete for locations near the best individual (leader) – Switch positions • if there is a neighbor of lower rank on the shortest path to the leader



– The leader follows the cell which yields the highest succes frequency across all generations Adaptive Terrain-Based Memetic Algorithms, Azevedo and Gordon – GECCO’09


– The leader follows the cell which yields the highest succes successfrequency frequency across all generations Adaptive Terrain-Based Memetic Algorithms, Azevedo and Gordon – GECCO’09

Hierarchical Adaptive-TBMA (HA-TBMA) • Self-tuning mechanism (every k generations) • Update the terrain-variables at cell C(xi, yi):


Hierarchical Adaptive-TBMA (HA-TBMA) • Self-tuning mechanism (every k generations) • Update the terrain-variables at cell C(xi, yi):

The cardinality of the population The rank of the i-th individual The value of terrain-variable In usage by the current leader Adaptive Terrain-Based Memetic Algorithms, Azevedo and Gordon – GECCO’09

Motioner TBMA (mTBMA) • An agent-based TBMA with movements – Movements BUT no meme transmission – Multiple individuals per cell

• Each individual is modeled as agent – Two global movement rules for all agents – All agents are free to join and leave many subpopulations • Agents are denoted as citzens • Subpopulations are denoted as cities Adaptive Terrain-Based Memetic Algorithms, Azevedo and Gordon – GECCO’09

Motioner TBMA (mTBMA)



Useful definitions



Useful definitions



Useful definitions


Motioner TBMA (mTBMA) Movement rules




A steady-state MA sTBMA is called to diffuse the best genes of neighboring cities

The GAKM Algorithm [Azevedo et al., 2008]


The GAKM Algorithm [Azevedo et al., 2008] • The Lee et al. method corresponds to an accelerated version of K-Means algorithm. – It updates codevectors according to

–  is a scale factor parameter which affects the acceleration performed by GAKM on its evolutionary process; –  must lie in [1.0 2.0]; –  = 1.0  standard K-Means; – Look ahead approach aiming at improving convergence. Adaptive Terrain-Based Memetic Algorithms, Azevedo and Gordon – GECCO’09



PART IV

EXPERIMENTAL METHODOLOGY

Experimental methodology • Data set used in experiments – Three 256  256 monochrome images, originally encoded at 8 bits per pixel (bpp)


Experimental methodology • Data set used in experiments – Composition of codevectors for image VQ applications. 220 238   242   230   Example of the construction  205 xi    of an input vector of pixels    from the original image 190  encoded at 8 bpp   195  200   205


Experimental methodology • Distribution of the scale factors over the terrain – For1 and 2, we use the sequence [1.3 1.1 1.0 1.2 1.4] 1.3 1.3

1.1

1.0

1.2

1.4

Correspond to 5  5 terrains, i.e., popsize = 25

1.1 1.0 1.2 1.4


Experimental methodology • For each image and codebok size (N) combination, 20 runs are performed for each TBMA • The methods’ performances are compared with that of a simple Cellular Memetic Algorithm (CMA), in which standard K-Means is applied for each generated offspring


PART V

RESULTS AND DISCUSSION

Results and Discussion


Results and Discussion – All the MAs always outperformed K-means – All TBMAs outperformed the CMA, though not always with statistical significance – The sTBMA, LA-sTBMA and HA-TBMA, are not statistically different in performance – The mTBMA outperformed all other algorithms with statistical significance




Conclusion • The MAs outperformed K-Means in all cases • Among the MAs, the TBMAs outperformed CMA in all cases. • Among the TBMAs, the mTBMA significantly outperformed the other TBMAs and was always the best performing algorithm


Conclusion • The mTBMA was able to exploit dynamicallychanging parameter values – An effective correspondence with the trajectory through the solution space during evolution

• Real-world human cultural dynamics – individuals are allowed to move semi-freely and form cities in a dynamic terrain

• Memetic evolution is most effective when it can adapt dynamically, for the problems we tested Adaptive Terrain-Based Memetic Algorithms, Azevedo and Gordon – GECCO’09

Ongoing works • The modeling of the movement dynamics in mTBMA


Thank you. Questions?

UFPE, Brazil

[email protected]

CSUS, U.S.

[email protected]
