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Paper Review for ENGG6140

Memetic Algorithms

By: Jin Zeng

Shaun Wang

School of Engineering

University of Guelph

Mar. 18, 2002

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ContentsContents

Introduction MA and GABasic MAExamplesConclusions

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IntroductionIntroductionHistory of MAHistory of MA

‘Meme’: word introduced by Richard Dawkins when he describe cultural evolution in his best-seller book “The Selfish Gene’’ (‘76).

“Memetic Algorithms’’ Analogous role of gene but in the field of cultural evolution.‘Memetic Algorithms’ , firstly proposed by P. Moscarto. (‘89)

MA has been widely applied in optimization and solving many NP hard problems successfully.

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Introduction Introduction What is ‘Meme’?What is ‘Meme’?

Meme is the basic unit of cultural transmission, in analagy to gene in genetic transmission.

Meme is replicated by imitation. It can be changed by the owner for adaption. Examples: ideas, clothing fashion and NBA. High-extent variation occurs in cultural

transmission.

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IntroductionIntroductionCultural EvolutionCultural Evolution

When a meme passed between individuals, the individual will adapt the meme as it sees best.

Shared characteristics are not inherited due to simple processes of recombination of previous solutions

Using historical information and an external logic to speed-up the process.

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Introduction Introduction What is MA?What is MA?

MA mimics the process of cultural evolution Characterization of evolutionary algorithms that

can hardly fit the GAs methaphor - no, or small, relation with biology

‘Hybrid GAs’ MAs ‘Scatter Search’ (Glover, ‘77) MAs

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IntroductionIntroductionWhy MA?Why MA?

In general, there are two ways to searching the solution space: Exploration: Investigate the new and unknown

areas in the search space; Exploitation: Make use of knowledge found

before to help find better solutions Both are necessary but contradictory in solving an

optimization problem.

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IntroductionIntroduction Why MA? (cont.)Why MA? (cont.)

The limitation of former algorithms: GA: using parallel searching technique.

Good at avoiding local optima Not well suited for finely tuned search.

LS: improvement heuristics. Find local optima quickly. Highly depending on the start point. Hard to find a global optimum.

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IntroductionIntroduction Why MA? (cont.)Why MA? (cont.)

Combination of GA + Local SearchMA

GA: For exploration; LS: For exploitation; Result: higher efficiency and better effect.

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IntroductionIntroductionCombination MethodsCombination Methods

Two kinds of Combinations:

Baldwin Effect Based Lamarkian Evolution Based

LS is used to modify the structure of the problem. The improvement is not inherited by the children.

The improvement of LS will be inherited in the children.

Wrong in biological evolution. But effective in optimization.

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MA and GAMA and GASimilaritiesSimilarities

Both MA and GA model an evolutionary process. Both MA and GA have the process of

generalization, recombination (crossover) and mutation. Some changes occur in the process.

Both MA and GA use fitness function to evaluate the changes in the process thus both of them are applied in optimization successfully.

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MA and GAMA and GADifference Difference

MA GA Models Cultural Evolution Bio Evolution Basic Unit Meme Gene Flow Process Information Bio Characteristics Evolution Speed Fast Slow Copying Fidelity Low High Mutation Rate High Low

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Basic MABasic MAFlow Chart ProcessFlow Chart Process

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Basic MABasic MAPseudo Code of MAPseudo Code of MA

procedure Memetic Algorithm(); begin Generalization(); repeat Crossover(); Mutation(); P := select (P); if P converged then );(: PdLSMutationAnP until terminate=true; end;

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Basic MABasic MAGeneralizationGeneralization

Generalization ( ) begin for 1:j to popsize do ();: lutionGenerateSoi );(: ihLocalSearci Add individual i to P endfor end

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Basic MABasic MACrossoverCrossover

Crossover ( ) begin for 1:i to crossover# do Select two parents Pii ba , randomly; );,(: bac iiCrossoveri );(: cc ihLocalSearci

Add individual ci to P ; endfor end

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Basic MABasic MAMutationMutation

Mutation ( ) begin for 1:i to mutations# do Select and individual Pi randomly );(: iMutationim );(: mm ihLocalSearci

Add individual mi to P ; endfor end

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Basic MABasic MALocal SearchLocal Search

Full Local Search and Partial Local Search Demo of FLS

Y Original Solution

Solution after Recombination or Mutation

Solution after Local Search

X

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Basic MABasic MADemonstration of MADemonstration of MA

Example Problems: Y= f(x);• Parameters of MA:• Population: 5;• Xover rate:0.4; (# of Xover: 5x0.4=2)• Mutation rate: 0.4; (# of Mutation: 5x0.4=2)• Local Search: Full

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Basic MABasic MADemonstration of MA (Continued)Demonstration of MA (Continued)

Y

X

Random Generalized Solution

Solutions After Local Search

X

Solutions After Mutation

Solutions After Crossover

Solutions After Local SearchY

A. Generalization and LS

B. Crossover and Mutation

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Basic MABasic MADemonstration of MA (Continued)Demonstration of MA (Continued)

Y

X

Solutions After Crossover

X

Y

Solutions After Local SearchSolutions After CrossoverSolutions After MutationSolutions After Local Search

C. Local Search after Crossover and Mutation

D. Population Selection

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Basic MABasic MAEffect of Crossover and MutationEffect of Crossover and Mutation

Both can be used for exploring the search space by “jumping” to new regions to start new local search;

Crossover

Searching the region between two or more specified points; Mutation

Searching the undirected region randomly;

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Basic MABasic MAAdvantage of MAAdvantage of MA

Combining the advantages of GA and LS while avoid the disadvantages of both;

GA ensures wide exploration in the solution space Through local search, the space of possible

solutions can be reduced to the subspace of local optima.

When the scale of problem increases, the advantages becomes remarkable.

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Basic MABasic MADisadvantage of MADisadvantage of MA

The proportion of computations used in exploration and exploitation depends on the real optimization problem.

It is hard to determine the best depth of local search,.

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MA ExamplesMA ExamplesSome Implementation Examples of MASome Implementation Examples of MA

Quadratic Assignment Problem (QAP) Traveling Salesman Problem (TSP) Vehicle Routing Graph Partitioning Scheduling The Knapsack Problem

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MA ExamplesMA ExamplesApply Local Search to MA in QAPApply Local Search to MA in QAP

For any permutation solution being explored, the procedure for the local search be executed once or several times –– partial local searchpartial local search (PLS) (PLS)

The procedure for the local search be repeated many times until no further improvement is possible –– full local searchfull local search (FLS) (FLS)

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MA ExamplesMA ExamplesDerived Two different MAs for QAPDerived Two different MAs for QAP

PGAPGA –– starts with an initial population of randomly generated individuals. For each individual, after xover and mutation, a PLS is performed.

FGAFGA –– relies on FLS, full local search are carried out on all individuals at the beginning and at the end of a SGA run.

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MA ExamplesMA ExamplesBriefly Steps involved for the PGABriefly Steps involved for the PGA

The steps for PGA is same as the Basic MA. The procedures for the local search only executed

once or several times after each xover and mutation.

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MA ExamplesMA ExamplesBriefly Steps involved for the FGABriefly Steps involved for the FGA

1. Randomly generate an initial population. Perform FLS on each individual.

2: While terminating criterion is not reached, continue with procedures as spelled out for the SGA.

3: Perform FLS on the best solution and output the final solution.

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MA ExamplesMA ExamplesComparison of FGA and PGAComparison of FGA and PGA

The effectiveness of FLS depends on the starting solution and the exchange routine.

PLS can be carried out more frequently, the algorithm is therefore able to spread out the search by exploring many small-localized regions, thus reducing the likelihood of the algorithms being trapped in a local optimum.

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MA ExamplesMA ExamplesComparison of FGA and PGA (cont.)Comparison of FGA and PGA (cont.)

As the size of the problem scales up, it is difficult to carry out FLS freely due to its great computational intensity.

PLS is carried out for almost all the individuals in addition to the SGA evolutionary mechanisms, the capability of the SGA in evolving towards fitter individuals is greatly enhanced.

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MA ExamplesMA ExamplesComparison of FGA and PGA (cont.)Comparison of FGA and PGA (cont.)

FLS limits the exploratory capability of the SGA, it will reduce the chance of the FGA reaching the global optimum.

PGA has a greater chance of obtaining the global optimum as compared to FGA.

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MA ExamplesMA ExamplesComparison of a typical run on problem Els19 Comparison of a typical run on problem Els19

for SGA, PGA and FGAfor SGA, PGA and FGA

Average Cost

Generation1.6x107

1.8x107

2.0x107

2.2x107

2.4x107

2.6x107

2.8x107

3.0x107

10 110 210 310 410

-Optimum

-FGA-PGA

-SGA

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ConclusionConclusion

MA provides a more efficient and more robust way to the optimization problem.

MA combines global and local search by using EA to perform exploration while another local search method performs exploitation.

MA can solve some typical optimization problem where other meta-heuristics have failed.

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Thank you!Thank you!