Lecture 3 Evolutionary Algorithms (I) & Metaheuristics and Parallelism (II)

Transcription

1 Bio-inspired Optimization Techniques in Parallel and Distributed Systems - Biologisch inspirierte Optimierungstechniken in parallelen und verteilten Systemen Lecture 3 Evolutionary Algorithms (I) & Metaheuristics and Parallelism (II)

2 Evolutionary Computation Inspiration Darwinism Transmutation of species Evolution Origin of species 1809 Altering of species Natural selection

3 Evolution through the Giraffe Example

4 Alteration of Species Species were (are) able to create new species never seen so far Reproduction (sexual reproduction) With another (or same specie) having different genetic material Pure alterations Sometimes, because of hazard, some modification in the genetic information (DNA) of a given specie is modified Giving rise to advantages Better capabilities than original genetic information

5 Natural Selection Mechanism by which evolution of species takes place In every environment, there are species which are better adapted than others In difficult situations, better adapted species have a higher probability to survive than others

6 Evolution Combines alteration of species and natural selection Some species will evolve altering its genetic material and become well adapted to the environment They will have higher chances of surviving than others At the end, new species better adapted to the environment will appear This cycle will continue forever

7 Evolutionary Computation How is possible to create an optimization technique based on these principles? What do we need? We need an environment We need something like genetic information (DNA) We need something to measure how well-adapted is a solution We need populations of individuals living in the environment We need a way of altering solutions Recombination Pure alteration We need a natural selection mechanism

8 Evolutionary Computation Environment? The target problem Genetic information or DNA? Problem representation Adaptation of solutions to the environment? Fitness function (for now, the function/problem value) Reproduction We should define a way to create new solutions given two (or more) parents Pure alteration Define a way of altering a solution

9 Evolutionary Computation Evolutionary algorithms are methods inspired by Alteration of species Natural selection They apply Recombination of solutions Alteration of solutions Selection Having all these ideas in mind, it is really easy to work out a generic skeleton for an evolutionary computation algorithm

10 Evolutionary Computation Pseudo-code of a generic evolutionary algorithm 1. P generateinitialpopulation(); // creation 2. evaluate(p); //assign fitness to all the solutions 3. while!(terminationcriteria()) do 4. P' recombine(p); 5. P'' mutate(p'); 6. evaluate(p''); 7. P select(p,p''); 8. end 9. return best solution found so far

11 Types of Evolutionary Computation Algorithms Genetic Algorithms Evolutionary Strategies Genetic Programming Evolutionary Programming Differential Evolution Some people also consider Ant Colony Optimization (ACO) Particle Swarm Optimizers (PSO) Scatter Search (SS)

12 Types of Evolutionary Computation Differences arise In their main use Representation Operators used

13 Types of Evolutionary Computation Genetic Programming Note (Genetic Programming!= Genetic Algorithm) Every solution is a computer program Tree representation Idea: Evolve complete programs trying to optimize different goals Speed up Robustness Features Example Design of distributed algorithms

14 Types of Evolutionary Computation Genetic Algorithm Most famous one Widely used in engineering and research Initially developed only for combinatorial programs Solutions representation could be whatever representation Initially was only for binary strings Disclaimer!!! A blind application of a genetic algorithm will probably result in poor and slow results

15 Types of Evolutionary Computation Evolutionary Programming The idea is similar to genetic programming Programs to be evolved Here the structure of the problem is fixed No tree representation Only some parameters in the representation have to be optimized

16 Types of Evolutionary Computation Evolutionary Strategies It only uses alteration No recombination of solutions Still a population based metaheuristic

17 Genetic Algorithms Originally were conceived only for binary string representation We are going to develop all the knowledge about genetic algorithms using binary string, however: Permutations Real variables Vectors of real variables are also possible!

18 Some Terminology Every solution to the problem is called individual A set of individual is called population We refer to a solution (individual) representation as genotype or chromosome We refer to the value of a solution (i.e., y, where y = f(x) and x our solution) as phenotype We refer to the measure of how well a solution is adapted as fitness The recombination operator is called crossover The alteration operator is called mutation

19 Crossover Operator Once we have a representation we need to define a way to combine (recombination) two solutions A, and B A B A and B are called parents in the crossover terminology

20 Crossover Operator Basic idea some parts of A represent good values for a given feature, function Some parts of B represent good values for another different feature or function A B

21 Crossover Operator Basic idea The combination of those parts could produce a good solution in these two (or more) different features New The new solution is called offspring

22 Different Types of Crossover Single Point Crossover: choose a cutting point in both parents. Create a new solution which contains the first half of one parent, and the second half of the other A B new

23 Different Types of Crossover Two Points Crossover: choose two cutting points. Use the first part of the first parent, the second of the second parent, and the third again from the first parent A B new

24 Different Types of Crossover Uniform Crossover: Combine, at random, parts of the first and second parent A B new

25 Mutation Operator Basic idea We have a solution A, which is good in some parts but... would it be possible to get a better solution (better adapted to the environment)? A

26 Mutation Operator Basic idea make a small modification in A with the aim of producing a better adapted solution A B

27 Bit Flip Mutation Idea: flip the value of a bit A A How many bits should be modified? Every bit is modified with a probability 1/L L is the string length In average only one bit is modified

28 Natural Selection Where does it takes place the natural selection in a Genetic Algorithm? 1. P generateinitialpopulation(); // creation 2. evaluate(p); //assign fitness to all the solutions 3. while!(terminationcriteria()) do 4. P' recombine(p); 5. P'' mutate(p'); 6. evaluate(p''); 7. P select(p,p''); 8. end 9. return best solution found so far

29 Natural Selection Where else? P' recombine(p); Selection also takes place through the selection of individuals to be recombined (i.e., selection of parent solutions) Which solutions are selected to be recombined? The best ones? The worse ones? Does it matter? Different selection mechanisms Roulette based Binary tournament K tournament

30 Genetic Algorithm Behavior Two key concepts Intensification: exploitation of already known good solutions Diversification: try solutions not visited so far High intensification means fast convergence towards the optimal solutions But it could mean a local optimum High diversification means lower possibility of hitting a local minimum But also low convergence speed towards the global minimum A trade-off between these two concepts is required However it highly depends on the problem

31 Sources of Intensification and Diversification on a GA Intensification Selection mechanism Crossover operator Diversification Mutation operator Intensification and diversification Population Size

32 Further Issues When does a GA stop? What happens when all the individuals in the population are identical? What happens if we never update the population with new individuals? What happens when we include an already-known good solution in the initial population? How can we accelerate the convergence speed of a GA?

33 When does a GA stop? After generating a maximum number of offspring After computing the desired solution The optimal This we do not know (only in our experiments) Meeting some criteria Does a GA stop at some moment by itself? When finding a global minimum When no new (better) solutions are produced

34 What happens when all the individuals are identical? The crossover operator has no effect The only chance of producing better solutions is by means of the mutation operator The mutation operator modifies every bit with a probability 1/N (N=length of the string) In average, after N movements (with an identical population) all the different possibilities have been produced The algorithm stops!

35 What happens if we do not update the population with new individuals? The crossover operator has no effect neither The mutation operator has no effect Natural selection Has only effect when selecting the parents Taking all these things into account It behaves like a Random Search But this effects also appears if we update the population in a naive way

36 What happens when including a good solution in the population? That solution will have a high probability of being selected as a parent in the crossover Its genetic information will be transferred with high probability Many offspring solutions will be produced using that solution as parent Convergence towards that solution Is that good or bad?

37 How can we accelerate a GA? Obviously, including a good solution in the initial population Applying a local search after crossover + mutation Not a complete local search but some steps at least Changing representation This means new crossover operators New mutation operators Parallelism!

38 You must know... It is very easy to develop a basic genetic algorithm It is very easy to apply it You do not need to be a genius to do it Xin Yao (Best quote ever I heard about this topic) however If you do not think carefully your representation, your crossover, and your mutation operators Do not expect your GA to perform as the best and fastest technique in the world

39 Parallel and distributed systems overview It is a matter of study in many subjects Plenty of books and scientific work about this topic What do we need to know? We need only some basic concepts about parallel architectures to see how they match the requirement of metaheuristic techniques

40 Parallel Computing Basic Idea Many computations/calculations are carried out simultaneously How do we do it? Parallel architectures Today s situation Different kind of parallel architectures Different capabilities and features Flynn's classification

41 Parallel Computing

42 Parallel Architectures Shared memory All the threads have access to the data Fast data accesses Scalability? Other classifications: Parallel Architectures 5-7 years ago only possible in expensive, complex, dedicated machines Today Easy to have 8 cores in our personal computers (cheap) In more complex and dedicated machines up to cores using a shared memory system Easy access for practically everyone Still room for researching in parallel metaheuristics in those systems Easily programmable with OpenMP or threads

43 Parallel Architectures Distributed memory Data is private to some processors Data exchange using message passing Highly scalable Other classifications: Parallel Architectures Advances in technology and communication networks make it possible and cheap Some example of this kind of systems are Clusters GRID Cloud Huge room for researching in those topics with parallel metaheuristics Example of programming languages for these systems are MPI, RMI, frameworks like ProActive (still alive?), Condor Master-Worker, or similar

44 Parallel Architectures GPU Not so many years ago, graphic processors were complex to program Few people interested in doing general purpose computations in GPU The appearance of systems like CUDA or OpenCL brought an easy way of doing it It can be classified under the category of SIMD (simple instruction multiple data) GPU consist of a bunch of multi-processors which allow to execute thousand of threads simultaneously Shared memory system but Other classifications: Parallel Architectures many schemes like Multi-GPU or Cluster of GPU have been used with success. CUDA 5.0 and OpenCL 3.0 may help pushing forward in that direction

45 Parallel Architectures and Metaheuristics Goal when designing a parallel metaheuristic Approach 1 Analyze the sequential behavior, identifying parts that can be parallelized or simply to figure out parallel extensions Identify which architecture suits better with the new parallel metaheuristic Approach 2 We have a parallel architecture Analyze how a given technique can be extended in order to take advance of our hardware

46 Measuring the Performance of Parallel Metaheuristics Once you have your parallel metaheuristic and the parallel architecture where it will be executed? How to measure the performance of our parallel implementation? Exact technique: time reduction when computing the optimal solution Approximation technique: time reduction when computing the near optimal solution? Near optimal solution can be different We can even find a better near optimal solution

47 Parallel Architectures and Metaheuristics Exact techniques Theoretical analysis Allow us to characterize the order to which an algorithm belong e.g., O(n), O(n 2 ), O(n Log(n)), Approximation techniques Lack of theoretical models Empirical analysis is performed To execute the parallel and sequential technique taking measurements about the execution time

48 Speed-up Basic definition: Ratio between the time on a single processor (t 1 ) and the time of the parallel version (t n ) Speed-up : t 1 / t n Stochastic methods (possible non-deterministic time) Speed-up : E[t 1 ] / E[t n ] where E[x] denotes the mean of x, and x a distribution of different values (example, the times of k different executions)

49 Speed-up Issues How to measure the time? Uni-processor system CPU time Typically exclude input/output data System overhead activities Multi-processor system Wall-clock time Communication should be taken into account (price to pay for parallelizing a given algorithm) Having in mind that t 1 and t n are measured we can find different taxonomies for speed-up measures Strong speed-up Weak speed-up with solution stop Speed-up with predefined effort Proposed by E. Alba et al.

50 Speed-up Taxonomy Strong speed-up To compare the parallel run time with the best-so-far sequential algorithm Weak speed-up To compare the parallel version of an algorithm with its own sequential version When to stop? When the searched solution (or a solution of a given quality is found) After a predetermined number of evaluations has been carried out

51 Speed-up Taxonomy Stop after a predefined computational effort Sequential algorithm find a solution a Parallel algorithm find a solution b Is it fair to compare then? NO Many authors discard this kind of speed-up since it is against the aim of the speed-up to compare algorithms yielding different results or accuracy

52 Super linear Speed-up Several authors have reported super lineal speed-up Its existence is still controversial How it is possible to get super-lineal speed-up? Implementation source The algorithm being run on one processor is inefficient somehow Numerical source The order in which the search is done is changed Physical source More CPUs, more cache, more memory. A metaheuristic technique may take advantage of these results

53 Computational Effort of Parallel Metaheuristics Two key factors: superior (better) solutions and speed of computation Speed of computation Number of evaluations Drawback: Evaluations can take different times Wall time Drawback: Many different implementations Best option seems to be to use the ratio evaluations / time to a solution

54 Parallel and Sequential Metaheuristics: Same principle, Different behavior The behavior of a parallel metaheuristic is many times different to its sequential counterpart Different ways of navigating the search space Every parallel instance could work in a reduced portion of the search space Introduces diversity etc., Parallelism is then a way not only to reduce time but also as a mean for obtaining possible better solutions That a sequential implementation could probably not reach

55 Parallel Trajectory-based Metaheuristics Three main models Parallel Multi-start Parallel moves Move acceleration

56 Classical Local Search Method Pseudo-code of a Local Search Method 1. s initialsolution(); // start with a complete solution 2. n(s) getneighborhood(s); 3. s' getbetterthan(n(s),s) 4. while (s'!= null) 5. s s' 6. n(s) getneighborhood(s) 7. s' getbetterthan(n(s),s); 8. end

57 Parallel multi-start model Simultaneously launching several local searches for computing better and robust solutions Heterogeneous or homogeneous The different searches can collaborate between then or not Search can start from the same initial solution Using different neighborhood for example Using different parameters

58 Parallel moves model Similar to a master-slave model Every solution in the neighborhood is evaluated in a different machine Does not change the behavior of the algorithm The sequential counterpart will reach the same results using a higher computational time

59 Move acceleration model The quality of every movement is evaluated in parallel The evaluation function can be parallelized The whole evaluation of the function can be seen as an aggregation of different small sub-evaluations Do not get it wrong In parallel moves, the whole evaluation of different solutions of the neighborhood are made in parallel. In this model, only the evaluation of one solution is

60 Parallel Variable Neighborhood Search Basic Idea of the technique: Successively explore a set of predefined neighborhood to provide a better solution How can we parallelized the VNS? Multi-start model Parallelizing the local search phase Using a parallel multi-start mode Parallel cooperative multi-start model

61 Parallel Variable Neighborhood Search: Examples Parallel multi-start methods Parallel evaluations of solutions Parallel neighborhood exploration Hierarchical solution

62 Parallel evaluation of solutions

63 Parallel Neighborhood Exploration

64 Parallel Hierarchical Neighborhood Exploration