Lecture 10: Memetic Algorithms - I. An Introduction to Meta-Heuristics, Produced by Qiangfu Zhao (Since 2012), All rights reserved

Transcription

1 Lecture 10: Memetic Algorithms - I Lec10/1

2 Contents Definition of memetic algorithms Definition of memetic evolution Hybrids that are not memetic algorithms 1 st order memetic algorithms 2 nd order memetic algorithms Summary Lec10/2

3 Definition of Memetic algorithms - 1 Heuristic algorithm: use heuristics to increase search efficiency Hill climbing, best first, A* algorithm, Meta-heuristic algorithms: use some heuristics for local search, and some others to control the search process, to increase the efficacy, or opportunity of obtaining the global optimum. Tabu search, simulated annealing, genetic algorithms, particle swarm optimization, ant colony optimization, Lec10/3

4 Definition of Memetic algorithms - 2 Hyper-heuristic algorithms: hybrid the heuristics in different ways, not limited by levels : GA + TS, GA + PSO, Memetic algorithms: Hyper-heuristic algorithms (current definition) Lec10/4

5 Definition of Memetic algorithms 3 Proper hybridization of different heuristics can improve the efficiency and the efficacy simultaneously. Proper hybridization can provide reasonably good solutions for large scale and complex problems, with limited computing resources (time, computing power, etc.). Lec10/5

6 Definition of Memetic algorithms 4 The term meme was produced by Dawkins to mean a unit of imitation in cultural transmission which in some aspects is analogues to the gene. Some good local search strategies can be considered as memes (cultures), and can be shared by different search agents. It is for this reason that Moscato and researchers in this field has named hyper-heuristic algorithms as memetic algorithms (MAs). Lec10/6

7 Definition of Memetic algorithms 5 Usually, an MA contains a population of search agents, which is often implemented by GA or some other population based heuristic algorithm. The agents can produce or find good memes (i.e. local search heuristics) through evolution or innovation, and share these memes with other agents. If the memes are produced (e.g. evolved) and shared (imitated) properly, MA can obtain global optimum with high opportunity. Lec10/7

8 Definition of Memetic algorithms 6 So far, MAs have been applied very successfully to solving large scale complex problems, such as Classical NP problems: graph partitioning, multidimensional knapsack, travelling salesman problem, quadratic assignment problem, minimal graph coloring, etc. Other applications: neural network training, pattern recognition, robotic motion planning, circuit design, machine scheduling, automatic timetabling, clustering of gene expression profiles, etc. Lec10/8

9 What is the problem? An MA should have the ability to produce the memes and to preserve good memes through evolution/adaptation. Many MAs studied in the literature, however, DO NOT HAVE this ability. Definition of MA has been wrong! Correct definition should be Memetic algorithm = memetic (culture, mental) evolution + genetic (agent, body) evolution Lec10/9

10 Definition of memetic evolution 1 Darwin's theory of evolution is universal, and is not limited to evolution of biological lives on the earth. The universal Darwinism is also applicable to evolution of cultures. For the latter, Dawkins introduced the term meme to represent a unit of imitation in cultural transmission which in some aspects is analogues to the gene. Memes, according to Dawkins, are a kind of replicators that can evolve. That is, they have the three fundamental properties for evolution, namely variation, selection, and retention. Lec10/10

11 Definition of memetic evolution 2 Similar to gene, genotype, and phenotype, we have meme, memotype, and memeplex (short for meme complex). A group of memes form a memotype; and a memotype defines a memeplex. Example: To make an origami airplane, a kindergarten teacher may tell the children how to do, step by step, while she makes a demonstration. Here, the ways for selecting the paper, folding the corners, folding the edges, etc. form the memeplex; the instructions form the memotype; and the words used in the instructions are memes. Lec10/11

12 Definition of memetic evolution 3 Children in group A may try to remember what their teacher says, memorize the instructions, and then make the origami airplane in the same way. Children in group B may imitate their teacher step by step, try to describe the process using their own languages and memorize, and then make the paper airplanes in similar ways. In either case, the memotype and the memeplex can be defined using speaking language, and the memes are the words or phrases contained in the memotype or memeplex. Usually, the memeplex is more complex than memotype. Ex. in the case of learning to ride a bicycle, the memotype can be as simple as: just practice, and you can ride it!, but the memeplex must be described using some non-spoken language (tacit knowledge). Lec10/12

13 fitness of memes - 1 Good memes form good memotypes, good memotypes form good memeplexes, and many good memeplexes together can form a good brain (mental). A person with a good mental brain can be very clever, and can be more successful than others. A successful person has more chance to be imitated or learned by others. Through imitation or learning people wish to be equally or more successful. Thus, good memes can be passed from brain to brain easily, and can survive for a long time. Lec10/13

14 fitness of memes - 2 Similar to evaluation of a gene, the fitness of a meme is evaluated indirectly based on the fitness of the memotypes containing this meme. The memotypes in turn are evaluated by the fitness of the corresponding memeplexes. Any methods used for evaluating genes based on genotypes and phenotypes can be used to evaluate memes based on memotypes and memeplexes. Ι αµ α γοοδ ανδ χαν ηελπ ψου ανγελ Lec10/14

15 fitness of memes - 3 Only when a memeplex is meaningful, the corresponding memotype can be accepted more easily by many brains. We accept some memotypes if we believe (through observations) that the corresponding memeplexes are useful. However, what we believe may not be true or correct. In the process of memetic evolution, some memotypes may become so clever that they can be easily passed and accepted by many brains and can grow-up inside the brains gradually later. These memotypes may not be useful or even harmful to our humans. But we may accept them before realizing their real values. Lec10/15

16 fitness of memes - 4 In addition, the fitness of a meme does not depend (only) on the fitness of the human body. People with weak bodies may have strong mental brains, which are constructed by strong memeplexes. Clever memes do seek for more chances to immigrate to brains with strong bodies so that they can have more opportunity to influence other people and thus have more chances to spread. Clever memes also tries to govern the brains in which they live to keep the bodies health and strong, so that they can have longer time to seek for chances to spread. Lec10/16

17 Process of memetic evolution - 1 The basic evolution process of memes is the same as that of genes. Imitation or learning is the fundamental memetic operation. Imitation is the process to learn or emulate the leader(s) or the parent(s); Imitation is a crossover operation that recombines the original memotype or memeplex with others (social factor); Imitation can also be a mutation operator to change one memotype of memeplex into another (personal factor). Good memes are evolved as good building-blocks. Lec10/17

18 Process of memetic evolution - 2 When a memotype is transmitted to a brain, memeplexes (agents) already living there may not accept this new comer, at least they may not accept the new comer as is. Existing agents will make a collective decision, force the new comer to make some changes (mutation), and then accept. As a result, the same memotype (and thus the corresponding memeplex) can have different variations in different brains. Memotypes that cannot find any place to go will die and disappear (selected against). Lec10/18

19 Process of memetic evolution - 3 There are many memeplexes, and they can exist in different forms. Some are living in the human brains (the cyber-space formed by the brain), some are sleeping in the libraries, and some are wandering around. Each person accepts some memeplexes (exist in the brains or other places) that he/she believes useful, recombines them with the memeplexes already in the brain, produces variations, and posts them to some mass media (e.g. books, papers, reports, etc.) if he/she believes that the new memeplexes are useful to other people. Lec10/19

20 Process of memetic evolution - 4 We human beings are one of the media for receiving, carrying, reproducing, amplifying, and distributing the memeplexes. In certain sense, we are just the computing machines for the memeplexes to evolve. There is no any evidence that memetic evolution is for human. In the future the memeplexes may find better computing machines (e.g. the cyber-space) to evolve and forget completely the old machines they are using now. Lec10/20