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Competitive coevolution through evolutionary complexification

Competitive coevolution through evolutionary complexification
Competitive coevolution through evolutionary complexification

Competitive Coevolution through Evolutionary Complexi?cation

Kenneth O.Stanley and Risto Miikkulainen

Department of Computer Sciences

The University of Texas at Austin

Austin,TX78712USA

kstanley,risto@https://www.doczj.com/doc/4e1309782.html,

Technical Report UT-AI-TR-02-298

December,2002

Abstract

Two major goals in machine learning are the discovery of complex multidimensional solutions and con-

tinual improvement of existing solutions.In this paper,we argue that complexi?cation,i.e.the incremental

elaboration of solutions through adding new structure,achieves both these goals.We demonstrate the power

of complexi?cation through the NeuroEvolution of Augmenting Topologies(NEAT)method,which evolves

increasingly complex neural network architectures.NEAT is applied to an open-ended coevolutionary robot

duel domain where robot controllers compete head to head.Because the robot duel domain supports a wide

range of sophisticated strategies,and because coevolution bene?ts from an escalating arms race,it serves

as a suitable testbed for observing the effect of evolving increasingly complex controllers.The result is an

arms race of increasingly sophisticated strategies.When compared to the evolution of networks with?xed

structure,complexifying networks discover signi?cantly more sophisticated strategies.The results suggest

that in order to realize the full potential of evolution,and search in general,solutions must be allowed to

complexify as well as optimize.

1Introduction

Evolutionary algorithms are a class of algorithms that can be applied to open-ended learning problems in

Arti?cial Intelligence.Traditionally,such algorithms evolve?xed-length genomes under the assumption

that the space of the genome is suf?cient to encode the solution.A genome containing genes encodes

a single point in an-dimensional search space.In many cases,a solution is known to exist somewhere in that space.For example,the global maximum of a function of three arguments must exist in the three

dimensional space de?ned by those arguments.Thus,a genome of three genes can encode the location of

the maximum.

However,many common structures are de?ned by an arbitrary number of parameters.In particular,

those solution types that can contain a variable number of parts can be represented by any number of genes.

For example,the number of parts in neural networks,cellular automata,and electronic circuits can vary

(Miller et al.200a;Mitchell et al.1996;Stanley and Miikkulainen2002d).In fact,two neural networks with

different numbers of connections and nodes can approximate the same function(Cybenko1989).Thus,it is not clear what number of genes is appropriate for solving a particular problem.Because of this ambiguity, researchers evolving?xed-length genotypes must use heuristics,such as smaller neural networks general-izing better than larger ones,in order to estimate a priori the appropriate number of genes to encode such structures.

A major obstacle to using?xed-length encodings is that heuristically determining the appropriate num-ber of genes becomes impossible for very complex problems.For example,how many nodes and connec-tions are necessary for a neural network that controls a ping-pong playing robot?Or,how many bits are needed in the neighborhood function of a cellular automata that performs information compression?The answers to these questions can hardly be based on empirical experience or analytic methods,since little is known about the solutions.One possible approach is to simply make the genome extremely large,so that the space it encodes is extremely large and a solution is likely to lie somewhere within.Yet the larger the genome,the higher dimensional the space that evolution needs to search.Even if a ping-pong playing robot lies somewhere in the10,000dimensional space of a10,000gene genome,searching such a space may take prohibitively long.

Even more problematic are open-ended problems where phenotypes are meant to improve inde?nitely and there is no known?nal solution.For example,in competitive games,estimating the complexity of the “best”possible player is dif?cult because making such an estimate implicitly assumes that no better player can exist.How could we ever know that?Moreover,many arti?cial life domains are aimed at evolving increasingly complex arti?cial creatures for as long as possible(Maley1999).Fixing the size of the genome in such domains also?xes the maximum complexity of evolved creatures,defeating the purpose of the experiment.

In this paper,we argue that the right way to evolve arbitrarily structured phenotypes is to start evolution with a population of small,simple genomes and systematically complexify solutions over generations by adding new genes.That way,evolution begins searching in a small easily-optimized space,and adds new dimensions as necessary.This approach is more likely to discover highly complex phenotypes than an approach that begins searching directly in the intractably large space of complete solutions.In fact,natural evolution has itself utilized this strategy,occasionally adding new genes that lead to increased phenotypic complexity(Martin1999;Section2).In biology,this process is called complexi?cation,which is why we use this term to describe our approach as well.

When a good strategy is found in a?xed-length genome,the entire representational space of the genome is used to encode it.Thus,the only way to improve it is to alter the strategy,thereby sacri?cing some of the functionality learned over previous generations.In contrast,complexi?cation elaborates on the existing strategy by adding new structure without changing the existing representation.Thus the strategy does not only become different,but the number of possible responses to situations it may face increases(?gure1).

This idea is implemented in a method for evolving increasingly complex neural networks,called Neu-roEvolution of Augmenting Topologies(NEAT;Stanley and Miikkulainen2002b,c,d).NEAT begins by evolving networks without any hidden nodes.Over many generations,new hidden nodes and connections are added,resulting in the complexi?cation of the solution space.This way,more complex strategies elabo-rate on simpler strategies,focusing search on solutions that are likely to maintain existing capabilities.We use NEAT to demonstrate the power of complexi?cation.

NEAT was tested in a competitive robot control domain with and without complexi?cation.Coevolu-tion was used to evolve robot controllers against each other to?nd better strategies.We chose this domain because it is open-ended;there is no known optimal strategy but it is possible to come up with increasingly more sophisticated strategies inde?nitely.The main results were that(1)evolution did complexify when possible,(2)complexi?cation led to elaboration,and(3)signi?cantly more sophisticated and successful

Figure1:Alteration vs.elaboration example.A robot(depicted as a circle)evolves to avoid an obstacle.In the alteration scenario(top),the robot?rst evolves a strategy to go around the left side of the obstacle.However,the strategy fails in a future generation when the obstacle begins moving to the left.Thus,the robot alters its strategy by evolving the tendency to move right instead of left.However,when the obstacle later moves right,the new,altered, strategy fails because the robot did not retain its old ability to move left.In the elaboration scenario(bottom),the original strategy of moving left also fails.However,instead of altering the strategy,it is elaborated by adding a new ability to move right as well.Thus,when the obstacle later moves right,the robot still has the ability to avoid it by using its original strategy.Elaboration is necessary for a coevolutionary arms race to emerge and it can be achieved through complexi?cation.

strategies were evolved with complexi?cation than without.These results imply that complexi?cation al-lows coevolution to continually elaborate on successful strategies,resulting in an arms race that achieves a signi?cantly higher level of sophistication than is otherwise possible.

We begin by reviewing biological support for complexi?cation,as well as past work in coevolution, followed by a description of the NEAT method,and experimental results.

2Background

2.1Complexi?cation in Nature

Mutation in nature not only results in optimizing existing structures:New genes are occasionally added to the genome,allowing evolution to perform a complexifying function over and above optimization.In addi-tion,complexi?cation is protected in nature in that interspeci?c mating is prohibited.Such speciation creates important dynamics differing from standard GAs.In this section,we discuss these important characteristics of natural evolution as a basis for our approach to utilize them computationally in genetic algorithms.

Gene duplication is a special kind of mutation in which one or more parental genes are copied into an offspring’s genome more than once.The offspring then has redundant genes expressing the same proteins. Gene duplication has been responsible for key innovations in overall body morphology over the course of natural evolution(Amores et al.1998;Carroll1995;Force et al.1999;Martin1999).

A major gene duplication event occurred around the time that vertebrates separated from invertebrates. The evidence for this duplication centers around HOX genes,which determine the fate of cells along the anterior-posterior axis of embryos.HOX genes are crucial in shaping the overall pattern of developmental in embryos.In fact,differences in HOX gene regulation explain a great deal of arthropod and tetrapod diversity (Carroll1995).Amores et al.(1998)explain that since invertebrates have a single HOX cluster while vertebrates have four,cluster duplication must have signi?cantly contributed to elaborations in vertebrate body-plans.The additional HOX genes took on new roles in regulating how vertebrate anterior-posterior axis develops,considerably increasing body-plan complexity.Although Martin(1999)argues that the additional clusters can be explained by many single gene duplications accumulating over generations,as opposed to massive whole-genome duplications,researchers agree that gene duplication contributed signi?cantly to important body-plan elaboration.

A detailed account of how duplicate genes can take on novel roles was given by Force et al.(1999):Base pair mutations in the generations following duplication partition the initially redundant regulatory roles of genes into separate classes.Thus,the embryo develops in the same way,but the genes that determine overall body-plan are con?ned to more speci?c roles,since there are more of them.The partitioning phase completes when redundant clusters of genes are separated enough that they no longer produce identical proteins at the same time.After partitioning,mutations within the duplicated cluster of genes alter different steps in development than mutations within the original cluster.In other words,duplication creates more points at which mutations can occur.In this way,developmental processes complexify.

In order to implement this idea in arti?cial evolutionary systems we are faced with two major challenges. First,such systems evolve variable-length genomes,which can be dif?cult to cross over without losing in-formation.For example,depending on when duplications occurred in the ancestral histories of two different genomes,the same gene may exist at different positions.Conversely,different genes may exist at the same position.Thus,arti?cial crossover may lose essential genes through misalignment.Second,it may be dif-?cult for a variable-length genome GA to?nd innovative solutions;Optimizing many genes takes longer than optimizing only a few,meaning that more complex genotypes may be eliminated from the population before they have a suf?cient opportunity to be optimized.

How has nature solved these problems?First,nature has a mechanism for aligning genes with their proper counterparts during crossover,so that data is not lost nor obscured.This alignment process has been most clearly observed in E.coli(Radding1982;Sigal and Alberts1972).A special protein called RecA takes a single strand of DNA and aligns it with another strand by attaching the strands at genes that express the same traits,which are called homologous genes.The process by which RecA protein aligns homologous genes is called synapsis.In experiments in vitro,researchers have found that RecA protein does not complete the process of synapsis on fragments of DNA that are not homologous(Radding1982).

Second,innovations in nature are protected through https://www.doczj.com/doc/4e1309782.html,anisms with signi?cantly divergent genomes never mate because they are in different species.Thus,organisms with larger genomes compete for mates among their own species,instead of with the population at large.That way,organisms that may initially have lower?tness than the general population still have a chance to reproduce,giving novel concepts a chance to realize their potential without being prematurely eliminated.

It turns out complexi?cation is also possible in evolutionary computation if abstractions of synapsis and speciation are made part of the genetic algorithm.The NEAT method(section3)is an implementation of this idea:the genome is complexi?ed by adding new genes which in turn encode new structure in the phenotype, as in biological evolution.

Complexi?cation is especially powerful in open-ended domains where the goal is to continually generate more sophisticated https://www.doczj.com/doc/4e1309782.html,petitive coevolution is a particularly important such domain,as will be reviewed in the next section.

2.2Competitive Coevolution

In competitive coevolution,individual?tness is evaluated through direct competition with other individuals in the population,rather than through an objective?tness measure.In other words,?tness signi?es only the relative strengths of solutions;an increased?tness in one solution leads to a decreased?tness for another. Ideally,competing solutions will continually outdo one another,leading to an”arms race”of increasingly better solutions(Dawkins and Krebs1979;Rosin1997;Van Valin1973).

In practice,it is dif?cult to establish an arms race.Evolution tends to?nd the simplest solutions that can win,meaning that strategies can switch back and forth between different idiosyncratic yet uninteresting variations(Darwen1996;Floreano and Nol?1997;Rosin and Belew1997).Several methods have been developed to encourage the arms race(Angeline and Pollack1993;Ficici and Pollack2001;Noble and Watson2001;Rosin and Belew1997).For example,a”hall of fame”can be used to ensure that current strategies remain competitive against strategies from the past.Recently,Ficici and Pollack(2001)and Noble and Watson(2001)introduced a promising method called Pareto coevolution,which?nds the best learners and the best teachers in two populations by casting coevolution as a multiobjective optimization problem.

Although such techniques improve the performance of competitive coevolution,they do not directly en-courage continual coevolution,i.e.creating new solutions that maintain existing capabilities.For example, no matter how well selection is performed,or how well competitors are chosen,if no better solution exists in the?xed solution space,elaboration is impossible since the global optimum has already been reached. Moreover,it may occasionally be easier to escape a local optimum by adding a new dimension of freedom to the search space than by jumping back out into the same space that led to the optimum in the?rst place.

Complexi?cation is an appropriate technique for establishing a coevolutionary arms https://www.doczj.com/doc/4e1309782.html,plexi?-cation naturally elaborates strategies by adding new dimensions to the search space.Thus,progress can be made inde?nitely long:even if a global optimum is reached in the search space of solutions,new dimensions can be added,opening up a higher-dimensional space in which even higher optima may exist.

To test this idea experimentally,we chose a robot duel domain that combines predator/prey interaction and food foraging in a novel head-to-head competition(Section4).We use this domain to demonstrate how NEAT uses complexi?cation to continually elaborate on strategies.The next section describes the NEAT neuroevolution method,followed by a description of the robot duel domain and a discussion of the results. 3NeuroEvolution of Augmenting Topologies(NEAT)

The NEAT method of evolving arti?cial neural networks combines the usual search for appropriate network weights with complexi?cation of the network structure.This approach is highly effective:NEAT outper-forms other neuroevolution(NE)methods,e.g.on the benchmark double pole balancing task by a factor of ?ve(Stanley and Miikkulainen2002b,c,d).The NEAT method consists of solutions to three fundamental challenges in evolving neural network topology:(1)What kind of genetic representation would allow dis-parate topologies to crossover in a meaningful way?Our solution is to use historical markings to line up genes with the same origin.(2)How can topological innovation that needs a few generations to optimize be protected so that it does not disappear from the population prematurely?Our solution is to separate each innovation into a different species.(3)How can topologies be minimized throughout evolution so the most ef?cient solutions will be discovered?Our solution is to start from a minimal structure and grow only when necessary.In this section,we explain how NEAT addresses each challenge.

Figure2:A NEAT genotype to phenotype mapping example.A genotype is depicted that produces the shown phenotype.There are3input nodes,one hidden,and one output node,and seven connection de?nitions,one of which is recurrent.The second gene is disabled,so the connection that it speci?es(between nodes2and4)is not expressed in the phenotype.In order to allow complexi?cation,genome length is unbounded.

3.1Genetic Encoding

Evolving structure requires a?exible genetic encoding.In order to allow structures to complexify,their representations must be dynamic and expandable.Each genome in NEAT includes a list of connection genes,each of which refers to two node genes being connected.(?gure2).Each connection gene speci?es the in-node,the out-node,the weight of the connection,whether or not the connection gene is expressed(an enable bit),and an innovation number,which allows?nding corresponding genes during crossover.

Mutation in NEAT can change both connection weights and network structures.Connection weights mutate as in any NE system,with each connection either perturbed or not.Structural mutations,which form the basis of complexi?cation,occur in two ways(?gure3).Each mutation expands the size of the genome by adding gene(s).In the add connection mutation,a single new connection gene is added connecting two previously unconnected nodes.In the add node mutation an existing connection is split and the new node placed where the old connection used to be.The old connection is disabled and two new connections are added to the genome.The new nonlinearity in the connection changes the function slightly,but new nodes can be immediately integrated into the network,as opposed to adding extraneous structure that would have to be evolved into the network later.

Through mutation,the genomes in NEAT will gradually get larger.Genomes of varying sizes will result,sometimes with different connections at the same positions.A dif?cult problem for crossover,with numerous differing topologies and weight combinations,is an inevitable result of allowing genomes to grow unbounded.Yet such growth is necessary if complexi?cation is to occur.How can NE cross over differently sized genomes in a sensible way?The next section explains how NEAT addresses this problem.

Figure3:The two types of structural mutation in NEAT.Both types,adding a connection and adding a node, are illustrated with the genes above their phenotypes.The top number in each genome is the innovation number of that gene.The bottom two numbers denote the two nodes connected by that gene.The weight of the connection,also encoded in the gene,is not shown.The symbol DIS means that the gene is disabled,and therefore not expressed in the network.The?gure shows how connection genes are appended to the genome when a new connection is added to the network and when a new node is added.Assuming the depicted mutations occurred one after the other,the genes would be assigned increasing innovation numbers as the?gure illustrates,thereby allowing NEAT to keep an implicit history of the origin of every gene in the population.

3.2Tracking Genes through Historical Markings

It turns out that there is unexploited information in evolution that tells us exactly which genes match up

between any individuals in the population.That information is the historical origin of each gene in the

population.Two genes with the same historical origin represent the same structure(although possibly with

different weights),since they were both derived from the same ancestral gene from some point in the past.

Thus,all a system needs to do to know which genes line up with which is to keep track of the historical

origin of every gene in the system.

Tracking the historical origins requires very little computation.Whenever a new gene appears(through

structural mutation),a global innovation number is incremented and assigned to that gene.The innovation

numbers thus represent a chronology of every gene in the system.As an example,let us say the two

mutations in?gure3occurred one after another in the system.The new connection gene created in the

?rst mutation is assigned the number,and the two new connection genes added during the new node

mutation are assigned the numbers and.In the future,whenever these genomes crossover,the offspring will inherit the same innovation numbers on each gene;innovation numbers are never changed.Thus,the

historical origin of every gene in the system is known throughout evolution.

A possible problem is that the same structural innovation will receive different innovation numbers in

the same generation if it occurs by chance more than once.However,by keeping a list of the innovations

that occurred in the current generation,it is possible to ensure that when the same structure arises more than

once through independent mutations in the same generation,each identical mutation is assigned the same

innovation number.Thus,there is no resultant explosion of innovation numbers.

Through innovation numbers,the system now knows exactly which genes match up with which.(?gure

Parent1

Parent2Figure 4:Matching up genomes for different network topologies using innovation numbers.Although Parent 1and Parent 2look different,their innovation numbers (shown at the top of each gene)tell us which genes match up with which without the need for topological analysis.Even without any topological analysis,a new structure that combines the overlapping parts of the two parents as well as their different parts can be created.In this case,equal ?tnesses are assumed,so the disjoint and excess genes from both parents are inherited randomly.The disabled genes may become enabled again in future generations:there’s a preset chance that an inherited gene is disabled if it is disabled in either parent.

4).Genes that do not match are either disjoint or excess ,depending on whether they occur within or outside the range of the other parent’s innovation numbers.When crossing over,the genes in both genomes with the same innovation numbers are lined up.Genes that do not match are inherited from the more ?t parent,or if they are equally ?t,from both parents randomly.

Historical markings allow NEAT to perform crossover without the need for expensive topological anal-ysis.Genomes of different organizations and sizes stay compatible throughout evolution,and the problem of comparing different topologies (Radcliffe 1993)is essentially avoided.Such compatibility is essential in order to complexify structure.However,it turns out that a population of varying complexities cannot main-tain topological innovations on its own.Because smaller structures optimize faster than larger structures,and adding nodes and connections usually initially decreases the ?tness of the network,recently augmented structures have little hope of surviving more than one generation even though the innovations they represent might be crucial towards solving the task in the long run.The solution is to protect innovation by speciating the population,as explained in the next section.

3.3Protecting Innovation through Speciation

NEAT speciates the population so that individuals compete primarily within their own niches instead of with the population at large.This way,topological innovations are protected and have time to optimize their structure before they have to compete with other niches in the population.Protecting innovation through speciation follows the philosophy that new ideas must be given time to reach their potential before they are prematurely eliminated.

Historical markings make it possible for the system to divide the population into species based on topo-logical similarity.We can measure the distance between two network encodings as a simple linear com-bination of the number of excess()and disjoint()genes,as well as the average weight differences of matching genes(

(1)

The coef?cients,,and adjust the importance of the three factors,and the factor,the number of genes in the larger genome,normalizes for genome size(can be set to1if both genomes are small,i.e., consist of fewer than20genes).Genomes are tested one at a time;if a genome’s distance to a randomly chosen member of the species is less than,a compatibility threshold,it is placed into this species.Each genome is placed into the?rst species from the previous generation where this condition is satis?ed,so that no genome is in more than one species.If a genome is not compatible with any existing species,a new species is created.

As the reproduction mechanism for NEAT,we use explicit?tness sharing(Goldberg and Richardson 1987),where organisms in the same species must share the?tness of their niche.Thus,a species cannot afford to become too big even if many of its organisms perform well.Therefore,any one species is unlikely to take over the entire population,which is crucial for speciated evolution to work.The adjusted?tness for organism is calculated according to its distance from every other organism in the population:

Figure5:The Robot Duel Domain.The robots begin on opposite sides of the board facing away from each other as shown by the lines pointing away from their centers.The concentric circles around each robot represent the separate rings of opponent sensors and food sensors available to each robot.Each ring contains?ve sensors,which appear larger or smaller depending on their activations.The robots lose energy when they move around,and gain energy by consuming food(shown as small sandwiches).The food is placed in a horizontally symmetrical pattern around the middle of the board.The objective is to attain a higher level of energy than the opponent,and then collide with it.Because of the complex interaction between foraging,pursuit,and evasion behaviors,the domain allows for a broad range of strategies of varying sophistication.Animated demos of such evolved strategies are available at https://www.doczj.com/doc/4e1309782.html,/users/kstanley/demos.html.

introduced over evolution.Thus,because NEAT protects innovation using speciation,it can start this way, minimally,and grow new structure only as necessary.

New structure is introduced incrementally as structural mutations occur,and only those structures sur-vive that are found to be useful through?tness evaluations.This way,NEAT searches through a minimal number of weight dimensions,signi?cantly reducing the number of generations necessary to?nd a solu-tion,and ensuring that networks become no more complex than necessary.This gradual production of in-creasingly complex structures constitutes complexi?cation.In other words,NEAT searches for the optimal topology by complexifying when necessary.

4The Robot Duel Domain

Our hypothesis is that complexi?cation allows discovering more sophisticated strategies,i.e.strategies that are more effective,?exible,and general,and include more components and variations than do simple strate-gies.To demonstrate this effect,we need a domain where it is possible to develop increasingly sophisticated strategies,and where sophistication can be readily measured.A coevolution domain is particularly appro-priate because a sustained arms race should lead to increasing sophistication.

In choosing the domain,it is dif?cult to strike a balance between being able to evolve complex strategies and being able to analyze and understand them.Pursuit and evasion tasks have been utilized for this purpose in the past(Gomez and Miikkulainen1997;Jim and Giles2000;Miller and Cliff1994;Reggia et al.2001), and can serve as a benchmark domain for competitive coevolution as well.While past experiments evolved either a predator or a prey,an interesting coevolution task can be established if the agents are instead equal and engaged in a duel.To win,an agent must develop a strategy that outwits that of its opponent,utilizing structure in the environment.

In the robot duel domain,two simulated robots try to overpower each other(?gure5).The two robots

begin on opposite sides of a rectangular room facing away from each other.As the robots move,they lose

was turned off in the remaining ten,in order to see how complexi?ed networks compared to those with

?xed topologies throughout evolution.The competitive coevolution setup is described?rst,followed by an

overview of the dominance tournament method for monitoring progress.

5.1Competitive Coevolution Setup

The evolution in the robot duel domain is open-ended in that it never reaches a?nal solution.Thus,the

question in such a domain is whether continual coevolution will take place,i.e.whether increasingly so-

phisticated strategies will appear throughout the run or eventually stop being https://www.doczj.com/doc/4e1309782.html,plexi?cation

should allow continual coevolution.The experiment has to be set up carefully for this process to emerge,

and to be able to identify it when it does.

In competitive coevolution,every network should play a suitable number of games to establish a good

measure of?tness.To encourage interesting and sophisticated strategies,networks should play a diverse

and high quality sample of possible opponents.One way to accomplish this goal is to evolve two separate

populations.In each generation,each population is evaluated against an intelligently chosen sample of

networks from the other population.The population currently being evaluated is called the host population,

and the population from which opponents are chosen is called the parasite population(Rosin and Belew

1997).The parasites are chosen for their quality and diversity,making host/parasite evolution more ef?cient

and more reliable than one based on random or round robin tournament.

A single?tness evaluation included two competitions,one for the east and one for the west starting

position.That way,networks needed to implement general strategies for winning,independent of their

starting positions.Host networks received a single?tness point for each win,and no points for losing.If a

competition lasted750time steps with no winner,the host received0points.

In selecting the parasites for?tness evaluation,good use can be made of the speciation and?tness shar-

ing that already occur in NEAT.Each host was evaluated against the champions of four species with the

highest?tness.They are good opponents because they are the best of the best species,and they are guaran-

teed to be diverse because their compatibility must be outside the threshold(section3.3).Another eight opponents were chosen randomly from a Hall of Fame(Rosin and Belew1997)that contained population

champions from all generations.Together,speciation,?tness sharing,and Hall of Fame comprise a compe-

tent competitive coevolution methodology.Appendix A contains the NEAT system parameter values used

in the experiments.

It should be noted that complexi?cation does not depend on the particular coevolution methodology.

For example Pareto coevolution(Ficici and Pollack2001;Noble and Watson2001)could have been used

as well,and the advantages of complexi?cation would be the same.However,Pareto coevolution requires

every member of one population to play every member of the other,and the running time in this domain

would have been prohibitively long.

In order to interpret experimental results,a method is needed for analyzing progress in competitive

coevolution.The next section describes such a method.

5.2Monitoring Progress in Competitive Coevolution

A competitive coevolution run returns a record of every generation champion from both populations.The

question is how can a sequence of increasingly sophisticated strategies be identi?ed in this data,if one

exists?This section describes the dominance tournament method for monitoring progress in competitive

coevolution(Stanley and Miikkulainen2002a)that allows us to do that.

123456

Figure7:Master tournament ambiguity.Champions of generations one through six are depicted.An arrow pointing from champion to champion denotes that is superior to in a direct288-way comparison.The master tournament reports that champion5defeats four other champions,while champion6only defeats three others.These results imply that5is superior to6.However,when5and6are compared directly against each other,6actually wins.This way,master tournament results can be misleading.A method that captures the order of dominance among different strategies avoids such a confusion.

First we need a method for performing individual comparisons,i.e.whether one strategy is better than another.Because the board con?gurations can vary during the game,champion networks were compared on144different food con?gurations from each side of the board,giving288total comparisons.The food con?gurations included the same9symmetrical food positions used during training,plus an additional2 food items,which were placed in one of12different positions on the east and west halves of the board. Some starting food positions give an initial advantage to one robot or another,depending on how close they are to the robots’starting positions.Thus,the one who wins the majority of the288total games has demonstrated its superiority in many different scenarios,including those beginning with a disadvantage. We say that network is superior to network if wins more comparisons than out of the288total comparisons.

Given this de?nition of superiority,progress can be tracked.The obvious way to do it is to compare each network to others throughout evolution,?nding out whether later strategies can beat more opponents than earlier strategies.For example,Floreano and Nol?(1997)used a measure called master tournament, in which the champion of each generation is compared to all other generation champions.Unfortunately, such methods are impractical in a time-intensive domain such as the robot duel competition.Moreover,the master tournament only counts how many strategies can be defeated by each generation champion,without identifying which ones.Thus,it can fail to detect cases where strategies that defeat fewer previous cham-pions are actually superior(?gure7).In order to track strategic innovation,we need to identify dominant strategies,i.e.those that defeat all previous dominant strategies.This way,we can make sure that evolution proceeds by developing a progression of strictly more powerful strategies,instead of e.g.switching between alternative ones.

The dominance tournament method of tracking progress in competitive coevolution meets this goal (Stanley and Miikkulainen2002a).Let a generation champion be the winner of a288game comparison between the two population champions of a single generation.Let be the th dominant strategy to appear over evolution.Then dominance is de?ned recursively starting from the?rst generation and progressing to the last:1

The?rst dominant strategy is the generation champion of the?rst generation;

dominant strategy,where,is a generation champion such that for all,is superior to (wins the288game comparison with).

This strict de?nition of dominance prohibits circularities.For example,must be superior to strate-gies through,superior to both and,and superior to.We call the th dominant strategy of the run.A network from a later generation that defeats but loses to has circular supe-riority,since it defeats newer strategies but loses to older ones.Since is circular,it would not be entered into the dominance hierarchy.The entire process of deriving a dominance hierarchy from a population is a dominance tournament,where competitors play all previous dominant strategies until they either lose a 288game comparison,or win every comparison to previous dominant strategies,thereby becoming a new dominant strategy.Dominance tournament allows us to identify a sequence of increasingly more sophisti-cated strategies.They also require signi?cantly fewer comparisons than the master tournament(Stanley and Miikkulainen2002a).

Armed with the appropriate coevolution methodology and a measure of success,we can now ask the question:Does the complexi?cation result in more successful competitive coevolution?

6Results

Each of the23evolution runs lasted500generations,and took between5and10days on a1GHz Pentium III processor,depending on the progress of evolution and sizes of the networks involved.The NEAT algorithm itself used less than1%of this computation:most of the time was spent in evaluating networks in the robot duel task.Evolution of fully-connected topologies took about90%longer than structure-growing NEAT because larger networks take longer to evaluate.

We de?ne complexity as the number of nodes and connections in a network:The more nodes and con-nections there are in the network,the more complex behavior it can potentially implement.The results were analyzed to answer three questions:(1)As evolution progresses does it also continually complexify?(2) How is complexi?cation utilized to create more sophisticated strategies?(3)Does complexi?cation allow better strategies to be discovered than does evolving?xed-topology networks?

6.1Evolution of Complexity

NEAT was run thirteen times,each time from a different seed,to verify that the results were consistent.The highest levels of dominance achieved were17,14,17,16,16,18,19,15,17,12,12,11,and13,averaging at15.15(sd=2.54).

At each generation where the dominance level increased in at least one of the thirteen runs,we averaged the number of connections and number of nodes in the current dominant strategy across all runs(?gure8). Thus,the graphs represent a total of197dominance transitions spread over500generations.The rise in complexity is dramatic,with the average number of connections tripling and the average number of hidden nodes rising from0to almost six.In a smooth trend over the?rst200generations,the number of connections in the dominant strategy grows by50%.During this early period,dominance transitions occur frequently (fewer prior strategies need to be beaten to achieve dominance).Over the next300generations,dominance transitions become more sparse,although they continue to occur.

Between the200th and500th generations a staircase pattern emerges,where complexity?rst rises dra-matically,then settles,then abruptly increases again.The reason for this pattern is speciation.While one

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050100150200250300350400450500A v e r a g e C o n n e c t i o n s i n H i g h e s t D o m i n a n t Generation Complexification of Connections 01234567050100150200250300350400450500

A v e r a g e N o d e s i n H i g h e s t D o m i n a n t Generation

Complexification of Nodes Figure 8:Complexi?cation of connections and nodes over generations.The graphs depict the average number of connections and the average number of hidden nodes in the highest dominant network in each generation.Averages are taken over 13complexifying runs.A hash mark appears every generation in which a new dominant strategy emerged in at least one of the 13runs.The graphs show that as dominance increases,so does complexity level on average.The differences in complexity between the average ?nal dominant and ?rst dominant strategies are statistically signi?cant for both connections and nodes ().

species is adding a large amount of structure,other species are optimizing the weights of less complex net-works.While it is initially faster to grow structure until something works,such ad hoc constructions are eventually supplanted by older species that have been steadily optimizing for a long period of time.Thus,spikes in complexity occur when structural elaboration leads to a better strategy,and complexity slowly settles when older structures optimize their weights and overtake more recent structural innovations.Even-tually,even more elaborate structures will emerge and again outperform the older structures.

Thus,there are two underlying forces of progress:the building of new structures,and the continual optimization of prior structures in the background.The product of these two trends is a gradual stepped progression towards increasing complexity.

Importantly,the dominant strategies did not have to complexify;Even though NEAT adds new structure to networks over generations,because of speciation many species remain simple even as some species become more complex.Thus,the results show more than just that the champions of each generation tend to become complex:The dominant strategies,i.e.the networks that have a strictly superior strategy to every previous dominant strategy,tend to be more complex the higher the dominance level .Thus,the results verify that continual progress in evolution is paired with increasing complexity.

6.2Sophistication through Complexi?cation

To see how complexi?cation contributes to evolution,let us observe how a sample dominant strategy de-velops over time.While many complex networks evolved in the experiments,we follow the species that

produced the winning network

in the third run because its progress is rather typical and easy to under-stand.Let us use for the best network in at generation ,and for the th hidden node to arise from a structural mutation over the course of evolution.We will track both strategic and structural innovations in order to see how they correlate.Let us begin with (?gure 9a),when had a mature zero-hidden-node strategy:

’s main strategy was to follow the opponent,putting it in a position where it might by chance

collide with its opponent when its energy is up.However,followed the opponent even when

Figure9:Complexi?cation of a Winning Species.The best networks in the same species are depicted at landmark generations.Nodes are depicted as squares beside their node numbers,and line thickness represents the strength of connections.Over time,the networks became more complex and gained skills.(a)The champion from generation10 had no hidden nodes.(b)The addition of and its respective connections gave new abilities.(c)The appearance of re?ned existing behaviors.

the opponent had more energy,leaving vulnerable to attack.did not clearly switch roles between foraging and chasing the enemy,causing it to miss opportunities to gather food.

.During the next100generations,evolved a resting strategy,which it used when it had signif-icantly lower energy than its opponent.In such a situation,the robot stopped moving,while the other robot wasted energy running around.By the time the opponent got close,its energy was often low enough to be attacked.The resting strategy is an example of improvement that can take place with-out complexi?cation:it involved increasing the inhibition from the energy difference sensor,thereby slightly modifying intensity of an existing behavior.

In(?gure9b),a new hidden node,,appeared.This node arrived through an interspecies mating,and had been optimized for several generations already.Node gave the robot the ability to change its behavior at once into a consistent all-out attack.Because of this new skill,no longer needed to follow the enemy closely at all times,allowing it to collect more food.By implementing this new strategy through a new node,it was possible not to interfere with the already existing resting strategy,so that now switched roles between resting when in danger to attacking when high on energy.This way,the new structure resulted in strategic elaboration.

In(?gure9c),another new hidden node,,split a link between an input sensor and.

Replacing a direct connection with a sigmoid function greatly improved’s ability to attack at appropriate times,leading to very accurate role switching between attacking and foraging.would try to follow the opponent from afar focusing on resting and foraging,and only zoom in for attack when victory was certain.This?nal structural addition shows how new structure can greatly improve the accuracy and timing of existing behaviors.

The analysis above shows that in some cases,weight optimization alone can produce improved strate-gies.However,when those strategies need to be extended,adding new structure allows the new behaviors to coexist with old strategies.Also,in some cases it is necessary to add complexity to make the timing or execution of the behavior more accurate.These results show how complexi?cation can be utilized to produce increasing sophistication.

In order to illustrate the level of sophistication displayed during competition,we conclude this section with a description of an observed competition between two sophisticated strategies,and,from another run of evolution.At the beginning of the competition,and collected most of the available food until their energy levels were about equal.Two pieces of food remained on the board in locations distant

Figure10:Sophisticated Endgame.Robot dashes for the last piece of food while is still collecting the second-to-last piece.Although it appeared that would lose because got the second-to-last piece,(gray arrow),it turns out that ends with a disadvantage.It has no chance to get to the last piece of food before, and has been saving energy while wasted energy traveling long distances.This way,sophisticated strategies evolve through complexi?cation,combining multiple objectives,and utilizing weaknesses in the opponent’s strategy. from both and(?gure10).Because of the danger of colliding with similar energy levels,the naive strategy would be to rush for the last two pieces of food.In fact,did exactly that.However, cleverly forfeit this race for the second-to-last piece,opting to sit still,even though its energy temporarily dropped below’s.After consumed the second-to-last piece,it headed towards the last piece,which was now far away.Even though had less energy,it was closer and got there?rst.It received a boost of energy while wasted its energy running the long distance from its current position.Thus,’s strategy ensured that it had more energy when they?nally met.Robot’s behavior was surprisingly deceptive,showing that a high level of strategic sophistication had evolved.

This analysis of individual evolved behaviors shows that complexi?cation indeed elaborates on exist-ing strategies,and allows highly sophisticated behaviors to develop that balance multiple goals and utilize weaknesses in the opponent.The last question is whether complexi?cation indeed is necessary to achieve these behaviors.

6.3Complexi?cation vs.Fixed-topology Evolution

To see whether complexifying coevolution is more powerful than standard coevolution in a?xed search space,we compared the two methods.Note that it is not possible to compare them using the standard crossvalidation methodology because no external performance measure exists in this domain.However, the evolved neural networks can be compared directly by playing a duel.Thus,a run of?xed-topology coevolution can be compared to a run of complexifying coevolution by playing the highest dominant strategy from the?xed-topology run against the entire dominance ranking of the complexifying run.The highest level strategy in the ranking that the?xed-topology strategy can defeat is a measure of its quality against complexifying coevolution.

By playing every?xed-topology champion against the dominance ranking from every complexifying run,we can measure the performance of non-complexifying evolution.In addition,we established a base-line for comparison by also playing the champions of the complexifying runs against the entire dominance ranking of every other complexifying run.The average levels reached by complexifying and?xed-topology coevolution can then be compared.

Accordingly,the performance of a particular run is the average highest dominance level of the strategies it can defeat among all complexifying runs,normalized by the total number of dominance levels for that

Figure11:The Best Complexifying Network.The highest performing network from complexifying coevolution is depicted.The network has11hidden units and202connections,plotted as in?gure9.This network makes signi?cant use of structure.While it still has basic direct connections,its strategy has been elaborated through the addition of new nodes and https://www.doczj.com/doc/4e1309782.html,teral and recurrent connections are used to make more re?ned decisions based on past experiences.While complexi?cation makes good use of this high-dimensional space,it is dif?cult for?xed-topology evolution to take advantage of similarly complex structures.

run.For example,if a strategy can defeat up to and including the13th dominant strategy out of15,then its performance against that run is

D o m . L e v e l

C o m p l e x i f y i ng

D o m . L e v e l G e n e r a t i o n s Figure 12:Comparing Typical Runs of Complexifying Coevolution and 10-hidden-unit Fixed-Topology Coevo-lution.Dominance levels are charted on the y-axis and generations on the x-axis.A line appears at every generation where a new dominant strategy arose in each run.The height of the line represents the level of dominance.The arrow shows that the highest dominant strategy found in 10-hidden-unit ?xed-topology evolution only performs as well as the 8th dominant strategy in the complexifying run,which was found in the 19th generation!(Average =24,sd =8.8)In other words,only a few generations of complexifying coevolution are as effective as several hundred of ?xed-topology evolution.

6.3.210-Hidden-Unit Fixed-Topology Coevolution

Fixed-topology coevolution uses fully-connected networks with a single hidden layer,and the number of hidden units must be chosen by the experimenter.Thus,in order to make the comparison between ?xed-topology and complexifying coevolution fair,a reasonable size must be chosen for networks in the ?xed-topology runs.One sensible approach is to choose a complexity that approximates the complexity of the highest dominant strategy from the highest performing complexifying run (?gure 11).This strategy utilized 11hidden units and 202connections including both recurrent connections and direct connections from input to output.In order to approximate this complexity,we chose to use 10hidden unit fully recurrent networks with direct connections from inputs to outputs,with a total of 263connections.A network of this type should be able to approximate the functionality of the most effective complexifying strategy.

Three runs of ?xed-topology coevolution were performed with these networks,and their highest domi-nant strategies were compared to the entire dominance ranking of every complexifying run.Their average performances were ,,and ,for an overall average of .Compared to the

performance of complexifying coevolution,it is clear that ?xed-topology coevolution produced consistently much inferior solutions.As a matter of fact,no ?xed-topology run could defeat any of the 13highest

D o m . L e v e l C o m p l e x i f y i ng

D o m . L e v e l G e n e r a t i o n s Figure 13:Comparing Typical Runs of Complexifying Coevolution and 5-hidden-unit Fixed-Topology Coevo-lution.As in ?gure 12dominance levels are charted on the y-axis and generations on the x-axis,a line appears every generation where a new dominant strategy arose in each run,and the height of the line represents the level of dominance.The arrow shows that the highest dominant strategy found in 5-hidden-unit ?xed-topology evolution only performs as well as the 12th dominant in the complexifying run,which was found in the 140th generation.(Average 159,sd =72.0)Thus,even in the best con?guration,?xed-topology evolution takes about twice as long to achieve the same level of performance.

dominant strategies from complexifying coevolution.

This difference in performance can be illustrated by computing the average generation of complexifying coevolution with the same performance as ?xed-topology coevolution.This generation turns out to be 24(sd =8.8).In other words,500generations of ?xed-topology coevolution reach on average the same level of dominance as only 24generations of complexifying coevolution!In effect,the progress of the entire ?xed-topology coevolution run is compressed into the ?rst few generations of complexifying coevolution (?gure 12).

6.3.35-Hidden-Unit Fixed-Topology Coevolution

One of the arguments for using complexifying coevolution is that starting the search directly in the space of the ?nal solution may be intractable.This may explain why the attempt to evolve ?xed-topology solutions at a high level of complexity failed.Thus,in the next experiment we chose instead to evolve fully-connected,fully-recurrent networks with ?ve hidden nodes.After considerable experimentation,we found out that this level of complexity was the most productive for ?xed-topology evolution,allowing it to ?nd the best

口罩的种类、功能以及使用方法全面讲解

口罩的种类、功能以及使用方法详细讲解 冬季由于天气寒冷、空气污染严重、预防传染病等原因,很多人会佩戴口罩,但是市面上售卖的口罩类型有很多种,佩戴哪种口罩能预防病毒传染?不同的口罩有哪些用途?特殊人群应该如何佩戴口罩?在这个特殊时期,小编就为大家带来了佩戴口罩预防口罩的种类选择和使用方法以及一些其他方面的注意事项,希望对大家有所帮助。 一、戴口罩能预防病毒感染吗? 常见的口罩有以下几种:普通棉布口罩、一次性口罩(如:医用外科口罩)、N95型口罩。 1、一次性口罩(医用外科口罩) 能在一定程度上预防呼吸道感染,无法防霾。 医用外科口罩有三层,从外到内分别是防水层、过滤层、舒适层。舒适层是一层无纺布,佩戴时白色的无纺布朝内,蓝色的防水层朝外,有金属片的一边朝上,不要戴反,橡皮筋挂上双耳后捏紧金属片和鼻子贴合,抚平两颊,使口罩和面部之间尽量不留缝隙。 购买时要注意,应当选择外包装上明确注明“医用外科口罩”字样的口罩。 2、N95型口罩 能有效预防呼吸道感染,可以防霾。 N95型口罩是是NIOSH(美国国家职业安全卫生研究所)认证的9种防颗粒物口罩中的一种。“N”的意思是不适合油性的颗粒(炒菜产生的油烟就是油性颗粒物,而人说话或咳嗽产生的飞沫不是油性的);“95”是指,在NIOSH 标准规定的检测条件下,过滤效率达到95%。 N95不是特定的产品名称。只要符合N95标准,并且通过NIOSH审查的产品就可以称为“N95型口罩”。

N95型口罩的最大特点就是可以预防由患者体液或血液飞溅引起的飞沫传染。飞沫的大小为直径1至5微米。美国职业安全与健康管理局(OSHA)针对医疗机构规定,暴露在结核病菌下的医务人员必须佩戴N95标准以上的口罩。 相比较医用外科口罩,N95型口罩密闭更好。在选用N95型口罩时,尽量选择不带呼吸阀的N95型口罩。 3、普通棉布口罩 它的材质可能为棉布、纱布、毛线、帆布及绒等,由于材质本身不够致密,无法起到预防感染目的。 二、如何正确佩戴口罩? N95型口罩 医用外科口罩

英雄传说空之轨迹FC配置魔法

英雄传说空之轨迹FC配置魔法

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导力魔法表 原表可查看游击士手册。要查阅各种魔法的配置要求,游戏中查看手册即可。此表和手册中的区别在于: 将魔法按照功能分类。 魔法的范围大小更精确。 增加了各攻击魔法的打击数(对于打击数概念的解释,请参考后文【战斗中获得的耀晶片数量与SEPITH UP奖励】部分) 增加了各魔法的驱动时间比。 注:魔法的范围 小圆、中圆、大圆、直线只是比较笼统的说法,大圆有大有小,直线有宽有窄。这里在范围后面补上了一个数字,以表示圆的半径或直线的宽度。例如“直线1”表示直线宽度为1格;“中圆3”表示圆的半径为3格,实际有效范围的直径为7格;“小圆2”表示圆的半径为2格,实际有效范围的直径为5格。 图示如下: 中圆3的有效范围小圆2的有效范围(黑色方块) □□■■■□□□□□□□□□ □■■■■■□□□■■■□□ ■■■■■■■□■■■■■□ ■■■■■■■□■■■■■□ ■■■■■■■□■■■■■□ □■■■■■□□□■■■□□ □□■■■□□□□□□□□□ 范围(非全体)魔法有两种指定范围的方式:目标指定和地点指定。 目标指定:最为常见。只能以某个敌人或队员/NPC为中心。在魔法驱动期间,如果目标移动,魔法的范围圈会跟着移动,如果目标失效(如战斗不能),范围圈会自动换到另一个有效目标上,因此不会发空。单体魔法也可以算是目标指定。 地点指定:圆范围可以指定在战场任何位置,直线可以朝向任何方向。同样范围大小,地点指定比目标制定有可能覆盖更多目标,但是敌人也有可能在驱动时逃出施法范围。所以最好赶在敌人行动前就发出,或者预估提前量,以免浪费。 此表中,范围的数字后面加了“◇”号的,表示此魔法为地点指定。否则为目标指定。

空之轨迹FC最详图文攻略

序章父亲、启程 在开篇剧情结束之后(如果不幸黑屏,请参阅置顶或者精品区本人FAQ,还是无法解决请在吧内求助吧友),小约和小艾需要前往洛连特市的游击士协会(PC版界面右上角可查看小地图),在游击士协会与爱娜对话后去二楼与雪拉对话,听过一些基础知识后艾约被带往导力工房,接下来请按照雪拉的要求合成回路并装到主角的导力器上(请至少合成HP1和行动力1,并在艾导力器上装HP1,约导力器上装行动力1)然后给主角中任意一位的导力器开封结晶孔。导力系统介绍完毕后艾约会前往地下水路,开始实地研修。

PS:在协会获得的游击士手册包含游戏大多数基础知识,且记录有游戏主线与支线任务的完成情况,请新手们务必仔细查阅(话说有些童鞋不知道手册能翻页?……)

PSP版的游击士手册、星杯手册为日文版,汉化版见此: https://www.doczj.com/doc/4e1309782.html,/mxf03/album/%BF%D5%D6%AE%B9%EC%BC%A3-%D3%CE%BB%F 7%CA%BF%CA%D6%B2%E1%2C%D0%C7%B1%AD%CA%D6%B2%E1 ◆主线任务⑴◆实地研修?回收宝物BP:1,500mira 此任务实质为战斗系统教学,请仔细看剧情并按照指示行动 研修结束后,前往里农杂货铺购买《利贝尔通讯》(在买书之前把身上钱全花完的话小约会帮忙付),可获得料理手册并学会枫糖曲奇的制作,并可以开始使用料理系统,料理一般需在酒店饭馆等处购买,也有宝箱开的和任务获得的。 ☆【料理手册】此时可获得的料理:枫糖曲奇、炸薯条(亚班特酒馆、格鲁纳门)、花色苏打(亚班特酒馆)、洋红之眼(亚班特酒馆)、一口气薏粉(亚班特酒馆,大盘料理) ☆收集齐全料理并没有什么特别奖励……没有收集癖的话无所谓,对于新手来说用料理不仅回复效果不错(非战斗状态建议去旅馆或者免费回复点回复,比较省钱),很多料理除了回 复HP外还附带特别效果,做料理也比买药便宜。

全面分析 功能性绝缘

功能性绝缘的定义: 3.3.5 functional insulation insulation between conductive parts of different potential which is necessary only for the proper functioning of the appliance。 功能性绝缘的电气间隙的要求: 29.1.4 For functional insulation, the values of table 16 are applicable. However, clearances are not specified if the appliance complies with clause 19 with the functional insulation short-circuited. Lacquered conductors of windings are considered to be bare conductors. However, clearances at crossover points are not measured. 看蓝色字体部分,只要在短路时,能满足clause 19的要求,可不要求functional insulation 的电气间隙。 看红色字体部分,漆包线被视为“裸露导体”。也就是在本标准中,漆包膜不被视为功能性绝缘。这个前提很重要,这意味著绕组间不必进行“短路测试”。 功能性绝缘的爬电距离的要求: 29.2.4 Creepage distances of functional insulation shall be not less than those specified in table 18. However, creepage distances may be reduced if the appliance complies with clause 19 with the functional insulation short-circuited. 看蓝色字体部分,只要在短路时,能满足clause 19的要求,functional insulation 的爬电距离的要求可减小。标准并没有说可以减小到多少,这就意味著,只要functional insulation 能在短路时满足clause 19的要求即可满足爬电距离的要求。 结论:从标准的理解来看,functional insulation 仅为设备正常工作所需的绝缘,如果functional insulation 能在短路时满足Clause 19 的要求,可不要求其电气间隙和爬电距离。 实际上,我也是这么处理的。只要在检查、评估中发现functional insulation 的距离(cl & cr)很小,那么就用短路测试来检验,如果满足不了短路测试,那么我就要求其CL & CR。 我们在日常判断一个器具的功能绝缘其实无处不在,只要存在电势差的两点都可视为功能绝缘,但绝大部分情况下短路都是可以满足Clause 19的要求的,所以我们考核功能绝缘的地方就大大减少了。典型的功能绝缘的例子是L/N输入的地方,发热元件或马达元件的输入端子之间等等 功能绝缘的定义为保障产品功能的绝缘类型,它不像基本、附加、加强绝缘是用来防触电的,也就是说如果这类绝缘距离不够的话,可能会对最终的用户造成触电的危险,而功能绝缘的距离即使不够,用户也不会有触电危险,只不过会造成产品无法正常工作,它也可以用来减少起火的危险.例如电流保险丝之前火线和零线之间或是变压器内置温度保险丝两脚之间的距离

《英雄传说空之轨迹rd》回路配法图文详解

:FC时期导力器很好,5-2链,由于驱动2在FC时期的属性值还算是?不错的,双时限定影响不大,短链正好装攻击,长链则用于配魔法,是最早?能合出炽炎地狱的人,SC导力器降级为5-3链,由于高级回路的出现驱动2?的属性值沦为鸡肋,所以其导力器基本与4-3链无异,还好小约SC,3RD主要?是菜刀,影响也不大 小约可以完全按菜刀回路配,也可以给自己配个强音之力复

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小艾的纯奶妈回路,主打时改时减全回复,这里银耀是为了出死亡咆哮,银?耀换成封魔/石化之理可出大地之墙,换成红耀可兼顾攻击

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满足一些灾难冲击波控的配法,主打时改时减、强音复、灾难冲击波、虚弱领域、导力停止、龙卷火焰、银色荆棘 传说中的根源屏障(--=无敌鸡肋魔法,普通难度完全无用),主打时改时?减、强音复、星守、导力停止、鬼魅、沉默十字、暗物质改、死亡咆哮,另?外附带范围2

空之轨迹FC超完美详细图文攻略

序章父亲、启程 在开篇剧情结束之后,小约和小艾需要前往洛连特市的游击士协会(PC版界面右上角可查看小地图),在游击士协会与爱娜对话后去二楼与雪拉对话,听过一些基础知识后艾约被带往导力工房,接下来请按照雪拉的要求合成回路并装到主角的导力器上(请至少合成HP1和行动力1,并在艾导力器上装HP1,约导力器上装行动力1)然后给主角中任意一位的导力器开封结晶孔。导力系统介绍完毕后艾约会前往地下水路,开始实地研修。

完成情况,请新手们务必仔细查阅(话说有些童鞋不知道手册能翻页?……)

◆主线任务⑴◆实地研修?回收宝物BP:1,500mira 此任务实质为战斗系统教学,请仔细看剧情并按照指示行动。 研修结束后,前往里农杂货铺购买《利贝尔通讯》(在买书之前把身上钱全花完的话小约会帮忙付),可获得料理手册并学会枫糖曲奇的制作,并可以开始使用料理系统,料理一般需在酒店饭馆等处购买,也有宝箱开的和任务获得的。 ☆【料理手册】此时可获得的料理:枫糖曲奇、炸薯条(亚班特酒馆、格鲁纳门)、花色苏打(亚班特酒馆)、洋红之眼(亚班特酒馆)、一口气薏粉(亚班特酒馆,大盘料理) ☆收集齐全料理并没有什么特别奖励……没有收集癖的话无所谓,对于新手来说用料理不仅回复效果不错(非战斗状态建议去旅馆或者免费回复点回复,比较省钱),很多料理除了回复HP外还附带特别效果,做料理也比买药便宜。 ★【红耀石】在研修结束后请尽快与在亚班特酒店左边的民家里的雷特拉对话(此人所在房间内全是书架),可获得《红耀石》第1卷(此卷若错过之后还有次机会购得),若已触发解救孩子的剧情与雷特拉对话就无法获得此书了。 ★此书关系到最终武器的获得,漏掉任何一卷都将无法获得最终武器,若想获得最终武器请收集齐全。 ◆主线任务⑵◆保护孩子们BP:3+1(选择和约修亚一起出击+1),1000mira

强劲入门单反 佳能650D功能全面解析(全文)

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此外,佳能EOS 650D还搭载了实时显示拍摄和短片拍摄时提高自动对焦性能的Hybrid CMOS AF系统,位于图像感应器中央区域的部分像素用于相差检测自动对焦,快速检测合焦位置后,再进行反差检测自动对焦完成精确合焦。沿袭自EOS 600D的3.0″可旋转液晶监视器在EOS系列中首次采用触控面板,带来了直观的操作与便捷的拍摄。短片拍摄模式中搭载了“短片伺服自动对焦”,可以在短片拍摄期间对被摄体进行自动对焦追踪,还能用内置立体声麦克风录音,进行充满临场感、更出色的短片拍摄。另外,支持作品创作的新功能“手持夜景”模式和“HDR逆光控制”模式拓展了表现范围。EOS 650D预计于2012年6月下旬发售。 佳能EOS 650D单反 佳能650D有哪些功能超越了同类入门单反? ·中央八向双十字全9点十字型自动对焦系统

·最高约5张/秒高速连拍 ·新研发CMOS图像感应器搭载Hybrid CMOS AF实现短片及实时显示拍摄高速对焦 ·支持短片拍摄中持续追踪被摄体的短片伺服自动对焦·搭载触控技术的大型可旋转液晶监视器以及众多创意功能EOS 650D是EOS数码单反相机系列中首款搭载了全十字型自动对焦感应器的3位编号机型。9个自动对焦点都配置了对应F5.6光束的十字型自动对焦感应器,可以不受被摄体形状和拍摄位置影响进行稳定对焦。使用频率高的中央对焦点斜上还配置了搭配大光圈镜头时可发挥效果的对应F2.8光束十字型自动对焦感应器。对应F2.8和F5.6光束的双十字型自动对焦提高了对焦精度。 取景器内的自动对焦点分布 中央八向双十字全9点十字型自动对焦感应器 自动对焦模式设置画面 自动对焦模式有3种,包括适合拍摄静止被摄体的单次自动对焦、动态被摄体追踪能力出色的人工智能伺服自动对焦和可以在单次自动对焦和人工智能伺服自动对焦之间自动切换的人工智能自动对焦。

空之轨迹SC支线详细图文攻略

支线详细图文攻略 作者:cokefish 第一章 ★来たれ食材ハンター[每样各4个以上BP+1] 魔獣の骨 魔獣の牙 魔獣の角 魔獣の鳥肉 魔獣の魚卵 魔獣の鳥卵 单纯的找怪麻烦...只要在海道以及通往学园的街景林道上就可以打全所需的食材。 注: 魔獣の鳥肉..魔獣の鳥卵打通往学园路上的大脚鸟..这两个掉落率似乎不太高..没有幸运回路的话就得多打几次了 此处有机会碰到熊猫..会掉落小艾目前最好的武器...熊猫的攻击力很高..大概2500左右的伤害........ ★ <<紺碧の塔>>の写真撮影[由小艾在正中拍摄BP+1,由朵洛希BP+2] 时间上的限定不是很严苛。可以等到幽灵事件逐渐明了,朵洛希加入队伍时完成。 来到塔顶,有3个点可供拍摄选择,左右两点拍出来的效果最好,不过...人家要的是研究照片...你的BP可就看不到附加咯。在拍摄时小艾会停下来问让她来拍是否恰当,选择第2项:由朵洛希来拍。这时候便会看到朵洛希的经典台词“好可爱啊~~~笑一个~~~”了。 当然了,你也可以鼓励小艾去拍,不过即使选择最好的取景点,拍出的也不过是“很不错”的而已,而朵洛希的则是...宽屏的...16:9的。TT同样的相机,专业和业余就差这么多啊。 ★灯台の試運転 你有空的时候(比如做“メーヴェ海道の手配魔獣”任务时),可以顺便到灯塔去看望一下那个固执的老头。 当小艾亲切地和老头打过招呼后正欲出走时,发现他似乎面有难色,便又亲切地接下这个任务(对话选择第一项),原来是老人的腰痛了,无法去操作灯塔,便请小艾代劳了,没办法,不想被人背后说游击士缺少热情,勉为其难了。书架上有说明书,导力灯的具体操作

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镜头最全面解析 镜头的全面分析解剖,全面的分析监控镜头,没有比我们更全的描述了,经过几年的搜集整理,今天真功夫安防慢慢分析,摄像机镜头的作用是把被观察目标的光像呈现在摄像机的靶面上,也称光学成像。将各种不同形状、不同介质(塑料、玻璃或晶体)的光学零件(反射镜、透射镜、棱镜)按一定方式组合起来,使得光线经过这些光学零件的透射或反射以后,按照人们的需要改变光线的传输方向而被接收器件接收,即完成了物体的光学成像过程。光学镜头应满足成像清晰、透光率强、像面照度分布均匀、图像畸变小、光圈可调等要求。一般来说每个镜头都由多组不同曲面曲率的透镜按不同间距组合而成。间距和镜片曲率、透光系数等指标的选择决定了该镜头的焦距。 一、镜头分类 摄像机镜头按其功能和操作方法分为常用镜头和特殊镜头两大类。常用镜头又分为定焦镜头(自动和手动光圈)和变焦镜头(自动和手动光圈)。特殊镜头是根据特殊工作环境而专门设计的,一般有广角镜头、针孔镜头等。 二、镜头参数 a、相对孔径 光圈的主要作用是通过控制镜头光量的大小满足成像所需的合适照度。光圈越大,靶面成像照度越大,摄像机输出信号强度越大,信噪比越高。若光圈的实际孔径为ψ,由于光线通过透镜后的折射使镜头的有效孔径D 比实际孔径大,光圈的相对孔径等于有效孔径与镜头焦距之比,即:A=D/f,f 为镜头的焦距。 b、光圈系数 通常将表征镜头光圈大小的参数定义成光圈系数,用F 表示。光圈系数为镜头光圈相对孔径的倒数。F值的规律是后一个值正好是前一个数值的√2 倍,这是由于成像面中心亮度与(1/F)2成正比。F值越小相应灵敏度越大。常用值为1.4、2、2.8、4、5.6、8、11、 16、22等几个等级。 c、视场角 我们常用视场角来表征观察景物的范围。所谓视场角是指在视场角内的景物可全部落入成像尺寸内,而视场角以外的景物将不被摄取。因此,镜头的视场角与摄像机的靶面及镜头的焦距有关。 根据几何原理可以得到视场角的计算公式如下: ωH=2tg-1(h/2f)ωV=2tg-1(v/2f) 式中ωH为水平视场角,ωV为垂直视场角,f 为镜头的焦距,h为摄像机靶面的水平宽度,v为摄像机靶面的垂直高度。具体数值可参阅摄像机一节。 当成像尺寸确定后,焦距越短,视场角越大。因此可将镜头分为长角镜头(视场角小于45°)、标准镜头(视场角为45°~50°)、广角镜头(视场角大于50°)、超广角镜头(视场角接近180°)、鱼眼镜头(视场角大于180°)等。 另外,我们还可以得到如下公式以计算其中任一未知项数据。 f/v=D/V f/h=D/H 其中:f───镜头焦距;D───镜头至景物距离; h───靶面宽度;H───靶面高度。 三、镜头接口 镜头的安装方式有C型安装和CS型安装两种。C型安装接口指从镜头安装基准面到焦点的距离为17.526mm,而CS型接口的镜头安装基准面到焦点距离为12.5mm。因此将C型镜头安装到CS接口摄像机时需要加装一个5mm厚的接圈。

空之轨迹fc图文攻略

PC版游戏的第0页有自动存档,如果不幸卡关或者黑屏死机什么的,请读第0页自动存档 地图原尺寸普遍较大,由于度娘会自动缩图,如果觉得看不清楚请点开原图查看 序章父亲、启程 在开篇剧情结束之后(如果不幸黑屏,请参阅置顶或者精品区本人FAQ,还是无法解决请在吧内求助吧友),小约和小艾需要前往洛连特市的游击士协会(PC版界面右上角可查看小地图),在游击士协会与爱娜对话后去二楼与雪拉对话,听过一些基础知识后艾约被带往导力工房,接下来请按照雪拉的要求合成回路并装到主角的导力器上(请至少合成HP1和行动力1,并在艾导力器上装HP1,约导力器上装行动力1)然后给主角中任意一位的导力器开封结晶孔。导力系统介绍完毕后艾约会前往地下水路,开始实地研修。

PS:在协会获得的游击士手册包含游戏大多数基础知识,且记录有游戏主线与支线任务的完成情况,请新手们务必仔细查阅(话说有些童鞋不知道手册能翻页?……)

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八大风格全面解析

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