Digital Ecosystems: Self-Organisation of Evolving Agent Populations

Digital Ecosystems: Self-Or ganisation of Ev olving Agent P opulations Gerard Briscoe Digital Ecosystems Lab Depar tment of Media and Communications London School of Economics United Kingdom g.briscoe@lse.ac.uk Philippe De Wilde Intelligent Systems Lab Depar tment of Computer Science Heriot Watt Univ ersity United Kingdom pdw@hw .ac.uk ABSTRA CT A primary motiv ation for our researc h in Digit al Ecosystems is the desire to exploit the self-organising prop erties of biological ecosystems. Ecosystems are though t to be robust, scalable architectures that can automatically solve complex, dynamic problems. Self-organisation is p erhaps one of the most desirable features in the systems that w e engineer, and it is imp ortan t for us to b e able to measure self-organising behaviour. W e in v estigate the self-organising asp ects of Digital Ecosystems, created through the application of ev olutionary computing to Multi-Agen t Systems (MASs), aiming to determine a macroscopic v ariable to characterise the self-organisation of the ev olving agent populations within. W e study a measure for the self-organisation called Ph ysical Complexity; based on sta tistical p h ysics, automata theory , and information theory , providing a measure of information relative to the randomness in an organism’s genome, b y calculating the entrop y in a p opulation. W e in v estigate an extension to include populations of v ariable length, and then built up on this to construct an efficiency measure to in vestigate clustering within evolvin g agent populations. Ov erall an insight has b een achi eved into where and ho w self-organisation o ccurs in our Digital Ecosystem, and how it can b e quan tified. Categories and Subject Descriptors C.2.4 [ Distributed Systems ]: N etw ork Op erating Sys- tems; D.2.11 [ Soft w are Arc hitectures ]: P atterns; H.1.0 [ Information Systems ]: General K eywords Complexit y , en tropy , clustering, ev olution, p opulation. 1. INTR ODUCTION Digital Ecosystems are distributed adaptiv e op en so cio- tec hnical systems, with prop erties of self-organisation, scal- abilit y and sustainabilit y , inspired by natural ecosystems [9], and are emerging as a nov el approach to the catalysis . of sustainable regional dev elopment driven by Small and Medium sized Enterprises (SMEs). Digital Ecosystems aim to help lo cal economic actors b ecome active play ers in globalisation, v alorising their lo cal culture and vocations, and enabling them to in teract and create v alue net works at the global level [16]. With its technical component being the digital coun terpart of a biological ecosystem, providi ng for the ev olution of softw are services (agent s) in a distributed net w ork [13, 12]. W e considered t he a v ailable literature on self-o rganisation, for its general properties, its application to MASs (the dom- inan t tec hnology in Digital Ecosystems), and its application to the evolving agen t p opulations of our Digital Ecosystem. Self-organisation has b een around since the late 1940s [5], but has escaped general formalisation despite man y attempts [24]. There hav e instead b een man y notions and definitions of self-organisation, useful within their different con texts [19]. They ha ve come from cyb ernetics [5, 7], thermodynamics [24], mathematics [21], information theory [26], synergetics [18], and other domains [20]. The term self-or ganising is widely used, but there is no generally accepted meaning, as the abundance of definitions would suggest. Therefore, the philosoph y of self-organisation is complicated, b ecause organisation has differen t meanings to differen t p eople. So, w e would argue that an y definition of self-organisation is context dep enden t, in the same w ay that a c hoice of statist ical measure i s dependent o n the data being analysed. Therefore, in the con text of our Digital Ecosystems [11, 10] we shall further considering its self- organisation. 2. SELF-ORGANISA TION Proposing a definition for self-organisation faces the cy- b ernetics problem of defining system , the c o gnitive problem of p ersp e ctive , the philosophic al problem of defining self , and the c ontext dep enden t problem of defining or ganisation [17]. The system in this context is an evolving agent p opulation , with the replication of individuals from one generation to the n ext, the recom bination of the individuals, and a selection pressure providing a differential fitness betw een the individuals, whic h is b ehaviour comm on to an y ev olving p opulation [8]. Persp e ctive can b e defined as the perception of the o bserv er in perceiving the sel f-organisation of a system [7], match ing the intuitiv e definition of I wil l know it when I se e it , whic h despite making formalisation difficult shows that organisation is p ersp e ctive dep endent (i.e. relative to the c ontext in whic h it occurs). In the c ontext of an evolutionary system, the observ er do es not exist in the traditional sense, but is the sele ction pr essur e (HIGH organisation) (LOW organisation) Figure 1: Self-Organisation in Evolving Agent P opulations: The agen t p opulation on the left in- tuitiv ely shows organisation through the uniformit y of the colours across the agen t-sequences, whereas the population to the right sho ws little organisation. imposed by the environmen t, which sele cts individuals of the population ov er others based on their obser vable fitness . Therefore, consisten t with the theoretical biology [8], in an ev olutionary system the self-organisation of its population is from the p ersp e ctive of its environmen t. Whether a system is self -organising or being organised dep ends on whether the process causing the organisation is an internal comp onen t of the system under consideration. This intuitiv ely makes sense, and therefore requires one to define the boundaries of the system b eing considered to determine if the force causing the organisation is internal or external to the system. F or an evolving p opulation the force leading to its organisation is the sele ction pr essur e acting up on it [8], whic h is formed by the environmen t of the population’s existence and competition b et we en the individuals of the population [8]. As these are in ternal components of an ev olving agent p opulation [8], it is a self-organising system. No w that we hav e defined, for an evolving agent pop- ulation, the system for which its or ganisation is c ontext dependent, the p ersp e ctive to which it is relative, and the self b y whic h it is caused, a definition for its self- or ganisation can b e considered. The c ontext , an evolving agen t p opulation in its environmen t, lacks a 2D or 3D metric space, so it is necessary to consider a visualisation in a more abstract form. W e will let a single square, , represen t an agent, with colours to represent differen t agen ts. Agen t-sequences will therefore b e represented by a sequence of coloured squares, , with a p opulation consisting of m ultiple agent-sequences, as sho wn in Figure 1. In Figure 1 the num b er of agen ts, in total and of eac h colour, is the same in b oth populations. Ho wev er, the agen t p opulation on the left intuitiv ely shows organisation through the uniformity of the colours across the agen t- sequences, whereas the p opulation to the righ t shows little or no organisation. While alternative definitions hav e b een prop osed [15, 6, 25, 14], with each defining what property or properties demonstrate self-organisation, they lack applicability to ev olving agent populations, b ecause of the context dep en- den t nature of self-organisation. Ho w ever, the prop erties of Physical Complexity [4] closely matc hed our intuitiv e understanding, and so was chosen for further inv estigation. 2.1 Physical Complexity Ph ysical Complexity was b orn [1] from the need to determine the prop ortion of information in sequences of DNA, b ecause it has long b een established that the infor- mation contained is not directly prop ortional to the length, kno wn as the C-v alue enigma/parado x [27]. Ho w ever, because Physical Complexity analyses an ensemble of DNA sequences, the consistency b et w een the different solutions sho ws the information, and the differences the redundancy [2]. En trop y , a measure of disorder, is used to determine the redundancy from the information in the ensemble. Ph ysical Complexit y therefore provides a context-rela tiv e definition for the self-organisation of a p opulation without needing to define the context (environmen t) explicitly [3]. Ph ysical Complexity was deriv ed [3] from the notion of c onditional c omplexity defined by Kolmogoro v, which is differen t from traditional Kolmogoro v complexit y and states that the determination of complexity of a sequence is conditional on the environmen t in whic h the sequence is in terpreted [23]. So, the complexity of a p opulation S , of sequences s , C = ` − ` X i =1 H ( i ) , (1) is the maximal entrop y of the p opulation (equiv alent to the length of the sequences) ` , min us the sum, o v er the length ` , of the per-site entropies H ( i ), H ( i ) = − X d ∈ D p d ( i ) log | D | p d ( i ) , (2) where i is a site in the sequences ranging b et ween one and the length of the sequences ` , D is the alphab et of characters found in the sequence s, and p d ( i ) is the probabilit y that site i (in the sequences) takes on character d from the alphab et D , with the sum of the p d ( i ) probabilities for eac h site i equalling one, P d ∈ D p d ( i ) = 1 [3]. So, the equiv alence of the maxim um complexit y to the length matches the intuitiv e understanding that if a p opulation of sequences of length ` has no redundancy , then their complexity is their length ` . If G represents the set of all p ossible genotypes con- structed from an alphab et D that are of length ` , then the size (cardinalit y) of | G | is equal to the size of the alphab et | D | raised to the length ` , | G | = | D | ` . (3) F or the complexity measure to b e accurate, a sample size of | D | ` is suggested to minimise the error [3], but such a large quan tit y can be computationally infeasi ble. The definitio n’s creator, for practical applications, chooses a p opulation size of | D | ` , which is sufficient to show an y trends presen t. So, for a population of sequences S we c hoose, with the definition’s creator, a computationally feasible p opulation size of | D | times ` , | S | ≥ | D | `. (4) The size of the alphab et, | D | , dep ends on the domain to which Ph ysical Complexity is applied. F or RNA the alphabet is the four nucleotides, D = { A, C , G, U } , and therefore | D | = 4 [3]. 2.2 V ariable Length Sequences Ph ysical Complexit y is curren tly form ulated for a pop- ulation of sequences of the same length [3], and so we will now inv estigate an extension to include populations of v ariable length sequences, which will include p opulations of v ariable length agen t-sequences of our Digital Ecosystem. This will require c hanging and re-justifying the fundamental assumptions, sp ecifically the conditions and limits upon whic h Ph ysical Complexity op erates. In (1) the Ph ysical Complexit y , C , is defined for a p opulation of sequences of length ` [3]. The most imp ortant question is what do es the length ` equal if the p opulation of sequences is of v ariable length? The issue is what ` represents, whic h is the maxim um p ossible complexity for the p opulation [3], whic h w e will call the c omplexity p otential C P . The maximum complexit y in (1) o ccurs when the p er-site entropies sum to zero, ` P i =1 H ( i ) → 0, as there is no randomness in the sites (all contain information), i.e. C → ` [3]. So, the c omplexity p otential equals the length, C P = `, (5) pro vided the p opulation S is of sufficient size for accurate calculations, as found in (4), i.e. | S | is equal or greater than | D | ` . F or a p opulation of v ariable length sequences, S V , the complexity p oten tial, C V P , cannot b e equiv alent to the length ` , because it do es not exist. Ho w ev er, given the concept of minim um sample size from (4), there is a length for a population of v ariable length sequences, ` V , b et ween the minimum and maxim um length, such that the num b er of p er-site samples up to and including ` V is sufficien t for the p er-site entropies to b e calculated. So the c omplexity p otential for a p opulation of v ariable length sequences, C V P , will be equiv alent to its c alculable length, C V P = ` V . (6) If ` V where to b e equal to the length of the longest indi- vidual(s) ` max in a p opulation of v ariable length sequences S V , then the op erational problem is that for some of the later sites, b etw een one and ` max , the sample size will b e less than the p opulation size | S V | . So, having the length ` V equalling the maxim um length would be incorrect, as there w ould b e an insufficient num b er of samples at the later sites, and therefore ` V 6≡ ` max . So, the length for a population of v ariable length sequences, ` V , is the highest v alue within the range of the minim um (one) and maxim um length, 1 ≤ ` V ≤ ` max , for whic h there are sufficient samples to calculate the en trop y . A function whic h provides the sample size at a given site is required to sp ecify the v alue of ` V precisely , sampleS iz e ( i : site ) : int, (7) where the output v aries b etw een 1 and the p opulation size | S V | (inclusive). Therefore, the length of a population of v ariable length sequences, ` V , is the highest v alue within the range of one and the maximum length for which the sample size is greater than or equal to the alphab et size m ultiplied b y the length ` V , sampleS iz e ( ` V ) ≥ | D | ` V ∧ sampl eS iz e ( ` V + 1) < | D | ` V , (8) where ` V is the length for a p opulation of v ariable length sequences, and ` max is the maxim um length in a p opulation of v ariable length sequences, ` V v aries b etw een 1 ≤ ` V ≤ ` max , D is the alphabet and | D | > 0. This definition in trinsically includes a minim um size for populations of v ariable length sequences, | D | ` V , and therefore is the coun terpart of (4), which is the minimum p opulation size for populations of fixed length. The length ` used in the limits of (2) no longer exists, and therefore (2) must b e up dated; so, the p er-site entrop y calculation for v ariable length sequences will be denoted by H V ( i ), and is, H V ( i ) = − X d ∈ D p d ( i ) log | D | p d ( i ) , (9) where D is still the alphab et, ` V is the length for a population of v ariable length sequences, with the site i now C V =4 . 420 , % E = 88 . 4 C V =0 . 575 , % E = 11 . 5 Figure 2: Abstract Visualisation for Populations of V ariable Length Sequences: The Physical Complexit y and Efficiency v alues are consisten t with the in tuitive understanding one w ould ha ve for the self-organisation of the sample p opulations. ranging b et wee n 1 ≤ i ≤ ` V , while the p d ( i ) probabilities still range betw een 0 ≤ p d ( i ) ≤ 1, and still sum to one. It remains algebraically almost identical to (2), but the conditions and constra in ts of its use will change, specifically ` is replaced b y ` V . Naturally , H V ( i ) ranges b et ween zero and one, as did H ( i ) in (2). So, when the entrop y is maxim um the character found in the site i is uniformly random, and therefore holds no information. Therefore, the complexity for a p opulation of v ariable length sequences, C V , is the c omplexity p otential of the population of v ariable length seq uences min us the sum, ov er the length of the p opulation of v ariable length sequences, of the per-site en tropies (9), C V = ` V − ` V X i =1 H V ( i ) , (10) where ` V is the length for the p opulation of v ariable length sequences, and H V ( i ) is the entrop y for a site i in the population of v ariable length sequences. Ph ysical Complexity can now b e applied to p opulations of v ariable length sequences, so we will consider the abstract example p opulations in Figure 2. W e will let a single square, , represent a site i in the sequences, with different colours to represent the differen t v alues. Therefore, a sequence of sites will b e represen ted b y a sequence of coloured squares, . F urthermore, the alphab et D is the set { , , } , the maxim um length ` max is 6 and the length for p opulations of v ariable length sequences ` V is calculated as 5 from (8). The Physical Complexity v alues in Figure 2 are consisten t with the i nt uitiv e understanding one w ould hav e for the self- organisation of the sample populations; the population with high Ph ysical Complexity has a little randomness, while th e population with low Physical Complexity is almost entirely random. 3. EFFICIENCY Using our extended Physica l Complexit y w e can construct a measure sho wing the use of the information space, called the Efficiency E , whic h is calculated by the Physical Complexit y C V o ve r the complexity p oten tial C V P , E = C V C V P . (11) The Efficiency E will range b etw een zero and one, only reac hing its maximum when the actual complexity C V equals the complexity p oten tial C V P , indicating that there is no randomness in the p opulation. In Figure 2 the populations of sequences are shown with their resp ectiv e Efficiency v alues as p ercentages, and the v alues are as one w ould expect. The complexity C V (10) is an absolute measure, whereas the Efficiency E (11) is a relativ e measure (based on the complexit y C V ). So, the Efficiency E can b e used to compare the self-organised complexit y of populations, independent of their size, their length, and whether their lengths are v ariable or not (as it is equally applicable to the fixed length p opulations of the original Physical Complexit y). 4. SIMULA TION AND RESUL TS A simulated p opulation of agent-sequences, [ A 1 , A 1 , A 2 , ... ], w as evolv ed to solv e user requests, seeded with agen ts and agen ts from the agent-p o ol of the habitats in whic h they w ere instantiated. A dynamic p opulation size was used to ensure exploration of the av ailable combinatorial searc h space, which increased with the av erage size of the popu- lation’s agen ts. The optimal com bination of agen ts (agen t) w as ev olved to the user request R , by an artificial selecti on pr essur e created by a fitness function generated from the user request R . An individual (agent) of the p opulation consisted of a set of attributes, a 1 , a 2 , ... , and a user request consisted of a set of required attributes, r 1 , r 2 , ... . So, the fitness function for ev aluating an individual agen t A , relativ e to a user request R , was f itness ( A, R ) = 1 1 + P r ∈ R | r − a | , (12) where a is the mem b er of A such that the difference to the required attribute r was minimised. Equation 12 w as used to assign fitness v alues betw een 0.0 and 1.0 to each indi- vidual of the current generation of the p opulation, directly affecting their abilit y to replicate into the next generation. The evolutionary computing pro cess was enco ded with a lo w m utation rate, a fixed selection pressure and a non- trapping fitness function (i.e. did not get trapp ed at lo cal optima). The type of selection used fitness-pr op ortional and non-elitist , fitness-pr op ortional me ans that the fitter the individual the higher its prob ability of surviving to the next generation. Non-elitist means that the b est individual from one generation was not guaranteed to survive to the next generation; it had a high probabilit y of surviving in to the next generation, but it was not guaranteed as it migh t hav e b een mutated. Cr ossover (recom bination) w as then applied to a randomly chosen 10% of the surviving population, a one-p oint cr ossover , by aligning tw o paren t individuals and pic king a random p oin t along their length, and at that p oin t exchanging their tails to create tw o offspring. Mutations were then applied to a randomly c hosen 10% of the surviving p opulation; p oint mutations w ere randomly lo cated, consisting of insertions (an agent w as inserted into an agent-sequen ce), r eplac ements (an agen t w as replaced in an agent-sequ ence), and deletions (an agent was deleted from an agen t-sequence). The issue of bloat was controlled by augmen ting the fitness function with a p arsimony pr essur e which biased the searc h to shorter agen t-sequences, ev aluating larger than a vera ge agen t-sequences with a reduced fitness , and thereby provid- ing a dynamic control limit which adapted to the av erage length of the ev er-changing evolving agent p opulations. Figure 3 sho ws, for a t ypical evolving agen t p opula- tion, the Physical Complexit y C V (10) for v ariable length sequences and the maximum fitness F max o ver the gen- erations. It shows that the fitness and our extended Ph ysical Complexity; both increase ov er the generations, sync hronised with one another, un til generation 160 when the maximum fitness tap ers off more slo wly than the Ph ysical Complexit y . A t this p oin t the optimal length for 0 10 20 30 50 100 138 150 200 250 300 0 20 40 60 80 100 Physical Complexit y % Fitness Generation Maximum Fitness F max Physical Complexit y C V Figure 3: Graph of Physical Complexity and Maxim um Fitness ov er the Generations: The Ph ysical Complexity for v ariable length sequences increases o ver the generations, showing short-term decreases as expected, such as at generation 138. the sequences is reac hed within the simulation, and so the adv en t of new fitter sequences (of the same of similar length) creates only minor fluctuations in the Physical Complexity , while having a more significan t effect on the maximum fitness . The similarity of the graph in Figure 3 to the graphs in [4] confirms that the Physical Complexity measure has been successfully extended to v ariable length sequences. 4.1 Efficiency Figure 4 is a visualisation of the simulation, showing t wo alternate populations that w ere run for a thousand generations, with the one on the left from Figure 3 run under normal conditions, while the one on the righ t was run with a non-discriminating selection pressure. Eac h m ulti-coloured line represen ts an agen t-sequence, while eac h colour represents an agen t (site). The visualisation shows that our Efficiency E accurately me asures the self-organised complexit y of the tw o populations. 7 7 9 15 2 9 4 4 11 9 1 8 12 7 15 11 13 11 2 5 8 6 4 4 10 10 7 6 14 14 13 4 14 11 13 14 4 12 11 5 15 10 2 12 12 12 13 4 4 11 15 15 9 15 15 3 8 10 2 13 10 12 10 13 2 10 6 1 15 8 7 1 13 4 8 5 1 1 7 11 7 7 1 13 4 8 5 1 7 11 7 15 3 8 10 2 13 10 12 10 13 2 10 1 15 8 4 13 13 15 15 9 15 15 7 12 15 15 7 12 15 4 13 11 15 15 9 15 3 8 10 2 13 10 12 13 2 10 15 8 7 1 13 4 8 5 1 7 11 7 7 10 13 4 8 5 1 7 11 7 15 3 8 10 2 13 10 12 10 13 2 10 1 15 8 4 13 11 15 9 15 4 12 11 5 15 10 2 12 12 12 13 4 7 14 14 13 4 14 11 13 13 14 13 11 2 8 6 4 4 10 10 4 7 15 11 13 7 9 15 2 9 4 4 11 9 1 8 12 11 1 12 3 10 1 9 1 14 13 10 2 11 13 7 13 1 7 14 3 13 2 8 1 2 3 5 13 3 4 2 4 3 3 6 1 10 12 1 12 14 2 14 5 5 9 14 11 6 4 4 15 10 12 14 14 7 11 9 6 15 9 15 13 8 10 11 2 5 1 15 15 1 6 1 12 9 10 9 4 1 8 12 13 5 11 15 7 5 14 14 4 12 9 12 13 4 12 4 3 13 9 15 11 12 5 8 6 13 15 4 6 11 2 8 11 4 9 2 4 13 11 10 8 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14 2 9 10 14 6 2 2 10 4 1 5 9 11 6 10 7 8 1 8 14 2 9 10 14 6 2 2 10 4 1 5 9 11 6 10 7 8 1 8 14 2 9 10 14 6 2 2 10 4 1 5 9 11 6 10 7 8 1 8 14 2 9 10 14 6 2 2 10 4 1 5 9 11 6 10 7 8 1 8 14 2 9 10 14 6 2 2 10 4 1 5 9 11 6 10 7 8 1 8 14 2 9 10 14 6 2 2 10 4 1 5 9 11 6 10 7 8 1 8 14 2 9 10 14 6 2 2 10 4 1 5 9 11 6 10 7 8 1 8 14 2 9 10 14 6 2 2 8 4 1 5 9 11 6 10 7 8 1 8 14 2 9 10 14 6 2 2 10 4 5 9 11 6 10 7 8 1 8 14 2 9 10 14 6 2 2 10 4 1 5 9 11 6 10 7 8 1 8 14 2 9 10 14 6 2 2 10 4 1 5 9 11 6 10 7 8 1 8 14 2 9 10 6 2 2 10 4 1 5 9 11 6 10 7 8 1 8 14 2 9 10 14 6 2 2 10 4 1 5 9 11 6 10 7 8 1 8 14 2 9 10 14 6 2 2 10 4 1 5 9 11 6 10 7 8 1 8 14 2 9 10 14 6 2 2 10 4 1 5 9 11 6 10 7 8 1 8 14 2 9 10 14 6 2 2 10 4 1 5 9 11 6 10 7 8 1 8 14 2 9 10 14 6 2 2 10 4 1 5 9 11 6 10 7 8 1 8 14 2 9 10 14 2 2 10 4 1 5 9 11 6 10 7 8 1 8 14 2 9 10 14 6 2 10 4 1 5 9 11 6 10 7 8 1 8 14 2 9 10 14 6 2 2 10 4 1 5 9 11 4 10 7 8 1 8 14 2 9 10 14 6 2 2 10 4 1 5 9 11 4 10 7 8 1 8 14 2 9 10 14 6 2 2 10 4 1 5 9 11 4 10 7 8 1 8 14 2 9 10 14 6 2 2 10 4 1 5 9 11 4 10 7 8 1 8 14 2 9 10 14 6 2 2 10 4 1 5 9 11 4 10 7 8 1 8 14 2 9 10 14 6 2 2 10 4 1 5 9 11 4 10 7 8 1 8 14 2 9 4 10 14 6 2 2 10 4 1 5 9 11 4 10 7 8 1 8 14 2 9 10 14 6 2 2 10 4 1 5 9 11 4 10 7 8 1 8 14 2 9 10 14 6 2 2 10 4 1 5 9 11 4 10 7 8 1 8 14 2 9 10 14 6 2 2 10 4 1 5 9 11 4 10 7 8 8 14 2 9 10 14 6 2 2 10 4 1 5 9 11 4 10 7 8 1 8 14 2 9 10 14 6 2 2 10 4 1 5 9 11 4 Population (normal conditions) Population (non-discriminating) Agent-sequence (length) 1 1 ! V ! V E ffi ciency % E = 96.8% C V = 19 . 351 ,C V P = 20 E ffi ciency % E = 47.0% C V =4 . 227 ,C V P =9 Figure 4: Visualisation of Ev olving Agen t p opu- lations at the 1000th Generation: The population on the left from Figure 3 was run under normal conditions, while the one on the right w as run with a non-discriminating selection pressure. 0.6 0.7 0.8 0.9 1 0 100 200 300 Efficiency Generation Figure 5: Graph of Population Efficiency ov er the Generations for the p opulation from Figure 3: The Efficiency tends to a maximum of one, indicating that the p opulation consists of one cluster. Figure 5 sho ws the Efficiency E (11), o ver the generat ions, for the p opulation from Figure 3. The Efficiency tends to a maxim um of one, indicating that the p opulation consists of one cluster, whic h is confirmed b y the visualisation of the population in Figure 4 (left). 5. CONCLUSIONS W e extended Ph ysical Complexity to provide a greater understanding of MASs with evolutionary dynamics , sp ecif- ically evolving agent p opulations, including our Digital Ec osystem . W e then built up on this to define an Efficiency measure. Collectiv ely , the exp erimen tal results confirm that Physical Complexity has been successfully extended to evolving agen t p opulations. Most significantly , Physical Complexit y has b een reformulated algebraically for p opula- tions of v ariable length sequences, which w e hav e confirmed experimentally through simulati ons. Our Efficiency definition not only provides a macroscopic v alue to characterise the level of self-or ganisation , but the understanding and tec hniques we hav e dev eloped hav e applicabilit y beyond evolving agent p opulations; as wide as the original Ph ysical Complexity , whic h has b een applied from DNA [3] to simulations of self-replicating programmes [22]. 6. A CKNO WLEDGMENTS The authors w ould lik e to thank the follo wing for en- couragemen t and suggestions; Dr P aolo Dini of the Lon- don School of Economics and Political Science, and Dr Christoph Adami of the California Institute of T echnol- ogy . This work was supp orted b y the EU-funded Open Philosophies for Associative Autopoietic Digital Ecosystems (OP AALS) Netw ork of Excellence (NoE), Contract No. FP6/IST-034824. 7. REFERENCES [1] C. Adami. Intr o duction T o Ar tificial Life . Springer, 1998. [2] C. Adami. Sequence complexity in darwinian ev olution. Complexity , 8:49–56, 2003. [3] C. Adami and N. Cerf. Ph ysical complexity of sym b olic sequences. Physic a D , 137:62–69, 2000. [4] C. Adami, C. Ofria, and T. Collier. Evolution of biological complexity . Pro c e edi ngs of the National A c ademy of Scienc es , 97:4463–4468, 2000. [5] W. Ashb y . Principles of the self-organizing dynamic system. Journal of Gener al Psycholo gy , 37:125–128, 1947. [6] A. Barron, J. 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