Cellular Automata and Agent-Based Models - Springer

Cellular Automata and Agent-Based Models

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Keith C. Clarke

Contents 62.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.2 Complexity and Models of Complexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.3 Cellular Automata: Origins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.4 Cellular Automata: Key Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.5 Cellular Automata: Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.6 Agent-Based Models: Origins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.7 Agent-Based Models: Key Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.8 Agent-Based Models: Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.9 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract

Two classes of models that have made major breakthroughs in regional science in the last two decades are cellular automata (CA) and agent-based models (ABM). These are both complex systems approaches and are built on creating microscale elemental agents and actions that, when permuted over time and in space, result in forms of aggregate behavior that are not achievable by other forms of modeling. For each type of model, the origins are explored, as are the key contributions and applications of the models and the software used. While CA and ABM share a heritage in complexity science and many properties, nevertheless each has its own most suitable application domains. Some practical examples of each model type are listed and key further information sources referenced. In spite of issues of data input, calibration, and validation, both

K.C. Clarke Department of Geography, University of California, Santa Barbara, Santa Barbara, CA, USA e-mail: [email protected] M.M. Fischer, P. Nijkamp (eds.), Handbook of Regional Science, DOI 10.1007/978-3-642-23430-9_63, # Springer-Verlag Berlin Heidelberg 2014

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modeling methods have significantly advanced the role of modeling and simulation in geography and regional science and gone a long way toward making models more accountable and more meaningful at the base level.

62.1

Introduction

Models are simplifications of real-world systems that are amenable to tests and simulations of the reactions of the real systems to changes in their state and function. For extant and complicated regional systems, such as the United States Interstate Highway system, experiments on society would be unacceptable (closing highways to measure traveler delays, for example) – yet the computer allows such experiments in silico. Models, of course, are only of value if their structures are based on knowledge or data about an actual system and if they give results which are reasonable and credible. Foremost among the challenges of modeling is the fine-tuning of models so that they achieve the best results (calibration), of meaningfully converting a system’s components into structural and behavioral equivalents within the model (design), of the model’s effective use of computing power (tractability), of the ability to match actual or expected results (performance), and of their ability to create accurate predictions (validity). Regional science has employed a large number of modeling approaches over time, yet in the last three decades, two paradigms of modeling have emerged that have made achievements against these challenges and that have led to breakthroughs in model performance and accuracy for regional systems. These two approaches are cellular automata (CA) models and agent-based models (ABM). In this chapter, we examine these two modeling approaches. Both have been termed “individual-based modeling approaches” in ecology, and this reflects the fact that both types of models are bottom-up – that is, they model the primitive or elemental level of behavior associated with a system. Aggregate patterns are achieved by summing the results of many individual actions, which has led to the related terms “disaggregated models” and “micro-simulation models.” Both these approaches are similar in that they are simple, easy to program and implement, and use an iterative approach. Both require initial conditions to be set and have challenges around calibration procedures. Cellular models are preferred when geographic space can be represented in the form of a geographic grid, such as the cells in a raster Geographic Information System. They are also favored when model states and the probabilities of transitions among those states are known and stable. They are most suitable for dissipative processes, such as land use change and urban growth. On the other hand, agent-based models are superior when the basis of a model is a behavioral unit, such as a person, household, business, landholder, or farmer (the “agent”), and when the modeled process consists of interactions over time among one or more types of agents that produce a spatial form, such as land use, crop choice, or habitat type. It has been said that the two modeling forms differ only in the fact that in CA the agents remain in place and interact only with their neighbors. This statement, however, ignores

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both major and subtle differences between the two modeling approaches, such as their means of calibration and validation. We return to this contrast in the concluding section.

62.2

Complexity and Models of Complexity

Complex systems theory was originally developed in physics and has origins in Lorenz’s work on weather forecasting, which in turn reflect chaos theory and work on the three-body problem by Poincare´ in 1890. Initially, Lorenz observed that a system’s behavior in the long term reflects the initial conditions of the system, such as the locus of an attraction point being a function of where a point subject to the attraction started its path. The values of variables that separate different system behaviors are called thresholds, and crossing them leads to nondeterministic and nonlinear behavior. Complexity is that behavior phase which is neither static nor deterministic. An early demonstration of complexity was in sand piles. When sand is poured from a nozzle, it forms a pile, which grows in a simple linear fashion. However, at some point in its growth, the sides of the pile are subject to failure. Even though the exact failure gradient is known, it is impossible to tell when a failure will take place and how much of the sand pile it will take down. Such behavior has been called self-organized criticality. As chaos and complexity theory became more known, largely due to the Santa Fe Institute and the work of scholars like Murray Gell-Mann and John Holland, applications in many different fields became commonplace. Complexity has a natural link to the science of fractals and self-similarity, as noted by Batty (2000). Many of the fields that adopted the complex systems approach were related to physical geography, such as meteorology, fire modeling, and ecological succession. However, Batty and Longley’s (1994) demonstration of the fractal nature of cities led to some degree of acceptance within urban and human geography. Many systems in human geography exhibit complexity, including land use change, residential segregation, urban growth, road network growth, and intercity interactions. Important concepts in complexity theory are that dynamical systems – those subject to feedbacks – exist in three aggregate states or phases: chaos, stability, and complexity. In chaos, no discernable rules, structures, or even heuristics apply, such as in the business cycle or the stock market. In stability, behavior is linear or can be modeled by polynomials, that is, the change is differentiable and solvable with differential equations, equilibrium theory, and optimization. Complexity, however, is marked by periods (time) or subregions (space) of both stability and chaos. A system can move from one aggregate behavior state to another (a phase change), but each behavior type is robust (resilient) against perturbation to some degree (Waldrop 1993). Tipping a system beyond a threshold provokes a phase change, and the system then trends away from the original state. An example often used is a lake, which is subject to inputs of phosphates. The ecosystem of the lake is able to counter the impact of the phosphates up to a certain concentration. Beyond that, even by a fraction, the lake cannot return to its initial state, and eutrophication takes

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place, leading to a new ecosystem based on the higher phosphate levels and different plant and animal species. An unknown, possibly large, proportion of human and natural systems exhibit such complexity. The attraction of both cellular automata and agent based models is they represent some of the simplest frameworks possible for demonstrating complex systems behavior. Largely for this reason, the models were quickly adopted and used to test many new types of urban and economic systems models. John Holland has suggested a defining condition for identifying complex systems and complexity, which he has termed emergence (Holland 1998). Emergence has been criticized as too subjective a criterion by which to indentify complexity but is said to exist in a system when new and unpredicted patterns or global-level structures arise as a direct result of local-level procedures. The structure or pattern that emerges cannot be understood or predicted from the programmed or assumed behavior of the individual units alone. An example of emergence in CA is the glider (see Sect. 62.3). An example in the SLEUTH CA urban model (Clarke et al. 2007) is the aggregation of new settlements at the junctions of roads, a behavior nowhere inherent in the model’s programmed behavior.

62.3

Cellular Automata: Origins

A cellular automaton (plural cellular automata) is a discrete model originally theoretical, but now implemented in disciplines from physics to biology, geography to ecology, and computer science to regional science. CA have been defined as “discrete spatio-temporal dynamic systems based on local rules” (Miller 2009). As noted above, they are the simplest modeling framework in which complexity can be demonstrated. Using CA, extremely complex behavior and emergence can be demonstrated with terse conditions and minimal rules. They are inherently attractive as spatial models because they map closely onto the raster grid in a geographic information system, because they use only local interactions among cells, and because of their simplicity. Nevertheless, they are capable of modeling and simulating extraordinarily complex behavior (Batty 2000) and of demonstrating emergence. A CA has four elements: (i) a grid of cells, each of which can assume a finite number of states; (ii) a neighborhood, over which a change operator applies, usually the Moore (8-cell) neighborhood surrounding a cell in the grid; (iii) a set of initial conditions, that is, an instance of the states for each and every cell in the system; and (iv) one or more rules, which when applied change the state of a cell based on properties or states of the neighborhood cells. The model advances by applying the rules to every cell one at a time, then swapping the changed grid with the initial grid, and by repeating this procedure. CA were invented by Stanislaw Ulam, while he was employed at the Los Alamos National Laboratory in the 1940s. At the same time, John von Neumann was working on the problem of self-replicating systems. Von Neumann proposed the kinematic model, a robot that could rebuild itself from spare parts. Ulam recommended that von

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Fig. 62.1 A 2D cellular automaton Game of Life. Configuration shows a glider gun, a cell form that remains static and sends out streams of gliders. Gliders and glider guns are emergent behavior from the simple rules of the Game of Life

Neumann develop his idea around a mathematical abstraction, such as the one he was using to study crystal growth on a lattice network. Like Ulam’s lattice network, von Neumann’s cellular automata used a two-dimensional grid, with his self-replicator implemented algorithmically, working within a CA with a 4-cell neighborhood and with 29 states per cell. This CA is now termed a von Neumann universal constructor. At about the same time, Norbert Wiener and Arturo Rosenblueth developed a CA model and mathematical description of impulse conduction in cardiac systems, implying broad applicability of the theory. By the 1960s, CA were being studied as a simplification of dynamical systems – models developed to simulate natural systems with feedbacks, such as air flow, turbulence, and weather, and human systems such as cities and economies. In 1969, Gustav Hedlund compiled many CA results into a seminal paper on the mathematics of CA (Hedlund 1969). Nevertheless, CA remained largely a mathematical curiosity until John Conway’s creation of a CA game, the Game of Life. Martin Gardner drew popular attention to the game in a 1970 issue of his games column in Scientific American (Gardner 1970). Life was a two-state, two-dimensional CA with only four rules: (i) Any live cell with fewer than two live neighbors dies (death), (ii) Any live cell with two or three live neighbors remains alive (survival), (iii) Any live cell with more than three live neighbors dies (overcrowding), (iv) Any dead cell with exactly three live neighbors becomes alive (birth). Despite the game’s simplicity, it can create astonishing variety in its long-term patterns. An “emergent” phenomenon is the “glider,” a cell arrangement that perpetuates itself by continuous movement across the grid (Fig. 62.1). It is possible to arrange the automata so that gliders interact to perform computations, and it has been proven that the Game of Life can emulate a universal Turing machine, thus completing von Neumann’s line of research.

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Cellular Automata: Key Contributions

In the 1980s, Stephen Wolfram published a series of papers systematically investigating an unknown class of one-dimensional cellular automata, which he called elementary cellular automata (Wolfram 1986). The demonstration that what is now termed “complex systems behavior” can be simulated from the simplest of CA led to a host of explorations within the social and physical sciences into the range of what CA could simulate. Wolfram continued this work, and in 2002 published A New Kind of Science (Wolfram 2002). In the book, Wolfram argues that discoveries about cellular automata are not isolated facts but have significance for all disciplines of science. Using a one-dimensional CA, Wolfram demonstrated that virtually any mathematical function can be simulated, and he explored applications across disciplines. Wolfram proposed a four-class set of possible CA. In Class 1, nearly all patterns quickly evolve into a stable homogenous set and randomness disappears. In Class 2, nearly all patterns quickly evolve into an oscillating structure, with some randomness remaining. In Class 3, nearly all patterns evolve into pseudo-random or chaotic structures. Any regular structures are quickly eliminated by randomness, which dissipates through the entire system. In Class 4, nearly all initial patterns evolve into structures that interact in complex and interesting ways. Wolfram has conjectured that many class 4 cellular automata are capable of universal computation. This has been proven for Conway’s Game of Life and for Wolfram’s Rule 110. Rule 110 is a unique achievement, defined as a one-dimensional CA that for the input neighboring configuration set {111, 110, 101, 100, 011, 010, 001, 000} yields the equivalent outputs {0,1,1,0,1,1,1,0}. Of the 88 possible unique elementary cellular automata, Rule 110 is the only one for which Turing completeness has been proven, making it arguably the simplest known Turing complete system. Rule 110 exhibits Class 4 behavior, which is neither completely stable nor completely chaotic. Localized structures appear and interact in various complicated-looking ways, demonstrating the properties of emergence and phase change. There have been several attempts to place CA into other formally rigorous classes, inspired by Wolfram’s classification. For instance, Culik and Yu proposed three well-defined classes (and a fourth one for the automata not matching any of these) called Culik-Yu classes. From the perspective of geocomputation, Batty (2000) surveyed the variants of CA possible for simulating urban and similar systems. He pointed out that strict CA models are on one end of a computational spectrum and that at the other end are simple Cell Space models, really no different than raster grids with a finite set of states that transition over time. He distinguished between cell space models, which are not at all CA models in the strict sense, and the concept of relaxing the CA assumptions. Key among the relaxations is the incorporation of action-at-adistance, which is excluded by strict CA’s use of the von Neumann or Moore neighborhoods only. CA development in modeling of urban areas and other geographical realms are covered in a literature review, and some useful information sources are listed (Batty 2000, p. 119).

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Beyond mathematics, CA applications have been less concerned with definitional rigor and more with making CA adjust to geographical variation. Approaches have included automatic learning methods to empirically derive rules from observed patterns, self-modification or rule changes triggered by aggregate system behavior, and the addition of “ghost” states, that fall between strict classes (e.g., “urban,” “nonurban,” and “under development” as land uses). Sante et al. (2010) note eight ways that formal CA models have been modified for use in urban growth modeling: using irregular spaces, nonuniform cell spaces, extended neighborhoods, nonstationary neighborhoods, complex transition rules, nonstationary transition rules, by adding growth constraints, and using irregular time steps. Theoretical work has also examined the synchronous versus asynchronous application of the rules. Applications of CA models in regional science have been commonplace. Most frequently, the models work on land use maps, often simplified to urban and nonurban states. Rules are derived and models calibrated using past data states, that is, by hindcasting. Land use maps derived from remotely sensed data at different time periods have commonly been used as data inputs, and other data are often zoning restrictions, transportation networks, and topography. Geographic Information Systems are used to compile and georegister the map layers, and to receive the modeling results. CA models have been applied at many scales, following the research on fractal urban forms pioneered by Michael Batty (Batty 2005), but most CA models use data at resolutions between 30 and 100 m. An early model by White and Engelen (1993) added action-at-a-distance by changing the Moore neighborhood assumption. Clarke et al. (1997) created the SLEUTH model, a CA that incorporated weighting of probabilities and self-modification, feedback from the aggregate to the local. Wu and Webster’s modeling of the rapid growth in Southern China was another significant contribution (Wu and Webster 1998). Sante et al. (2010) tabulated 33 urban CA models and compared their characteristics, and provided a useful summary of the theoretical and applied CA modeling surrounding geography, urban planning, and regional science. Silva has considered complexity theory in planning more generally, using CA as the specific example (Silva 2010). Sante et al. (2010) also offered a classification of CA transition rules. Type I rules are those of classical CA, that is, transitions can only occur based on the states of neighboring cells. Type II rules are based on potentials or probabilities altered by the land or environmental status of a cell. Type III rules are pattern development rules, which adjust the states based on shape or the existence of a network, such as roads. Type IV rules use computational intelligence methods to determine the rules from prior system behavior. Typical are Case-Based Reasoning, neural networks, data mining and kernel-based methods. Type V rules use fuzzy logic and uncertainty reasoning, while Type VI rules include those not compatible with types I–V.

62.5

Cellular Automata: Applications

Examples of cellular models in popular use include DINAMICA (See: www.csr. ufmg.br/dinamica), SLEUTH (See: www.ncgia.ucsb.edu/projects/gig), and

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Fig. 62.2 Input data for the SLEUTH model. Minimum layers are topographic slope, two land use maps, one exclusion map, four urban extent maps, two transportation maps, and a hill-shaded background image. Data shown are for the Environmental Protection Agency’s Mid Atlantic Regional Assessment study area

Simland (Wu 1998). Influential critical reviews of CA research include those by Batty (2005), Torrens and O’Sullivan (2001), and Benenson (2007). An important early theoretical framework was that of Takeyama and Couclelis (1997), and additional attempts at synthesis have been made by Benenson and Torrens (2004) and by Torrens and Benenson (2005). Nevertheless, interest in and use of the CA suite of models continues unabated, with applications of several of the models at many scales, across regions, for whole nations, and on all continents other than Antarctica. A representative CA model that has been long-lived in relation to others is the SLEUTH model. SLEUTH is an acronym for the data input layers required by the model (Fig. 62.2). The model was developed by the author and a host of collaborators with funding support from the United States Geological Survey, the National Science Foundation, and the Environmental Protection Agency. There are three retrospectives on SLEUTH’s now 15 years of use (Clarke et al. 2007; Clarke 2008a, b). SLEUTH actually consists of two CA models tightly coupled together and coded within the same open source C-language program: the Clarke Urban Growth model and the Deltatron Land Use Change model.

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T1

T0 spontaneous

spreading center

organic

road influenced

f (slope resistance, diffusion coefficient)

f (slope resistance, breed coefficient)

f (slope resistance, spread coefficient)

f (slope resistance, diffusion coefficient, breed coefficient, road gravity)

deltatron

For i time periods (years) Fig. 62.3 At each cycle in the CA model, five sets of behavior rules are enforced. These are controlled by the factors and parameters shown and are applied in sequence for each one “year” iteration of the model

The former is a classic CA, using a Moore neighborhood and simple sequential rules (Fig. 62.3), but using weighting for probabilities, Monte Carlo simulation, and self-modification – in which aggregates, such as the overall growth rate, feedback into the parameters controlling the rule sets. The latter differs in that it takes its input of quantity of transformation from the Urban Growth model and applies CA in change space rather than geographic space. In doing so, it relaxes the single timestep rule and allows persistence and aging of cells for longer than one time step. SLEUTH has over a hundred applications at many scales and for different cities worldwide. A typical forecasting result is shown in Fig. 62.4.

62.6

Agent-Based Models: Origins

Agent-based models (ABM) are a class of computational models for simulating the actions, behavior, and interactions of autonomous individual or collective entities, with the goal of exploring the impact of one agent or a behavior type on the system as a whole. Miller (2009) notes that the agents are independent units that attempt to fulfill a set of goals. The agents can be countries, landowners, residents, renters, farmers, shoppers, vehicles, or even people out for a walk. Unlike with CA, the purpose of ABM is often the exploration of variants in system behavior due to agent characteristics (such as the proportion of agents of different types) or rules, rather than resulting aggregate structures or maps. Multiagent models include more than one agent; for example, a habitat model may include plants, animals that eat the plants, and predators that eat the animals. ABMs combine game theory, complex

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Fig. 62.4 Land use in the Santa Barbara, California, region. Top: In 1998, the base year for modeling with SLEUTH. Bottom: In 2030, as forecast by SLEUTH for the Santa Barbara Regional Impacts of Growth Study (2003). Black: unclassed; Red: urban; yellow: agriculture; orange: rangeland; green: forest; blue: water; purple: wetland; Tan: barren land

systems theory, evolutionary programming, and stochastic modeling. In ecology and biology, ABMs are termed “individual-based models.” ABMs simulate the actions and interactions of multiple agents, in an attempt to emulate the overall system behavior and to predict the patterns of complex phenomena. Agents behave independently, but react to the environment, the aggregate properties of the system, and other agents. So, for example, a farmer agent in the Brazilian Amazon may clear land as he becomes more profitable, in response to a change in crop price, or because his neighbor is clearing his land. Agents are usually assumed to behave with bounded rationality, acting in their own interests such as reproducing, increasing profit, or increasing status, usually by simple heuristic rules. For example, the previously mentioned farmer may decide to have a child or build a house when profitability reaches a certain level. Agents can also “learn,” that is, avoid previously failed decisions while favoring successful ones. They can also adapt, that is, change behavior based on properties of the system. An ABM consists of (i) agents specified at specific model scales (granularity) and types; (ii) decision-making heuristics, often informed by censuses and surveys in the real world; (iii) learning or adaptive rules; (iv) a procedure for agent engagement, for example, sample, move, interact; and (v) an environment that can both influence and be impacted by the agents. Creating a model involves examining or surveying a system to extract the agents’ behavior and influential factors, quantifying these elements, then coding the model in an environment that allows control, examination of maps and time sequences, and metrics of system behavior and performance. Many ABMs are programmed in coding languages with Java being the most common, while others use one or more of the software tools,

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both open source and proprietary, in which the system and rules have to be specified. While there are many examples of software for ABM, relatively few of them are compatible with GIS or produce maps or images. Also of use is the ability to do Monte Carlo simulations and to let the models iterate to a steady state. ABMs share their origins with CA in the work of von Neumann, Ulam, and Conway. A pioneering agent-based model in urban systems was Thomas Schelling’s urban residential segregation model (Schelling 1971). Though not computational, the work embodied the basic concept of agent-based models as autonomous agents interacting within a fixed environment and with an observed aggregate outcome. In the 1980s, interest in game theory led to Robert Axelrod’s experiments with the game “Prisoner’s Dilemma,” showing that strategies evolved and coevolved over time among players. Craig Reynolds’ research on models of flocking behavior yielded the first biological agent-based models with embedded social characteristics. Modeling biological agents using ABM became known as artificial life. This led to artificial societies, artificial cities, computational economics, etc. Important software tools for ABM were StarLogo, SWARM, and NetLogo in the 1990s, and since then Ascape, Repast, Anylogic, and MASON (Railsback et al. 2006). Examples of early models include Construct by Kathleen Carley and Sugarscape by Joshua Epstein and Robert Axtell. These explored the coevolution of social networks and culture and the role of social phenomena such as segregation, migration, pollution, sexual reproduction, combat, and the transmission of disease. An early book on ABM in social simulation was Nigel Gilbert’s Simulation for the Social Scientist (1999). A key research journal has been the Journal of Artificial Societies and Social Simulation.

62.7

Agent-Based Models: Key Contributions

A survey of the recent ABM literature is that of Niazi and Hussain (2011). A key survey in Geography was that of Parker et al. (2003), resulting from a workshop (Parker et al. 2002). Also influential was a series of papers published by the Santa Fe Institute (Gimblett 2002). Agent-based modeling has been extraordinarily interdisciplinary. ABM has been applied to model organizational behavior, logistics, consumer behavior, traffic congestion, building and stadium evacuation, epidemics, biological warfare, and population demography. In these cases, a system encodes the behavior of individual agents and their interconnections. In some geographical applications, the models have been informed by field work, interviews, or from censuses that are used to derive behavioral characteristics and choices using qualitative methods. Agent-based modeling tools are then used to test how changes in individual and collective behavior impact the system’s aggregate behavior. In some cases, agents are allowed to learn from past choices, avoiding decisions with negative outcomes, for example. The following ABM development environments include the ability to ingest, output, and use spatial data: Anylogic, Cormas, Cougaar (via OpenMap),

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Fig. 62.5 User Interface for the Anylogic 6 Agent-Based modeling software (Source: http:// www.coensys.com/agent_based_models.htm)

Framsticks, Janus (using JaSIM), MASON, Repast, SeSAm, Netlogo, and VisualBots. Some of these, and other nonspatial packages, contain model libraries that include CA examples such as Game of Life, HeatBugs, demographic models, epidemiological models, and flocking. Many include the means to display charts, graphs, and maps and menus to input control variables and rules (Fig. 62.5).

62.8

Agent-Based Models: Applications

Recent topics in regional science that have been modeled with ABMs include crowd behavior during riots and outdoor events (Torrens 2012), innovation in businesses (Spencer 2012), commuting behavior (McDonnell and Zellner 2011), ecology and habitats, disease, and land use change. The most recent research on agent-based models has demonstrated the need for combining agent-based and complex network-based models. This has included a desire for models with reusable components, tools for proof of concept and design, descriptive agent-based modeling for developing descriptions of agent-based models by means of templates and complex network-based models, and a need for better validation. The latter point has been repeatedly used in critiques of ABM: their very nature makes

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Fig. 62.6 Israeli and Arab residential patterns of the Israeli towns of Yaffo and Ramle from the Israeli census, and their Schelling model simulations (Source: Hatna and Benenson (2012))

calibration and validation using data descriptive of real systems rather difficult, if not impossible. For example, a programmed behavior type will indeed emerge when enough agents are given enough time, so experiments with agents could be considered circular reasoning. Truly emergent behavior or new knowledge should be unanticipated during model construction. An example of a common ABM application is the Schelling model (Schelling 1971). This simple model of segregation, originally proposed as a game simulation, has been used as the basis of many agent-based models and theoretical discussions about ABMs. The model illustrates how individual tendencies regarding neighbors can lead to segregation in cities. The model has been extensively used to study residential segregation of ethnic groups where agents represent householders who relocate in the city. A concise statement of the model is that by Benenson et al. (2009), in which are enumerated the six behavior rules, assuming the model to be an ensemble of agents of two types, B and W, dispersed over a grid. The rules are: (i) at every iteration, the agents can move to a vacant cell; (ii) the decision to move to a cell is based on the fraction in the neighboring cells of the opposite type of agent; (iii) this fraction should be below a tolerance proportion; (iv) if this fraction is exceeded, then an agent moves; (v) the agent searches within a finite distance for cells that are below the tolerance threshold, and if none exists, does not move; (vi) vacated cells become available for other agents. In most applications, these rules produce residential segregation, depending on the two constants that must be determined. Benenson and his colleagues have repeatedly experimented with

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real-world data and the Schelling model. Figure 62.6 shows Jewish-Arab residential patterns of the Israeli towns of Yaffo and Ramle from the Israeli census, and their ABM equivalents (Hatna and Benenson 2012).

62.9

Conclusions

Cellular automata and agent-based models have both represented a new approach in modeling, that of complex adaptive systems. In this approach, models are microsimulations, run at the atomic level, and aggregate behavior emerges as a consequence of large numbers of agent interactions. The complex systems approach has favored CA and ABM over Forrester-type systems dynamics models and steady-state and equilibrium models. CA and ABM share in common their individual basis. In CA, the modeled entities are cells that remain static while spatial and other processes move across or through them. In ABM, the agents can move in space, interact with each other directly, and interact with other agent types. In both cases, a large number of independent autonomous lowest level actors create the overall landscape. The models can include extra data, such as environmental control layers, and parameters that influence the agents, such as prices or demands. CA models have been criticized as oversimplifications of reality, and those that have relaxed the rules have been criticized as not pure CA. CA are extremely sensitive to their initial conditions, and are very consumptive of CPU time. Since most use square grids, they are subject to error due to incorrect choice of map projection, and directional bias. In the long run, they are subject to equifinality arguments, since in most cases all developable land becomes developed, regardless of the exact sequence of development. They have also been criticized as difficult to implement and data hungry. Bithell et al. (2008, p. 625) have noted that ABM have the potential to create integrated models that cross disciplines, so that similar computational methods can be used to control the spatial search process, to deal with irregular boundaries, and display the changing of systems where the “preservation of heterogeneity across space and time is important.” They note that a principal challenge of ABM is to find sets of rules that best represent the beliefs and desires of human as agents, so that they reflect the cultural context, yet still allow system exploration. Clifford (2008, p. 675) noted that ABMs are most appropriate where decisions or actions are distributed around specific locations, and where structure is seen as emergent from the interaction among individuals. For this new and exploratory modeling framework, he calls for “a rediscovery and reappraisal of the richness and depth of insight in the model-building enterprise more generally.” Some have attempted to link ABM with other bodies of theory, for example, Neutens et al. (2007) have linked ABM and time-space geography. Andersson et al. (2006) have attempted to link networks, agents, and cells to model urban growth. Lastly, O’Sullivan and Hakley (2000) have suggested that using ABM encourages a modeling bias toward an individualist view of the social world, thereby missing many forces that shape

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real economic and human systems top down, such as planning and government. Read (2010, p. 329) noted that agent-based models “sometimes provide only a veneer of, rather than substantive engagement with, social behavior.” Both CA and ABM have enjoyed popularity in the regional modeling arena in the last 20 years due to their simplicity, ease of use and accuracy. When machine learning or optimization is involved, the models can produce simulations that are of excellent accuracy. However, the models are often only as good as the data with which they are trained or tested, and are highly sensitive to the context of these data. Relatively few CA or ABM models are highly ported across different applications. Even fewer have been rigorously tested for accuracy, repetition, and parameter sensitivity and validated using independent data. A major criticism of both model types is that while the simulations are accurate and engaging, they lack any causative description or policy-related link to actual system behavior. Thus, while they can create useful future scenarios or forecasts, the means by which the actual system can be steered toward that outcome is not forthcoming. CA models are best used for spatially distributed process simulation, such as spread and dispersal, and when the geometry, scale, and basic behavior of a system are known. ABM is suited to simulations with no prior precedent, no past data, or when system knowledge is absent. These applications are usually more exploratory than when CA are used. Nevertheless, both modeling methods have significantly advanced the role of modeling and simulation in regional science and gone a long way toward making models more accountable and more meaningful at the base level. Their joint impact on research and understanding of human systems has been profound.

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