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1 !LRESEARCH!M Generating the Explanation of the Complex Behaviors toward Self-Reorganization of Mobile Multi-Agent Systems Koichi KURUMATANI Mari NAKAMURA In order to deal with unexpected or illegal behavior of multi-agent systems, we have to reorganize the system's behavior by redening or re-planning each agent's behavior. In that case, the underlying mathematical model connecting the target system's behavior and each agent's behavior is indispensable. In this paper, we present a method for generating causal relations among the parameters which describe the target multi-agent system, consisting of arithmetic and dierential relations of explicitly dened parameters of agents and implicitly existing parameters embedded in the target system. The task consists of three components, 1) micro-macro translator which reasons about macrobehavior rules from the given micro-behavior of each agent, 2) causal network constructor with qualitative region grammar, and, 3) macro-behavior qualitative simulator. We took an example for the method from the foraging behavior of ant colonies, which is a typical mobile multi-agent system with a local communication method by chemical pheromone. x 1 Introduction Methods for automatically redening mobile agents' behavior-plans, and as the eect, for reorganizing the mobile multi-agent system's behavior are indispensable to eciently achieve the system's target. For instance, an automated cargo-control system which transports baggage from airport counters to airplanes and vice versa should have global goals of enlarging the transport ratio (pieces of baggage per hour) and shortening the total path length of cargo-carriers (reducing the energy consumption), under the constraints of the restriction of the area where the carriers move, collision avoidance, carrying-time limit (cargos should reach the plane by departure time), and so on. Since events such as plane delays, troubles in cargocarriers, and weather changes, unexpectedly occur in the system, the system cannot plan the exact schedule beforehand and should always observe the system's behavior and reorganize the system's behavior by replanning each agent's behavior. The scientic questions about the complex behaviors of the multi-agent systems arise in connection to the emergent property 1) 2) of the systems' behaviors, i.e., the systems' behaviors can be very complex in spite of the simple behavior of each agent. Although we have no way to entirely control such properties, we can understand and explain the behaviors once we get the underlying mathematical model by observing the system's behavior and verifying the assumptions about the tar- KEYWORDS: mobile multi-agent system, self-reorganization, explanation generation, qualitative region grammar, causal network, planning, articial life {(1){

2 2 Bulletin of the Electrotechnical Laboratory Vol. Vol No.No (1995) get system. In this paper, we propose a method for generating causal relations among the parameters which describe the target multi-agent system for re-planning each agent's behavior. By causal relations we mean the arithmetic and dierential relations of parameters in qualitative manner, which changes qualitatively according to the system status. All parameters which need to describe the target system is not given explicitly. There exists implicit parameters embedded in the target system, which must be salvaged. The method consists of three components, 1) micromacro translator which reasons about macro-behavior rules from the given micro-behavior of each agent, 2) causal network constructor with qualitative region grammar, and, 3) macro-behavior qualitative simulator. In the following section, we illustrates the example selected for the method, the foraging behavior of ant colonies with the communication method by chemical pheromone. x 2 Problem 2.1 Modeling the Foraging Behavior of Ant Colonies We selected an ant colony as an example for the causal network construction because it is a typical example of mobile multi-agent systems. It has macrogoals in the colony level which should be achieved by the cooperated behaviors of micro-agents (ants). Microagents have a local communication method by chemical pheromone, but the colony itself has no global communication methods, e.g., telecommunication, global map of environment, and so on. Because the lack of global communication methods, it is dicult for the target system to have centralized controlling mechanisms (the headquarters of ant colonies), and thus the target system should achieve macro-goals by coordinating or tuning micro-agents' behaviors. The nal goal of our research is to nd a way to coordinate or tune the micro-agents' behavior by 1) observing the macro-behavior of the target system, 2) constructing the underlying mathematical model (causal relations in the target system), and 3) redening the micro-behavior of each agent. In this paper, we describe the method for constructing the causal relations of the target system and generating the causal network. The foraging behavior of ant colony is an organized behavior of the ant society, and is a typical example of complex behaviors of biological multi-agent systems. Although the behavior (algorithm) of each ant is quite simple one with a communication method by chemical pheromone, the colony shows complex foraging behaviors which maximize the bait transport ratio and minimize the risk caused by environmental disturbance, i.e., climate, food competition, and so on 3). In this paper, the model of the foraging behavior of each ant is assumed as follows (they are described as an automaton in the reasoning system) (Fig.1) y1. [The foraging behavior of ant colonies] 1. At any time, an ant is in a mode, search, attracted, trace, or transport. 2. Search is the default mode. The ant walks randomly in search mode. 3. When an ant in any mode nds a bait-site, it tunes into transport mode, where it carries a bit of bait to the colony's nest. Bait can exist at several baitsites. Ants in transport mode secrete the recruitment pheromone on the line of the transportation which becomes the pheromone trail. The ant in transport mode becomes in search mode when they reaches the nest. 4. (The pheromone trail evaporates and diuses, which makes pheromone atmosphere.) 5. When an ant in search mode comes across pheromone atmosphere, it turns into attracted mode and is induced by the pheromone to the higher pheromone density. If it will nd pheromone y1 The model is not entirely faithful to the real ant behavior. It represents common aspects of many kinds of ant colonies. {(2){

3 0\F0$9$k%^%k%A!&%(!<%8% %s%h!&%7%9%f% %s%h!&%7%9%f% $NF0:n%"%k%4%j%:% $N<+8J:FJT$K8~$1$ trail, it traces the trail to a bait-site (in trace mode). Otherwise it continues to walk in the pheromone atmosphere. This simple algorithm of the ant (agent) implements the foraging behavior of the ant colony (multi-agent system), i.e., 1. to nd the site(s) of bait, 2. to mobilize ants in the colony in order to carry bait on a large scale, therefore, 3. to maximize bait transport ratio per time. Notice that this simple agent's algorithm (and the colony's strategy) can be easily inuenced by the environmental disturbance. When more than one bait sites exist and all the ants in the colony gather to a bait place simultaneously, enemy animals can easily attack the colony, or the colony might miss the other bait places which have more amount of bait than the current attacked bait place. Nest Search Mode Ant Transport Mode Ant Attracted Mode Ant Pheromone Trail Area of Pheromone Inducement (a) Behavior of each ant. Bait Place Trace Mode Ant Pheromone_density > threshold Area of Pheromone Inducement Diffusion Evaporation Active Trail Trail_magnitude > threshold Decreased Trail Trail_magnitude < threshold (b) Evaporation and diusion of pheromone. Fig.1. The foraging behavior system of ant colonies. 2.2 The Results of Numerical Simulations We have carried out the numerical simulations of the target system for several sets of parameters. A part of the results of the simulations is shown in Fig.2. In these simulations, there exists a nest in the center of the environment, and there exist eight bait places distributed in the same distance from the nest place. The dierence of the condition is only the number of ants in the colony. In Fig.2(a), there exist 60 ants searching 8 bait places, and some ants actually nd a bait place and generate a pheromone tail between the bait place and the nest. Since the trail evaporates quicker than the other ants gather to the trail, the continuous growth of the trail and the continuous large-scale transport are not achieved. In Fig.2(b), enough 600 ants gather to the trail, and the large-scale transport is achieved. The results tell that enough number of agents should exist in the system in order to conquer the time-delay between the gathering speed of ants and the evaporation speed of the pheromone, which can be explained by the causal relations embedded in the target system. In Fig.2(b), almost all ants gathers to the bait number 5, and the colony `forget' the other bait places. Actually the same phenomena that all the ants gathers to only one bait place is observed under almost all parameters whenever the large-scale transport is realized. The reason is that there exists a positive feedback among the dierential relations of the system parameters, i.e., the number of ants gathering to a bait, the amount of secreted pheromone by the ants, and the amount of evaporated pheromone atmosphere which attracts ants. Our nal target of this research is to redene or replan each agent's behavior to eciently achieve the system's goal, by propagating qualitative values on such causal networks. In the following section, we discuss a method for generating the causal networks, i.e., qualitative region grammar, causal network constructor, micro-macro translator. {(3){

4 4 Bulletin of the Electrotechnical Laboratory Vol. Vol No.No (1995) Search mode Attracted mode Trace mode Transport mode Bait 1 4 Bait 1 Nest Trail Nest Area of Pheromone Inducement 6 7 (a) Total 60 ants. (b) Total 600 ants. Fig.2.1. The map of ants after 1000 steps (a) Total 60 ants. t= ants 8 (b) Total 600 ants. Fig.2.2. The number of ants which reached the bate places. t= ants 100 % 0 t=0 (a) Total 60 ants. t=1000 Attracted Trace 100 Search % Transport 0 t=0 (b) Total 600 ants. t=1000 Fig.2.3. The percentage of ants in each mode. Fig.2. The results of the numerical simulation of the foraging behavior for 60 and 600 ants. {(4){

5 0\F0$9$k%^%k%A!&%(!<%8% %s%h!&%7%9%f% %s%h!&%7%9%f% $NF0:n%"%k%4%j%:% $N<+8J:FJT$K8~$1$ x 3 Generating Causal Networks The simulation of the complex behaviors of multiagent systems have been already studied 4), but they lack the underlying mathematical models. Statistical analysis for system behaviors with a xed simple behavior of agent 5) can describe the statistic relationship and distribution between agent's behavior and system's behavior, but they lack of the causal relations, and the explanation and re-planning ability are impossible. Self-Explanatory Simulation 6) generates explanations by causal relations, which is limited to simple physical systems (a ying ball, a pulley). Our approach is to prepare symbolic representations in which causal relations among parameters, spatial extents, and attributes of the target system are described, and to propagate qualitative values on the derived causal networks for re-planning of the agent's behavior. The method has the advantages 1) that spatial extent can be represented and reasoned about symbolically, therefore partial dierential equations (e.g., diusion) can be solved in qualitative (symbolic) manner, 2) that translation between micro and macro behaviors is possible, and 3) that the generated causal networks can be used to redene or re-plan the target multi-agent system, e.g., repressing the exponential amplication in the foraging behavior which is found in a causal network for ant colonies. 3.1 Qualitative Region Grammar By qualitative region we represent the spatial extent describing the attributes of the target system and their changes, e.g., how the pheromone tail or atmosphere spreads, or how ants in search mode are distributed. Mathematically saying, when a function f(x; y) and a meaningful value (landmark) l are given, a qualitative region r = region(f, l) denotes a closed line in x-y plane which is represented by f(x; y) = l: Usually we use the notation of r = region(f, l, +) which represents the closed region f(x; y) > l in the x-y plane (Fig.3) y2. Since our aim is not to represent such regions precisely (it can be done by numerical simulations), we represent their characteristic properties symbolically and to reason about behaviors of the target systems with them. landmark value O Fig.3. z (f(x,y)) C1 y C2 f(x,y) Denition of qualitative regions. We represent the characteristic properties of regions with predicates: static spatial relations between two regions identical(ra, rb), isolated(ra, rb), intersect(ra, rb), include(ra, rb), broader(ra, rb) dynamic changes of a region (t 1 > t 2 ) expand(r, t1, t2), shrink(r, t1, t2), no_change(r, t1, t2) expanding(r, t1), shrinking(r, t1), appear(r, t1), disappear(r, t1) some basic inference rules (independent from the target system) no_change(r, T1, T2) :- constant(r). expand(r, t1, t2) :- broader(region(r, t1), region(r, t2)). expand(r, t1, t2) :- include(region(r, t1), region(r, t2)). y2 If there exist more than one such regions, region(f, l, +) denotes separated regions r1, r2,..., rn. x {(5){

6 6 Bulletin of the Electrotechnical Laboratory Vol. Vol No.No (1995) no_change(r, t1, t2) :- identical(region(r, t1), region(r, t2)). expanding(r, t1) :- expand(r, t1 + delta_t, t1). 3.2 Macro-Behavior Rules A causal network is a graph representing the causal relations among the parameters, spatial extent, and attributes of the target system, on which qualitative properties are propagated. The nodes of the graph represent parameters of the macro behavior, i.e., the behavior of the target system rather than each agent (the behavior of each agent is called `micro behavior'), and the arcs are labeled by the relation of adjacent nodes. For instance, in a situation where ants in search mode come across pheromone atmosphere and they turn into attracted mode, the transition ratio (frequency) of the ants from search mode to attracted mode is qualitatively proportional to the density (population) of the ants in search mode, and also to the area of pheromone atmosphere, i.e., y3 M0+(s_a_trans, search_ant_pop). M0+(s_a_trans, area(pheromone_atmos)). Such a macro-behavior reasoning rule is used to generate the causal networks, and is written in the form of predicate: transit(search, attracted) :- region(s, search_region), region(p, pheromone_atmos_region), intersect(s, P), transit_s_a(p). transit_s_a(phero) :- /* new region */ assertz( region(attracted_zero, attracted_region)), assertz(include(phero, attracted_zero)), /* transition frequency */ assertz( trans_freq(s_a_trans, search, attracted)), assertz( y3 M0+(a,b) means that a is qualitatively proportional to b, is positive, and a = 0 when b = 0. m_zero_plus(s_a_trans, search_ant_pop)), assertz( m_zero_plus(s_a_trans, area(phero))). The macro-behavior reasoning rules are generated by the micro-macro translator 7) at the beginning of the reasoning process. The micro-macro translator receives an automaton which describes the agent behavior (in section 2.1), and generates macro-behavior reasoning rules which are used to construct the causal networks throughout the reasoning process. 3.3 Micro-Macro Translator The reasoner receives 1) agent's behavior as an automaton, 2) descriptions of environment (e.g., how the evaporation of pheromone is represented in qualitative region grammar), and 3) the initial state of the target system as each agent's state. First of all, the reasoner invokes the micro-macro translator in order to generate macro-behavior reasoning rules. The translator is a production system which receives an automaton of the micro-behavior description as a state transition graph, and translates the graph to macro-behavior rules by applying production rules which are independent from the target system. The independence of the rules from the target system is not surprising, because our targets are limited to `mobile' multi-agent systems, therefore the micro-macro translation can exploit the metric of Euclidean spaces. For instance, the positions of mobile agents, which are originally represented as parameters in micro-behavior level, can be easily translated to qualitative regions in macro-behavior vocabulary, since the metric of the twodimensional plane prepares a simple mapping between position (point) and spatial extent (region). When we apply our approach to other kinds of multi-agent systems which do not originally have the metric, the micromacro translation could become target-dependent, but even in such cases there is a possibility that the environment of the target system is metrizable. In the current implementation, we assume that mo- {(6){

7 0\F0$9$k%^%k%A!&%(!<%8% %s%h!&%7%9%f% %s%h!&%7%9%f% $NF0:n%"%k%4%j%:% $N<+8J:FJT$K8~$1$ bile agents stay in two-dimensional plane. When they moves in three-dimensional spaces, we need to modify the qualitative region grammar which will have more complex inference rules. in Fig.2(b), where enough numbers of ant are attracted by pheromone, and will trace the trail and transport the bait with secreting recruitment pheromone. 3.4 Collecting Qualitative Relations for Constructing Causal Networks The macro-behavior reasoning rules generated by the micro-macro translator are the collection of the declaration \how the target system behaves in a certain situation" described in macro-level. We reason about the target system's behavior in the following process. population(search_1) M0+ Q- trans_rate(search_1, attracted_1) Q+ population(attracted_1) M0+ Q- trans_rate(attracted_1, trace_1) Q+ population(trace_1) total_amount(trail_1) Q- evaporation_rate = + (const) Q+ total_amount(phero_1) Q- M0+ diffusion_rate = + 1. Set the initial state to the current state. 2. Apply the macro-behavior reasoning rules to the current state, and determine the rule to become active. M0+ Q- Q+ M0+ trans_rate(trace_1, transport_1) area(phero_1) Q+ population(transport_1) Fig.4. A generated causal network. 3. If there is no activated rule, stop. 4. Collect the qualitative (causal) relations of parameters in activated rules, i.e., generating the causal network corresponding to the current state. 5. Examine the possibility for each parameter to cross the landmark which denes the corresponding qualitative region (spatial version of limit analysis). 6. Collect the fragments of the next state in the activated rules, and set it to the current state. 7. Go to 2. This process resembles one in Qualitative Process Theory 8) 9). The dierence is that 1) the macrobehavior reasoning rule, which corresponds to individual view and process in Qualitative Process Theory, is generated from micro-behavior of agents by the translator, 2) spatial extents such as pheromone diusion can be represented and reasoned about by qualitative regions. An example of the generated causal networks is shown in Fig.4 y4. This network represents the state x 4 Explanation Generation An application of the causal network is to generate the explanation of the system's behavior by propagating the qualitative value in the network. The reasoner computes the directions of change of parameters (increasing, decreasing, or stable) and generates the explanation of the state. In the case of the transition from search mode to attracted mode, the following explanation is generated. transition from search mode to attracted mode is proportional to the population of search ants. the number of search ants is positive. the transition is positive.... Such an explanation is generated for each state until the reasoner nds no more possibility of state transitions of the target system. As a result, explanations along the state transitions of the target system are obtained. y4 represented in predicate form in the system. the area of pheromone atmosphere expands. {(7){

8 8 Bulletin of the Electrotechnical Laboratory Vol. Vol No.No (1995) transition from search to attracted is positive. transition from attracted to trace is positive. transition from trace to transport is positive. 1) Andrew M. Assad and Norman H. Packard: Emergent colonization in an articial ecology, In Fran- the area of pheromone atmosphere expands.... (repeated) cisco J. Varela and Paul Bourgine, editors, Toward a Practice of Autonomous Systems (Proc. of In the generated explanation, the reasoner nds a positive feedbacks among the parameters. This means that ECAL'91), 143{152. The MIT Press(1992). there is a possibility that pheromone atmosphere and 2) Alexis Drogoul, Jacques Ferber, Bruno Corbara, gathering ant population grow exponentially. and Dominique Fresneau: A behavioral simulation The fact that the reasoner can nd such the causal model for the study of emergent social structures, relation in the target system is important, because we In Francisco J. Varela and Paul Bourgine, editors, can use our results in order to redene or re-plan each Toward a Practice of Autonomous Systems (Proc. agent behavior, which the next target of our research. of ECAL'91), 161{170. The MIT Press(1992). The system described in this paper, including the 3) B. Hoelldobler and E.O. Wilson: The Ants, The explanation-generator, is implemented in SICStus Prolog (ver.2.1) on Sun SPARCstation20, which consists of Belknap Press(1990). about 700 clauses. 4) T. S. Ray: An approach to the synthesis of life, In x 5 References C.G. Langton et al., editors, Articial Life II, 371{ Conclusion 408. Addison-Wesley(1991). A method for generating causal network of mobile multi-agent systems is discussed. Our method consists of 1) generating macro-behavior reasoning rules by micro-macro translator, and 2) constructing the causal network among system parameters, in which the directions of change of the parameters are determined, by qualitative simulation with qualitative region grammar. The method is applied to the explanation generation of the foraging behavior of ant colonies. Since the causal network represent the underlying mathematical structures of the target system, the reasoner can nd the macro properties of the target system such as positive/negative feedbacks embedded in the target system, which will be used in redening or re-planning each agent behavior. Our method is powerful enough to reason about many kinds of mobile multi-agent systems including ant colony, cargo-control system, trac navigation, and ow control of industry. 5) R. Axelrod: The Evolution of Cooperation, Basic Books Inc.(1984). 6) K.D. Forbus and B. Falkenhainer: Self-explanatory simulations: An integration of qualitative and quantitative knowledge, In Proc. of AAAI-90(1990) 380{ ) S.A. Rajamoney and S.H. Koo: Qualitative reasoning with microscopic theories, In Proc. of AAAI- 90(1990) 401{406. 8) K.D. Forbus: Qualitative process theory, Articial Intelligence, 24(1984) 85{168. 9) B. Falkenhainer and K.D. Forbus: Setting up largescale qualitative models, In Proc. of AAAI-88(1988) 301{306. {(8){

9 0\F0$9$k%^%k%A!&%(!<%8% %s%h!&%7%9%f% %s%h!&%7%9%f% $NF0:n%"%k%4%j%:% $N<+8J:FJT$K8~$1$ The Authors <VC+ Koichi Kurumatani Cooperative Architecture Project Team He is interested in machine learning and self-reorganization algorithms for multi-agent systems. CfB<??M} Mari Nakamura Life Electronics Research Center She is interested in mathematical biology and neuro-dynamics, especially in bifurcation theory and pattern formation theory on nonlinear distributed systems. {(9){

Qualitative Analysis of Causal Graphs. with Equilibrium Type-Transition 3. LERC, Electrotechnical Laboratory. previous works in the literature.

Qualitative Analysis of Causal Graphs with Equilibrium Type-Transition 3 Koichi Kurumatani Electrotechnical Laboratory Umezono 1-1-4, Tsukuba, Ibaraki 305, Japan kurumatani@etl.go.jp Mari Nakamura LERC,