Coevolutionary Characteristics of Knowledge Diffusion and Knowledge Network Structures: A GA-ABM Model

: The co-evolutionary dynamics of knowledge diffusion and network structure in knowledge management is a recent research trend in the field of complex networks. The aim of this study is to improve the knowledge diffusion performance of knowledge networks including personnel, innovative organizations and companies. In order to study the co-evolutionary dynamics of knowledge diffusion and network structure, we developed a genetic algorithm-agent based model (GA-ABM) by combining a genetic algorithm (GA) and an agent-based model (ABM). Our simulations show that our GA-ABM improved the average knowledge stock and knowledge growth rate of the whole network, compared with several other models. In addition, it was shown that the topological structure of the optimal network obtained by GA-ABM has the property of a random network. Finally, we found that the clustering coefficients of agents are not significant to improve knowledge diffusion performance.


Introduction
. Knowledge management including the creation, sharing, absorption and the transmission of knowledge is becoming ever more essential for the development of society and the economy today, i.e., the so-called knowledge economy era (Herie & Martin ; Phelps et al. ). Knowledge is di used through knowledge networks including personnel, innovative organizations and companies that have socio-economic relevance (Hansen ; Molm et al. ). Therefore, problems related to knowledge di usion in knowledge networks, which become a very important part of knowledge management, can be classified into two main categories; the modelling of knowledge di usion and the evolution of knowledge networks. In order to solve such problems, coevolutionary dynamics combining the knowledge di usion of agents with the topological evolution of network structure is urgently needed and is a recent research trend in the field of complex network (Gross & Blasius ; Vazquez ; Luo et al. ). .
Research on the co-evolutionary dynamics of knowledge di usion and network structure have been purposed to improve the spread of knowledge indicated as average knowledge stock and knowledge growth rate etc. . . Thus, previous work has mainly focused on the modeling of knowledge di usion process based on agent-based approach and the evolution of network structure based on probabilistic methodology (Paruchuri ; Boone & Ganeshan ). Cowan & Jonard ( ) considered the knowledge di usion process as a barter process and .
With the exception of this latter research, several other studies on the co-evolution of agents' opinion forming and network structure have been conducted (Gil & Zanette ; Vazquez ; Hegselmann & Krause ; Su et al. ; Luo et al. ). All of these used the probabilistic methodology to change the connection between agents and update the network structure. From the previous studies, the following summary can be drawn. Firstly, the studies on the co-evolutionary dynamics of knowledge di usion and network structure, in which mainly adopted agent-based approach, focused on making the knowledge di usion models as close as to the real world on the basis of knowledge network's formation mechanism. Secondly, in the evolution of network structure, researchers simply tried to exploit the probabilistic methodology to implement the rewiring between agents and update the network structure based on the knowledge di usion model.
. Since the actual mechanism of the co-evolution of knowledge di usion and network structure is generally difficult to explore, it is reasonable to a certain extent to study the co-evolutionary dynamics by using various probabilistic methods that has however certain limits, too. The fact that the evolution of network structure depends on random factors, makes it impossible to accurately evaluate and improve the knowledge di usion performance of a co-evolution model. The knowledge di usion performance of a co-evolution model obviously depends on the initial knowledge distribution and the topological evolution mechanism of networks. That is, this mechanism determines whether the knowledge stock and growth rate of the whole network converges into the target maximum value rapidly or not. It is therefore necessary to develop the topological evolution mechanism of a knowledge network, which can maximize the knowledge stock and growth rate of the whole network during the process of co-evolution. .
In this study, we have developed a genetic algorithm-agent based model (GA-ABM) combining genetic algorithms (GA) with agent-based modelling (ABM) and evaluated its knowledge di usion performance compared to several other models. The genetic algorithm, which mimics biological evolution, was introduced into the evolution of a network structure to develop the topological evolution mechanism, which is combined with an agent-based model of knowledge di usion. From simulation, the proposed model was proven to improve the average knowledge stock and knowledge growth rate of the whole network, compared with other models. In addition, the topological structure of the optimal network obtained by GA-ABM has the property of random network, and the clustering coe icients of agents are not significant in improving knowledge di usion performance .
. The rest of this paper is organized as follows: In Section , we proposed a GA-ABM to investigate the co-evolutionary dynamics of knowledge di usion and network structure. In Section , the simulation of GA-ABM is performed, and the results are discussed. Finally, this paper is concluded in Section .

The Model
. Here, the knowledge di usion process is modeled by using an agent-based model, and the evolution of network structure is performed by using a genetic algorithm. This section provides a detailed description of the proposed model. For any agents i, j ∈ E(i = j), if there is a connection between i and j, e ij = 1, otherwise e ij = 0.
. Here, we referred to the KT (Knowledge transfer) rule of Luo et al. ( ) for modeling the knowledge di usion process in an agent-based model. We followed this rule because it is the most e ective when the knowledge distance between two interacting agents is neither too large nor too small. When the knowledge distance is greater than the given threshold, it is predicted that the lack of knowledge inhibits learning and there is no gain from the interaction. The knowledge distance is in essence, the knowledge di erence between two agents. The knowledge distance between two agents (i and j) that are connected to each other is expressed as follows.
The real gains in knowledge list l for two agents are as follows: In Equation , when k dij is less than the threshold k d , agent i obtains a limited amount of knowledge (less than the given upper limit, k u shown in Equation ) from agent j. When the knowledge distance is smaller than k u , the larger the knowledge distance, the more knowledge the agent receives from its neighboring agents. In contrast, when k dj exceeds k d , there is no any knowledge passed from the neighboring agents. The updated values of knowledge in agent i a er interaction and knowledge exchange are as follows.
Here, a genetic algorithm is applied to the structural evolution of the knowledge network, and genetic operators are developed to reflect our research assumptions. In general, genetic operators used in GA include selection, crossover, mutation and fitness tests. The process in which they are applied to the evolution of network structure is as follows:

Selection
. The selection operator selects excellent individuals in the current population, and the selected excellent individuals are included in the next generation of population. The first step in the selection process is to form a population of individuals. Here, the population consisting of knowledge networks with di erent topological structures is represented by A = {KN 1 , KN 2 , . . . , KN M }. Here, the size of E and L are the same for any networks KN i , KN j ∈ A. From the viewpoint of genetic algorithm, each knowledge network in a population can be regarded as one individual, and in a matrix that mathematically represents a network, each element is defined as a gene. That is, gene and agent are di erent concepts.
. Next, the selection operation is performed by using the Roulette wheel selection, which Holland proposed (Gen et al. ). The Roulette wheel selection is a well-known selection type. The basic idea is to determine the selection probability or survival probability of each individual in proportion to its fitness value. The Roulette wheel selection can be formulated as: where F is the fitness of the individuals.
The crossover operator randomly selects two individuals (parents) in the current population and subsequently some genes included in each individual and then creates new individuals (children) by exchanging (= crossing) those genes with each other. Since the knowledge network has the symmetric matrix structure in which the diagonal elements are zero, multi-dimensional crossover (Gen et al. ) is used in accordance with the characteristics of network structure to perform crossover operation and defined as follows: .
Definition: when p 1 and p 2 are the randomly selected parents (two individuals) in the population, the new individuals generated by Algorithm * , C 1 and C 2 , are called the children (two individuals) of the parents p 1 and p 2 in the viewpoint of the genetic algorithm.
In this algorithm, P ij and C ij are the arbitrarily selected genes from parents and children, respectively. This algorithm stochastically preserves the number of the genes that the child inherits from the parents. The generating process of children from parents is shown in Figure . In Figure , p 1 and p 2 are any pair of parents selected from the population, and C 1 and C 2 are the children generated from the parents. In order to preserve the number of individuals in a population, two children are created from a pair of parents. All individuals are symmetric matrices, where diagonal elements are all zero and other elements are only and , as shown in the figure. In other words, since the upper triangular matrix and the lower triangular matrix coincide with each other around the diagonal elements, only the change of the upper triangular matrix is considered.
. The crossover operation is as follows: If the genes (P 1 ij and P 2 ij ) of the parents (p 1 ij and p 2 ij ) are equal to each other, the genes (C 1 ij and C 2 ij ) of the children (p 1 ij and p 2 ij ) receive the same value as the parents. If the genes of the parents are di erent, the genes of the children resemble the parents with a probability of . . At this point, the numbers and in the parents and children are preserved.

Mutation .
The mutation operator arbitrarily selects one individual and then changes certain genes of the selected individual. The probability of mutation is defined as the proportion of the number of mutated genes to the total number of genes in a population. Here, the mutation operation is performed referring to the rewiring rule of Liu et al. ( ). These rules are as follows.
• The target agent i is rewired to the neighbors of its original neighbors with a probability of ω; otherwise, it is rewired to one of the randomly selected agents among all agents except its nearest neighbors with a probability of 1 − ω.   .
Figure illustrates the mutation process by citing the rewiring with a probability of ω as an example. If agent is the target agent, its connected neighbors are the agents , , and . Among these neighbors, if agent is randomly selected, its neighbor, agent , is rewired to agent . Then, the existing edge (marked with the dotted line) of agents and is cut o . Likewise, it is not di icult to implement the rewiring with a probability of 1 − ω.

A fitness test .
A fitness test is a process of evaluating the fitness of the newly created population a er crossover and mutation. In essence, the co-evolutionary dynamics of knowledge di usion and network structure is to determine the optimum network to improve knowledge di usion performance. Thus, the fitness of each individual in the population is calculated by applying Equation . .
The topological evolution mechanism of the network structure is constituted of the genetic operators developed in Sections . -. (selection, crossover, mutation, fitness test).
Overall execution procedure of GA-ABM .
The co-evolutionary dynamics model combining the agent-based model with the genetic algorithm is briefly called GA-ABM. Figure shows the flowchart of the simulation process of co-evolutionary dynamics by GA-ABM. The overall execution procedure of GA-ABM is as follows: Step : The generation of the initial population Randomly generate M networks. Here, all the network equally has N agents and K edges. (That is, the sizes of all the network are the same, but the topological structures are di erent.) Step : The initialization of networks (i.e., the initialization of individuals) Give the initial knowledge values to all networks. Here, the corresponding agents between networks have the same initial knowledge value.
Step : The simulation of knowledge di usion by ABM Compute the agent-based model of knowledge diffusion described in Sections . -. and update the knowledge value of each agent.
Step : The rewiring of edges in the network by genetic algorithm Rewire the edges in the network by using the genetic operators mentioned in Section . -. .
Step : The check on the end condition of the genetic algorithm Once the number of iterations reaches the predefined value, exit the step, return the updated population and the optimal network and go to Step .
If not, go to Step .
Step : The advance of knowledge di usion process Advance the time step and go back to Step .
Step : The check on the end condition of knowledge di usion process Once the number of iterations reaches the predefined value, end the procedure and output the results.

Simulation Results and Discussion
. Firstly, we used the WS small world model proposed by Watts & Strogatz ( ) to form populations by generating M random networks with N agents and K edges. At this point, the rewiring probability of the network was P = 0.2. In the process of co-evolution, the size of the population and the number of the agents and the edges in each individual remains constant. That is, N = 100, K = 800, and M = 100. Where K is the product of the mean degree and the number of agents in the network, i.e., K = m × N , where m is the mean degree of the network and m = 8. .
We introduced the following assumptions in the simulation process.
. Firstly, all the agents have only a single kind of knowledge. That is, the homogeneity of knowledge is guaranteed. Secondly, agents can have multiple levels of expertise. .
In addition, we examine the average knowledge stock and the knowledge growth rate, which are two macrostatistical values, to measure the knowledge di usion performance. If the knowledge network consists of N agents, the average knowledge stock of network by knowledge accumulation at each agent can be written as At time t, the knowledge growth rate of the whole network can be written as follows.
k is a basic parameter for evaluating knowledge di usion performance of knowledge network. In the knowledge network, agents have the following initial knowledge values, k i, . However, if all agents have similar knowledge values, it becomes di icult to spread knowledge. Therefore, we introduced experts with a highly specialized knowledge (Cowan & Jonard ). Each expert's initial knowledge value ranged from to . The upper limit of the knowledge amount to be exchanged per iteration  The comparison of GA-ABM with the models in which the co-evolutionary dynamics is not considered .
Here, we evaluated the knowledge di usion performance of GA-ABM by comparing the proposed model with the models in which the co-evolutionary dynamics was not considered. In case of not considering the coevolutionary dynamics, in essence, there was only knowledge di usion and no topological evolution of the network structure. Therefore for convenience, this model is simply called the agent-based model (ABM). We compared GA-ABM with ABM in terms of knowledge distribution of agents, average knowledge stock and knowledge growth rate of network. Figure shows the knowledge distribution in the initial and final states of the knowledge network by ABM. The initial and final states indicated the initial and last calculation time, respectively. .
In Figure , the dotted line shows the knowledge distribution of the network at the final state and the solid line shows the knowledge distribution at the initial state. On the solid line, we can see a few sharp peaks, which represent the knowledge values of a few experts in the network in the initial state. The value is close to at its maximum. Most agents have small knowledge values between and . The state of the dotted line shows that most agents reached some equilibrium values (approximately . ). However, there are still several peaks and the large di erence between its maximum and equilibrium values indicates that most agents did not fully absorbed the experts' knowledge. This meant that the knowledge stock of agents in a given network structure cannot be maximized. Figure : The knowledge distribution in the initial and final states of knowledge network by ABM.
.  . In other words, the GA-ABM had a time delay of about seconds to reach the equilibrium value compared to ABM, but the average knowledge stock was more than twice higher than ABM. This is because GA-ABM uses the genetic algorithm optimal for the topological evolution of the network structure. Thanks to the genetic algorithm, the network structure was evolved to the optimization of the knowledge level of agents at each time step; as a result, the knowledge level of each agent converged to its maximum value.
The knowledge growth rate of the GA-ABM decreased sharply at the beginning according to time, but gradually decreased at about s, and sharply decreased again at about s, converging to at around s. The knowledge growth rate of the GA-ABM was more than about twice the ABM, and the time to converge to zero was about seconds later. These results are also consistent with the analytical results shown in Figure on time and quantitative level. These results suggest that GA-ABM has superior knowledge di usion performance than the ABM. .
When not considering co-evolution, knowledge di usion is clearly related to the initial knowledge distribution and the network structure. Whether all agents in the network can have a high knowledge stock or not depends on the topological structure of the network under the condition that networks have the same value in the initial distribution of knowledge and the parameters. .
As shown in the calculation results, in the ABM, not all agents in the network had the maximum value of knowledge stock. This was entirely due to the topological structure of the network. This is because the original topological structure of network is not the ideal structure to maximize the knowledge stock and knowledge growth rate of agents. However, GA-ABM showed twice as more knowledge stock and knowledge growth rate as ABM, i.e., its knowledge di usion performance was higher. This is due to the co-evolutionary dynamics of the knowledge di usion and the network structure, particularly to the use of genetic algorithm, which is an optimization method for the evolution of network structure.

The comparison of GA-ABM with the models in which the co-evolutionary dynamics is considered .
Here, we selected the model of Luo et al. ( ), which is the most typical co-evolutionary dynamics model, as a comparison. In this model, an agent obtains new knowledge from its neighbor by using the KT rule with a probability of or uses the NA (Neighborhood Adjustment) rule with a probability of to conduct the network adjustment for rewiring the existing edges between the target and another agent. Therefore, the knowledge di usion performance of the knowledge network depends on the probability. For convenience, we will call this model a KT-NA (Co-evolutionary dynamics model of knowledge di usion and social network structure; see Luo et al. In other words, this shows that the knowledge value of the agents in the final state by both models was the same and reached an equilibrium value (about . ). This equilibrium value is consistent with the maximum value of the expert-possessing knowledge in the initial knowledge distribution. This means that all agents in the knowledge network fully absorbed the experts' knowledge through the co-evolutionary dynamics of the knowledge di usion and topological structure by both models.
.   That is, the larger the P value, the shorter the time to converge to zero, the values of s, s, and s, were respectively, in decreasing order of P value. In addition, the knowledge growth rate of the GA-ABM was about twice that of the KT-NA model. In other words, the average knowledge stock of the two models was the same, but the knowledge growth rate of the GA-ABM was faster than the KT-NA model. From these results, although both models were coevolutionary dynamics models, we can see that GA-ABM had superior knowledge di usion performance than the KT-NA model. .
When considering co-evolution, knowledge di usion is clearly related to the topological evolution mechanism of the knowledge network. By this mechanism, the knowledge stock of the whole network may or not rapidly converge to its maximum value over time. As the results showed, the average knowledge accumulations of the KT-NA model and GA-ABM were the same in the final state, but the knowledge growth rate of the GA-ABM was faster than one of KT-NA model. This was entirely due to the topological evolution mechanism of the network. This is also because the topological evolution mechanism of the KT-NA model is not an ideal mechanism to maximize the knowledge growth rate of agents. However, the GA-ABM had a twice as high knowledge growth rate as that of the KT-NA model. That is, its knowledge di usion performance was higher. This is because the GA-ABM generates an optimal network structure that maximizes the knowledge stock of agents at each time step of co-evolution through a topological evolution mechanism by using genetic algorithm.
Analysis of optimal network structure .
As described above, we can use the GA-ABM to obtain the network structure and knowledge distribution that can maximize knowledge di usion at each time step. Then, there is a question of what structural characteristics this optimal network has and what kind of rule it can derive from its analysis. Therefore, it is necessary to analyze the optimal network structure. The process of exploring and analyzing the optimal network structure by using the GA-ABM can be summarized as follows: . First, we searched for an individual (here, one knowledge network) whose fitness function value (knowledge di usion) is maximized at the execution stage of the genetic algorithm executed at each time step of knowledge di usion. This individual is the optimal network that maximizes the amount of knowledge di usion at this time.
We grouped the optimal networks that are searched at each time step to obtain a single time series.
. Next, we analyzed the topological structure of these optimal networks. The basic statistical values that characterize the topological structure of the network are the average path length and the clustering coe icient (Morone & Taylor ). The average path length of the network can better describe the connectivity of the network. .
The distance A di,j between two agents i and j in the network is defined as the number of edges on the shortest path connecting the two agents. The average path length AP L of the network is defined as the average of the shortest path between any two agents, i.e.
where N is the number of agents in the network. .
The clustering coe icient characterizes the clustering characteristics of the network, that is, the community characteristics. It is generally assumed that agent i in the network are associated with i k edges, that is, connected to other k i agents. Obviously, there may be up to k i (k i −1)/2 edges between the k i agents. The number of edges actually present between the k i agents is e i . Then the ratio of e i the number of edges actually existing between the k i agents and the total possible number of edges k i (k i −1)/2 is defined as the clustering coe icient C i of the agent i, i.e., .
The average of the clustering coe icients of all agents in the network is the clustering coe icient of the entire network, i.e., We analyzed the change characteristics of these two statistical values with time.
. Finally, the topological structure of the network was discriminated on the basis of the average path length and the clustering coe icient of the optimal network obtained. Its crucial equation is as follows (Neal ): SW I is an abbreviation for small-world index. Where CC l and AP L l are the clustering coe icient and average path length of the regular reference network, respectively, and CC r and AP L r are the clustering coe icient and average path length of the random reference network, respectively. These reference networks should have the same size, density and mean degree as the observed network (the optimal network in our study). In our case, the initial network and the optimal network had the same size and since the number of edges in the whole network was preserved during the evolution process, it matched the preconditions as mentioned above. These values were calculated as follows: where N is the size of the network and m is the mean degree of the network. If the SW I is equal to or near , the observed network can be discriminated as a regular network or a random network. If the is equal to or near , the observed network can be discriminated as a small world network. .
The results are shown in Figure , , and Table . Figure shows the variation of average path length and clustering coe icient with time. As can be seen from the figure, the average path length over time decreases slowly while vibrating, and the clustering coe icient causes only vibration in the range of minimum value . and maximum value . , and there is almost no change in the inclination.

.
Through several simulations, we found that this phenomenon is maintained even at the rewiring probability P ∈ [0.1, 0.6] of the initial network. .
The average path length of the optimal network obtained by the GA-ABM in our study is gradually decreasing over time. The average path length of the network is a measure of the network level and is a value that averages the shortest path lengths of all agent's pair belonging to the network. The shorter the average path length, the shorter the distance between agents, which makes it easier to transfer knowledge and absorb knowledge from other agents. Therefore, knowledge di usion performance such as the average knowledge stock and knowledge growth rate of the knowledge network will be higher (Watts & Strogatz ). Our results showed that the average shortest path length of the network had a significant e ect on knowledge di usion performance. .
Next, in our study, the clustering coe icient of the optimal network obtained by the GA-ABM did not change slope over time. That is, it only caused vibrations in a certain range of values, and did not show any tendency to increase or decrease. The clustering coe icient is a measure of the agent level, meaning that agents with large values had many neighbors connected to each other. The larger the clustering coe icient was, the more neighbors were connected and can be accessed with shorter distances, making it easier to acquire knowledge. On the other hand, it may not be possible to acquire higher knowledge because the knowledge level of neighbors can easily become similar. Therefore, the relationship between the clustering coe icient and knowledge di usion performance of the network is di icult to predict clearly (Cowan & Jonard ; Park ). Our results confirm these findings from previous work.
. Figure shows the (small-world index) of the optimal network over time, and Table shows the average path length and clustering coe icients of the rule and random networks. As shown in Figure , the SWI oscillates with a value close to zero over time.
AP L l CC l AP Lr CCr . . . . Table : Average path length and clustering coe icient of the reference networks (N = 100, m = 8) .
This means that the optimal network does not exhibit "small world" characteristics in the evolutionary process. In this case, the question is then whether this optimal network is a rule network or a random network. As shown in Figure , the average path length of the optimal network oscillates between a maximum of . and a minimum of . , and the clustering coe icient oscillates between a maximum of . and a minimum of . . As shown in Table , the average path length and clustering coe icients of the optimal network were much smaller than the values of the rule reference network and slightly larger than those of the random reference network. This means that the optimal network had random network characteristics in the co-evolution process. . Luo et al. ( ) reported that small world networks are created and destroyed in succession, and pointed out that the co-evolution of knowledge di usion and network structures is a key factor in the formation of a "small world" network. It is also known that a small world network has a relatively small average path length and a relatively large clustering coe icient, and its knowledge di usion performance is higher than other networks (Cowan & Jonard ; Kim & Park ).
. However, in our proposed model, the optimal network in the process of co-evolution did not show any "small world" characteristic and maintained the same random property as the initial network, but its knowledge di usion performance was very high. This implies that the small world network is not necessarily associated with a high knowledge di usion and that there is room for the improvement of knowledge di usion performance during co-evolution process, even in case of the random network which average path length is short and clustering coe icient is small. In future work, we will discuss this issue in more depth.

Conclusions
Summary and conclusions on the simulation results . In this paper, we studied the co-evolutionary dynamics of knowledge di usion and network structure in the knowledge network including agents such as personel, corporations and innovative organizations by developing a GA-ABM. We found first that the GA-ABM is superior to other models in knowledge di usion performance. As shown in our simulation results, our GA-ABM is able to maximize the average knowledge stock and knowledge growth rate of the knowledge network. In most previous work, the probabilistic rules or methods have been applied to the network's topological evolution mechanism. The purpose of this study was to overcome certain defects of such stochastic approaches and explore the optimal network structure that can maximize the knowledge di usion performance of knowledge network by using a deterministic method. We therefore developed a topology evolution mechanism of network by using genetic operators and proposed the GA-ABM with an excellent knowledge di usion performance by combining the genetic algorithm with an agent-based knowledge di usion model. Through the comparative simulation study, the GA-ABM was proven to have a higher knowledge di usion performance compared to several other models.
. Secondly, the analysis on the time series data of the opimal network structure obtained by GA-ABM shows that this model produced an interesting phenomenon di erent from previous studies. At first, the evolution of network structure in the co-evolution process does not necessarily represent small world characteristics. Cowan & Jonard ( ) and Kim & Park ( ) found that a small world network is the most e ective topology structure for knowledge di usion. The KT-NA model of Luo et al. ( ) showed that the topological structure is sequentially constructed and destroyed from random to small-world networks in the co-evolution process. Xuan et al. ( ) considered that the higher the adjustment rate, the farther the adjusted network deviates from the 'small world' region, and as a result, the improvement of knowledge di usion performance gets unclear. However, here, the optimal network maintained the same random characteristics as the initial network in the co-evolution process, but its knowledge di usion performance was very high. This also shows that the proposed topological evolution mechanism makes it possible to obtain a high knowledge di usion performance even in a random network. This is attributed to the superior optimization capability of the topological evolution mechanism proposed on the basis of a genetic algorithm. Next, the clustering coe icients of agents are not significant in the improvement of knowledge di usion performance. In other words, the larger the clustering coe icients, the larger the possibility that the knowledge levels between neighbors get similar and knowledge is not well absorbed. Note that such a result was also reported in Cowan & Jonard ( ) and Park ( ).

Managerial implications .
In knowledge networks consisting of agents such as personnel, companies and innovation organizations, the knowledge di usion is influenced by the network structure. Therefore, the formation and rewiring of the network structure are very important in knowledge management for the creation, retention, di usion and dissemination of knowledge. From this point of view, the information obtained here could o er a management implication that can promote knowledge di usion. In other words, regardless of the initial structure of knowledge network and the knowledge level of each agent, GA-ABM provides the optimal network structure that can maximize the knowledge di usion performance and allow the knowledge management to follow such a structure. .
Let us consider an innovation organization as an example. It is assumed that each member of an innovational organization has the same qualifications. In other words, they can freely exchange information with each other according to their capabilities. Of course, their knowledge levels are di erent from each other, and the linking structure between them is random. In case of the purpose to shorten the knowledge update cycle in the innovation organization and raise the knowledge levels of total members in the organization within the shortest period, the GA-ABM can be applied. .
The process is as follows: At first, quantitatively evaluate the initial knowledge holding of each member in the innovation organization and properly select various parameters (threshold, knowledge limit, etc.). Next, determine the time steps and the goal (the desired maximum value of knowledge) according to the property of organization and the level of each member. Then, implement the first calculation step in the co-evolution of knowledge di usion and network structure. As a result of this calculation, the knowledge update of members corresponding to this step and the topological evolution of the network structure is completed and the optimum network structure is obtained. The knowledge manager (or the network manager, in this case, the head of the innovation organization) rewires the members within the organization according to the optimal network structure. In this way, continue to advance the time steps, update the knowledge values of all the members and implement the rewiring of the network structure. As a result, all members of the organization have the maximum knowledge value at the final time step, and the knowledge update cycle is fast.
. This type of managerial implication belongs to macroscopic and approximate forecasting. In order to complete this model, many studies on agent and knowledge attributes should be conducted. In spite of these limitations, this study provides the possibility to enhance knowledge di usion performance and shorten the knowledge update cycle in knowledge network composed of such agents on the basis of a new co-evolutionary dynamics model.

Limitations and future work
. The evolution of knowledge network can be regarded as an evolution process of complex system and has nonlinear self-organization characteristics. In this study, the genetic algorithm that finds an optimal solution by mimicking the evolution of living organisms was used to study the co-evolutionary dynamics of knowledge di usion and network structure. Genetic algorithm is a powerful adaptive search method that can be used to solve multiple objects and multiple shape problems as well as the optimization problems of large and complex functions. In this study, we could not fully address the problem of the nonlinear self-organization characteristics of the knowledge network in combination with the principle of genetic algorithms. Moreover, more research on agent and network attributes should be performed to improve our understanding of the knowledge di usion model.

.
In future, we will focus on overcoming these limitations by further completing the knowledge di usion model for agent and knowledge attributes and elucidating their e ects on the topological evolution of network structure.