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Evolution of organizational adaptability: application of Hexie management theory.

Abstract: This article identifies organizational dynamic capabilities with adaptability and adopts the concept of fitness landscape by Wright and the NK model of population genetics by Kauffman. The article also applies the cellular automata (CA) model to the construction of organization structure and interaction scope within organization members. In this work, members in the organization are considered as agents who own the capacity of local search and self consciousness, and the elements of He principle and Xie principle based on Hexie Management Theory are regarded as two dimensions in the organization systems. By constructing the different interaction level and the task's complexity that the organization faces, this paper simulates the effect of Hexie management theory on individual behavior and the emergence adaptation of the whole organization. The results of the simulation show that, the Xie principle, which is based on optimization, can get the organization to the better optimization by local search and the coupling of He principle and Xie principle appears strong adaptive capability under complex and turbulent task environments.

Keywords: Organizational adaptation, Hexie Management Theory, NK model, Fitness Landscape

I. Introduction

Although organizational complexity has come up in 1960's and 1970's [1], [2], the application of relative concepts and study methods to organization study hit its peak in 90's. Since the establishing of SFI and some other research institutions, the application of the theory of organizational complexity has gained many achievements, especially the special issue of the application of complexity theory in organization science published in "Organization Science" in 1999 and the research on organization study models in "Computational & Mathematical Organization Theory". The key perspective of introducing complex systems theory into organization theory is to view the organization as complex adaptive systems which include four essential elements: agents with schemata, self-organizing networks sustained by importing energy, coevolution to the edge of chaos, recombination and system evolution [3]. Due to the organization is composed of people, resources and many things, organization is designed and constructed with non-linear characteristics and there are none mature models or algorithms to sustain the organization optimize. Nowadays the organizational complexity study on organizational adaptation mainly based on the framework of evolutionary perspective [4] and follows the fitness landscapes and NK model. [5-7].

In recent works of organizational adaptability, researchers pay much attention on the local search and routine-based logics of behavior but rarely consider the environment and task's complexity[8-10]. Based on the works of Boisot and Levinthal, we introduced two-dimension CA model to describe the organization structure and interactive neighborhoods of individuals. Concerning the response model of Chinese enterprises facing complex tasks, this paper constructs an adaptation search model according to Hexie management theory. The next section introduces the fitness landscapes and NK model, section 3 summarizes the HeXie Management Theory, section 4 describes the detail simulation process of the organization search on rugged landscapes with Hexie walk mechanisms, at last two sections we interprets the simulation results and draw a conclusion.

II. Fitness Landscapes and NK model

Wright introduced the concept of fitness landscape in 1932, and took it as the basic framework in study of biology evolution [11]. Fitness landscape distributes the genotype fitness value to corresponding points in the genotype space. Since the adaptation values of all genotype are different, the mountain like rugged landscape appeared (in figure 1). The peak of the fitness landscape corresponds to the high adaptation level of genotype and the valley of fitness landscape corresponds to a low adaptation level.


In the population genetics study of Kauffman, the fitness landscape topology is determined by the interaction level among the gene adaptations in an organism. Suppose every species has N genes, the contribution of every gene depends on a number of K other genes. Then, Kauffman discovered the NK model which could build a fitness landscape in a simple approach. In this model, N refers to the number of genes contained in a species and K shows the interaction level among the genes, the contribution of a gene is determined by other K genes' characteristics. Levinthal applied it to organizations. In his theory some certain organizations contain N types of characteristics, and every type of them has two values which are 1 and 0. Thus there are [2.sup.N] types of possible organization forms in the fitness landscape. In some certain organization form, the contribution of every characteristic is dependent on K other characteristics, and 0 [less than or equal to] K [less than or equal to] (N - 1). Therefore the fitness contribution of a gene is determined by the fitness value of K+1 genes (including the gene itself and K other genes). The character of NK model is that: change the value of K to adjust the smoothness and roughness of the fitness landscape. Eg. when K = 0, there is no interactions, then the contribution of every gene is only dependent on itself; but if K = N - 1, the contribution of every gene is determined by all other genes.

III. Hexie Management Theory

The theory of Hexie was firstly carried out by Dr. Xi Youmin in 1989[12], which was originated from Chinese traditional philosophy. The theory also contains the relative theory on system and organization study, regarding the system as an integrity based on rules and units autonomy, emphasizing the harmony among the sub systems in promotion of the efficiency of the whole system and taking the management control as a self evolution process with rational design and environment inducement [13].

This paper applies the basic theory of Hexie management in the two approaches when an organization faces uncertain situations.

1. The recognition of human and human behavior and the elimination and utilization of their uncertainty which is named He principle.

2. The recognition and optimization of the certainty relationship named Xie principle.

He principle applies environment inducement and self evolution. Xie principle applies substance optimization strategies to known affairs.

IV. Model Construction

As in a real organization, an individual hardly has interactions to all other individual but only to a few number of individual in vicinity [14], this paper adopts the network model organization structure of two-dimension cellular automata. In the networks, every cell shows an individual in an organization which interacts with its neighborhoods. We accept concept of Von Neumann Neighborhoods in the definition of neighbor (as shown in figure 2, the neighbor of the black cell contains four gray cells). Such a definition make sure the contribution of an individual is determined by the other neighbor units (it can be dependent on the all 4 members or one or even none of them). The state of the cell could be 1 or 0 which denotes the cell's attitude is certain or uncertain when the organization is faced with some task, 1 means certain and 0 means uncertain. When the case is 1, the Xie principle of Hexie management theory is implemented which is the member knows his task and reach its maximum fitness contribution without the effect of neighbor members. When the case is 0, the member does not clear its task, according to the He principle, with environment inducement, the fitness contribution of the member is randomly generated which is a result from the interaction with other neighbors. Also in this case, if the neighbor cells' state changed, the corresponding fitness changed too. Therefore, the distribution of an organization has 2N types of organization forms, every form has different corresponding member fitness. Under the circumstance of an average of fitness contribution, the different integrate fitness landscape in different backgrounds could be obtained. This paper will discuss the adaptation and application of Hexie management theory in the approach of the simulated organizations' searching process in rugged landscape of different task environments.


A. Mechanism of Simulation

The simulation is conducted under two different conditions:

(1) Organization is in a stable condition with simple and immobile tasks. In this organization the members are unknown of how to finish their tasks at the very start, thus the value of the nodes is 0. As the tasks are simple and single, the members apply He principle to seek a correct way by self mutation * k = 0, the members depend on self mutation alone to change the adaptation to the tasks * or the interaction with other members (k = 1 to 4, it implies that the interaction with its neighbors are from weak to strong) to change their value to 1 which means to know the task clearly. Because of the simplicity and singularity of the tasks, after the node has known his task, it could finish the task quickly with the He principle application of substance optimization system to maximize its contribution to organization adaptation to 1.

Based on the simulation approaches above, simulate the organization searching process of the following 5 different member interaction levels:

K = 0, the member depends on it own mutation to change its adaptation capacity to different tasks in order to improve the whole integrity's adaptation level. Now the given member could change its state to change its adaptation to task. When the original state is 0, change to 1, and set the adaptation to1. If the original state is 1, then change to 0, and generate a random adaptation in the uniform distribution of (0, 1). Compare the current adaptation and original adaptation, if the current adaptation is higher, adopt the current state and adaptation, if not, keep the original ones.

K = 1 to 4, the member change its adaptation capacity according to itself and the k neighbors' adaptation capacity. Depending on the adaptation change of itself and the affected neighbor members, the member will decide whether to change its state. When a certain member has changed its state from 0 to1 (or from 1 to 0), its adaptation will change to 1 (or random value) and the other members will be affected to regenerate a random adaptation value. When the average of the member and the neighbor members' adaptation value is greater than the original value, the state of the member changed, while if the average value is less than the original one, the state of member remains. We use [S.sup.i] (t) to represent the state of i member at t time:


We use [F.sub.i](t) to show the adaptation value of member i at time t, [F.sub.<i,0>]......[F.sub.<i,k>] denote the adaptation values of k members that affected by member i before the [S.sbu.i](t) changes, including [F.sub.<i,0>] shows the formerly adaptation of member i. [R.sub.<i,0>]......[R.sub.<i,k>] denote the adaptation values of k members that affected by member i after the [S.sub.i](t) changes, [R.sub.<i,0>] shows the new random adaptation value of member i.

At t time, for every member i (i from 0 to N-1), we execute the following step in sequence:


By changing the state of the given member constantly, applying the environment inducement search of He principle and uncertainty elimination of Xie principle and seeking the local adaptation of organization adaptation to raise the integrity adaptation.

(2) Organization is in a complex and protean environment, there is no a relatively certain way to solve the problem. Now the members of the organization are not certain about their tasks or they may have known their tasks but they could no make their contribution to 1 as in the simple environment with optimization and uncertainty elimination of Xie principle, but could only go on with local search to find a way to improve its adaptation level.

In such environment, simulate the adaptation walk in 5 types of interaction levels from k = 0 to k = 4. When the state of the given member changes from 0 to 1, a random value will be randomly generated instead of 1.

B. Initialization condition and simulation process

First, construct a 10x10 cell organization structure with 100 members whose original states are 0. Every member's adaptation contribution value is a uniform distributed random value in a span of 0 to1.

Begin with the left top cell, change the state and adaptation value of the cells from the left to right and from top to bottom, and generate the random adaptation of neighborhoods which were influenced by the state changed cell. Figure 3 shows three members in different location with symbol "+", "*" and "x". The black cell is the given cell, grey ones are the neighbor member of the given cell, the numbers 1,2,3,4 imply that, when k = 1, state of the black cell affects the adaptation of the node labeled 1, when k = 2, the state of the black cell affects the adaptation of both modes labeled 1 and 2, when k = 3, the adaptation of the 3 members labeled 1,2,3 are affected, when k = 4, the value of the adaptation of all four members is affected.


In every time period of the simulation, after the state and cells corresponding contribution to the organization adaptation was calculated, the cells' new state and the whole organization's adaptation are engendered. There are 100 time periods of organization adaptation change is computed to analyze the simulation result.

V. Simulation Result Analysis

According to the designed simulation mechanism, 100 times of simulation are made on different interaction level from k = 0 to k = 4 under two conditions of simple task and complex task. The result can be shown in figure 5 to figure 8 according to the average value of the 100 times of simulation.

A. When organization is faced with simple task environment

As shown in Figure 4 and Figure 5, when k=0, which means there is no interaction among members and they change their adaptation only dependent on the recognition and judgment on the task, there is no dependence among the members or effect from each other. Thus the members contribute to the organization independently, and to reach the highest level of adaptation of the optimization organization, only if the members could reach their greatest performance contribution. According to the fitness landscape theory, there is only one peak exists in the organization's fitness landscape, so the organization could reach its peak adaptation value 1 with the highest speed. But as K increases and the interaction among the members gets stronger, since the members have to consider their effect on other members when changing the their state and adaptation, the organization is in the most complex state and the members and their neighbor members are interdependent. As the fitness landscape is getting more rugged with the increase of value K, there are multi-peaks and the adaptation speed decreases which make the organization apt to fall into the local optimization point. Therefore, it can be seen that the greater the values of K, the lower the evolution of the organization which lead to the slow decrease the whole adaptation level.


B. When organization is faced with complex task Environment

As shown in figure 6, when organization is faced with complex task environment, the whole adaptation value of the organization is around 0.98 when k = 0, while as K increases, the whole adaptation level of the organization decreases, and when K = 4, which means the interaction level among the members is the highest, the adaptation reaches its lowest point of 0.89. The result resembles the simple task condition which shows that the lower the interaction among the organization members, the higher the organization adaptation could evolve.


Based on the result of Figure 7, the 3 time periods before the organization evolution, the evolution speed is low when K = 0 and K = 4 while it is high when K = 1 and 2. It implies that the adaptation speed will decrease either with frequent interaction or with no interaction among organization members, and proper communication and interaction will benefit the organization in reaching its satisfying point (not the optimal point) rapidly. However, considering the variability of the environment, the organizations require the capacity of adapting the environment rapidly, and pursuing the satisfying matching state rapidly, but not get the optimal point generally is the object of the organization. Hence the application of Hexie management theory could achieve the aim.


VI. Conclusion

According to the simulation study of different interaction level organization systems' whole adaptation change in different task environments, it can be found that organization members could apply Hexie theory's double rule systems to adjust the organizational adaptation. The local search of the organization fitness landscape shows that, when the organization is faced with a simple and stable environment, as the activities in the organizations are more certain, the activities of the members could be optimized according to the design. So in this case, the interaction and interdependence among the members should be decreased, the application of He principle should be decreased too, and Xie principle should be applied to eliminate the uncertainty to get the optimal adaptation of the organization rapidly. On the other hand, when the organization is faced with complex and protean environment, though according to a pure optimization procedure, the members could find a right Xie principle system to improve the organization's adaptation even there is no interaction among the members (K = 0). However as far as the uncertainty caused by the complex environment increased, it takes a long time to reach the optimal state. But when both He and Xie rules are applied, following the self optimization and uncertainty elimination (K = 1,2), though the adaptation level is not as good as the result when K = 0, it could improve the whole adaptation level in a shorter time than when K = 0. It shows that based on the Xie rule optimization, with limited interaction which contains both He and Xie, the organization could better adapt to the changeful environment and improve the whole adaptation level more quickly in new environment. On the other hand, if the He rule is misapplied, and give up the optimization effect of Xie, where the excessive interaction freedom is formed (K = 4), bad effect will appear and the improvement of the organization's adaptation level will be impeded, also the adaptation course of the organization to the changeable environment will be slowdown. Although the paper proved the double rule He, Xie of Hexie management theory's good performance in the procedure of organizational adaptation and adaptation speed under the changeable environment, the proposed research model and method is only a highly abstract image without detailed description and the effect mechanism of He rule and Xie rule. It is abstracts the He rule and Xie rule into the interaction among the members and the self saltation optimization, but the actual He and Xie contains wider and more profound meaning. In addition, the paper does not take the Hexie motif into account, and the simple and complex environment in the paper is not defined clearly, but only designed the two simulation mechanism according to the two kinds of task environments. For the study of complex open system interacted with the environment, the environment was not abstracted to influencing variable to study the coevolution between the organization and the environment, which is also a limitation of the paper. So those are the future study area.


We gratefully acknowledge the financial support from the National Nature Science Foundation of China under the grant number 70121001 & 70571062


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Author Biographies

Jun Ma was born in Oct. 1979, he received the B. E. degree in Computer Science in 2002 from Xi'an Jiaotong University, China. He is currently pursuing his Ph.D degree in Management at Xi'an Jiaotong University. His main research interest is knowledge transfer, organization adaptation and evolution, computational organization science.

Youmin Xi was born in Apr. 1957, he received the B. Sc. degree in Physics in 1982 from Xi'an Science and Technology University, he also received the M. E. degree in Systems Engineering in 1984 and the Ph.D degree in Management Engineering in 1987 both from Xi'an Jiaotong University (the first Ph.D. in Management Engineering in mainland China). Professor Xi became the Dean of Management School in 1996 and now he is the vice president of Xi'an Jiaotong University. His research is focused on Hexie management theory, group decision science, complex networks and computational organization science.

Pengxiang Li was born in Jan. 1964, he got his B.E. and M.E. in Applied Geophysics in 1985 and 1992 respectively from Jianghan Petroleum Institute. He has just received his Ph.D degree in Management in 2006 at Xi'an Jiaotong University, China. His research interests include social networks, complex networks, organization complexity, and computational modeling of organizations and society.

Ju'e Guo was born in Apr. 1961, she received the B. Sc. degree in Mathematics in 1983 from Shaanxi Normal University, and her M. E. degree from Institute of Systems Science, China Academy of Sciences, in 1991. She also received the Ph. D. degree in Management from Xi'an Jiaotong University in 2001. She is currently a professor at Xi'an Jiaotong University. Professor Guo's research interest is financial engineering, complex networks.

Jun Ma, Youmin Xi, Pengxiang Li and Ju'e Guo

School of Management, Xi'an Jiaotong University, Xi'an Shaanxi 710049, China Email: {junma, ymxi, lipengx, guojue}
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Author:Ma, Jun; Xi, Youmin; Li, Pengxiang; Guo, Ju'e
Publication:International Journal of Computational Intelligence Research
Geographic Code:1USA
Date:Jan 1, 2007
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