Crowd intelligence evolution based on complex network

2.1 Crowd intelligence

The concept of crowd intelligence was put forward with crowd computing [Miller (2012)] in the early days, emphasizing the importance of hum1an beings in computing science. The current research on crowd intelligence focuses on the internal mechanism within the group. For example:

• To study how human and computer systems form a group of interoperable computing to complete complex tasks that are difficult for computer systems to complete independently [Yu et al. (2017)].

• How the heterogeneous system composed of man-machine-software can cooperate to achieve the optimal control mechanism [Shirado and Christakis (2017)].

• Introduce people into the system as experts to participate in processing, feedback and decision-making, forming a mixed man-machine system, so as to maximize the role of human knowledge in the application system [Ooi et al. (2014)].

The calculation and measurement of intelligence quantity of intelligent agents usually refer to the measurement method of human intelligence, the measurement of human intelligence depends on the determined computing system. The existing methods for human measurement usually adopt IQ tests, which is similar to methods for machine intelligence measurement. The core idea is the accuracy rate of completing certain kinds of questions in unit time. In recent years, the population entropy [Zhang et al. (2008)], comparative entropy [Peter (2010)] and potential field [Neil et al. (2018)] analysis which measure crowd intelligence behavior have provided good ideas. However, for heterogeneous agents, there is no clear standard for the transformation method from the main space to the digital space.

Similar to the inter-transformation between heterogeneous intelligences, there is no unified model for the evolutionary pattern of crowd intelligence. Because there are massive uncertain interactions in the real world, the relationship and degree of interaction may even change over time. In this paper, we model, regulate and observe the evolutionary network of crowd intelligence from a macroscopic perspective.

2.2 Complex network

The complex network theory is the result of observation of relatively simple network topologies in different fields. It is found that these networks are different from the previous network systems, they are dynamic and open, growing and evolving with the characteristics of life. At the local level, it is disorganized, while at the whole level, it is highly clustered. In particular, when the fields involved are different, it is necessary to integrate the knowledge of various related disciplines to establish the transformation from the subject space to the digital body space, so as to form a complex network belonging to this field. The research field of complex network mainly involves: cellular network [Zhang et al. (2016)], social network [Wang et al. (2019)], epidemic disease transmission network [Zhuang and Yagan (2020)] and so on.

At present, the research work of complex networks mainly focuses on the following aspects:

• Research on the model and theory of complex network [Zhou et al. (2009)]. It includes more extensive empirical research and more in-depth theoretical characterization, such as matching patterns based on given degree distribution, various correlation [Geng et al. (2018)], statistical properties and description of weighted network and network clustering [Lei et al. (2019), Ooi et al. (2014)], etc.

• Evolution and mechanism model of complex network [Bettencourt (2014)]. It mainly studies the statistical law of actual network evolution [Yang et al. (2018)] and theoretically can develop a more perfect network mechanism model with specific geometric properties.

• Structure of complex network [Liu et al. (2014)]. Functional and network dynamics research, including network fault tolerance and attack robustness [Shang (2017)], as well as network propagation [Karyotis and Papavassiliou (2015)], synchronization and resonance dynamics processes.

In this paper, combined with the characteristics of complex networks, the science of public intelligence and its evolution model are expressed in the form of complex networks. The next section describes the details of complex network construction that incorporates the features of crowd intelligence.

3.1 Layout process

First, we exclude edges and consider the distribution of nodes only. Assuming that the number of summation nodes is n, the coordinates x and y of each node are uniformly distributed in the circular region x2+y2≤r2. Therefore, the distance between each node is almost equal. Figure 1 (a) shows the distribution of n = 150 nodes in a circle with radius r = 720Pix.

Next, we group n nodes. The purpose of this is to make the resulting distribution have multiple populations and thus contain a variety of evolutionary environments. Suppose each group contains g nodes, these g nodes are assigned new IDs 1 to g and participate in the edge establishment together. Base on Figure 1 (a), Figure 1 (b) shows the result of node linking. 150 nodes are divided into two groups, including 90 nodes and 60 nodes respectively. For the nodes i_g and j_g (make sure that i_g > j_g to avoid repeated links) in a group with g nodes, they are linked if and only if:

Then, for the nodes that are not linked in Figure 1 (b), we need to give these nodes a chance to link. Assuming that node i_u with no edges is assigned, the ID of the target correlation node we assign to i_u is:

Figure 1 (c) shows the result after adding edges. It can be seen that it is composed of two distinct large crowds and several other sporadic small crowds. The formation of two large crowds is the result of group division in the previous step.

3.2 Evolutionary process

After the whole crowd intelligence map G is established, the evolution process can be started. When constructing Figure 1 (a), our method randomly allocates intelligent quantities. Every element in Q follows the standard uniform distribution. The other two factors influencing the evolution of crowd intelligents are interaction rate α ∈ (0,0.5) and volatility rate v ∈ (0,1). Interaction rate α is used to represent the degree of correlation between nodes, volatility rate v is used to describe the possibility of uncertainty and degradation that may occur in the interaction process. In the evolution from generation t to generation t + 1, when two agents i_t and j_t interact with each other, their intelligence qit and qjt are change as:

3.3 Details

Figure 2 zooms in on Figures 1 (d) to show more detail. There are three main types of details:

1. Color distribution. Over the course of evolution, we’ve noticed an exponential increase in the intelligence of individuals. To better represent the process of evolution, we chose 4ⁿ as the step size and divided five different levels of intelligence.

2. No other crowds are allowed in the closed area. For example, in the closed circle composed by the nodes 69-88-59-62-71-67-33-76-60-87-69 in Figure 2, crowds like 142-136 are not allowed to be distributed in it, even if the FR algorithm allows it to happen.

3. Self-connection. In our linking process, there may be free nodes. This kind of nodes is not without links, but they are linked to themselves (e.g. node 90 in Figure 2).

4.1 Conventional evolutionary experiments

In the experiments, we first demonstrate the effect of changes in interaction rate α on the evolution of crowd intelligence. We start from 0.08 and set 3 sets of different interaction rates with 0.02 as the step size. Figure 3 shows the population intelligence distribution map at t = 60. The line graph corresponding to each distribution map reflects the individual’s intelligence status after each evolution. Q¯ represents the average intelligence of all agents and D_Q represents the variance of the intelligence of all agents.

It can be seen from the evolution trend of different interaction rates in Figure 3 that the higher the interaction rate, the faster the evolution. In particular, the complex evolutionary network with α = 0.12 evolves into smarter individuals significantly earlier than the network with α = 0.08. In addition, as the intelligence of the agent increases exponentially, even a small-scale fine-tuning of the interaction rate. After 60 times of evolution, the increase in intelligence presents a butterfly effect.

On the other hand, we also designed an experiment to test the sensitivity of volatility rate. Figure 4 shows the evolutionary situations after adjusting for volatility rate at a fixed interaction rate. Comparing with Figure 3(b) we find that volatility rate will hinder evolution to a certain extent. The evolutionary uncertainty caused by volatility rate will affect the progress of evolution. The higher the volatility rate, the greater the obstacle to evolution.

However, there are two evolutionary phenomena worth noting:

1. Normally, the node at the core of the interaction can first reach a higher level of intelligence in evolution (e.g. node 131 in Figure 2) and the node at the edge of the interaction or the end of the network usually evolves slowly.

2. In the experiment shown in Figure 4, although the volatility rate of node interaction is adjusted, it still does not significantly interfere with the evolutionary trend. In the following extreme observations, we will focus on the impact of extreme volatility rate on evolution.

4.2 Observations of extreme cases

When the volatility rate reaches a high level, it can block the trend of normal evolution. In the extreme situation experiment we designed, the interaction rate α is set to 0.2 and the volatility rate v is set as 1 in the first 120 iterations. The left side of Figure 5 shows the distribution and changes of crowd intelligence in this environment. In the first 50 iterations of evolution, the change of the agent is in a normal state. After 50 iterations of evolution, individuals with low intelligence and individuals with high intelligence gradually form a balance and are evenly distributed in space and almost converges. We extracted the distribution of low-intelligence individuals and high-intelligence individuals in the figure and calculated their Kullback–Leibler divergence R_e. Kullback–Leibler divergence is used to measure the distance between two distributions, the more similar the two distributions, the closer the Kullback–Leibler divergence between them is to 0.

From the 121st round of evolution, we suddenly set the volatility rate to 0 and continue to evolve. The right side of Figure 5 shows the evolution state of the crowd intelligent after the volatility rate mutation. After continuing to evolve for 60 rounds, the entire distribution showed a new balance, the intelligent evolution curve also converged again after a small change. However, the low-intelligence individuals and high-intelligence individuals present a new distribution in the complex interactive network diagram and are different from the distribution at t = 120. At t = 180, These two types of individuals with different intelligence no longer have the same distribution and their Kullback–Leibler divergence is also increased compared with the previous state.