This paper deals with the chaoticity and fractality analysis of price time series for artificial stock market generated by the multi-agent systems based on the co-evolutionary Genetic Programming (GP). By simulation studies, if the system parameters and the system construction are appropriately chosen, the system shows very monotonic behaviors or sometime chaotic time series. Therefore, it is necessary to show the relationship between the realizability (reproducibility) of the system and the system parameters. This paper describe the relation between the chaoticity of an artificial stock price and system parameters. We also show the condition for the fractality of a stock price. Although the Chaos and the Fractal are the signal which can be obtained from the system which is generally different, we show that those can be obtained from a single system. Cognitive behaviors of agents are modeled by using the GP to introduce social learning as well as individual learning. Assuming five types of agents, in which rational agents prefer forecast models (equations) or production rules to support their decision making, and irrational agents select decisions at random like a speculator. Rational agents usually use their own knowledge base, but some of them utilize their public (common) knowledge base to improve trading decisions. By assuming that agents with random behavior are excluded and each agent uses the forecast model or production rule with most highest fitness, those assumptions are derived a kind of chaoticity from stock price. It is also seen that the stock price becomes fractal time series if we utilize original framework for the multi-agent system and relax the restriction of systems for chaoticity.

There are several methods for generating multi-fractal time series, but the origin of the multi-fractality is not discussed so far. This paper deals with the multi-fractality analysis of time series in an artificial stock market generated by multi-agent systems based on the Genetic Programming (GP) and its applications to feature extractions. Cognitive behaviors of agents are modeled by using the GP to introduce the co-evolutionary (social) learning as well as the individual learning. We assume five types of agents, in which a part of the agents prefer forecast equations or forecast rules to support their decision making, and another type of the agents select decisions at random like a speculator. The agents using forecast equations and rules usually use their own knowledge base, but some of them utilize their public (common) knowledge base to improve trading decisions. For checking the multi-fractality we use an extended method based on the continuous time wavelet transform. Then, it is shown that the time series of the artificial stock price reveals as a multi-fractal signal. We mainly focus on the proportion of the agents of each type. To examine the role of agents of each type, we classify six cases by changing the composition of agents of types. As a result, in several cases we find strict multi-fractality in artificial stock prices, and we see the relationship between the realizability (reproducibility) of multi-fractality and the system parameters. By applying a prediction method for mono-fractal time series as counterparts, features of the multi-fractal time series are extracted. As a result, we examine and find the origin of multi-fractal processes in artificial stock prices.

This paper deals with the control of chaotic dynamics by using the approximated system equations which are obtained by using the Genetic Programming (GP). Well known OGY method utilizes already existing unstable orbits embedded in the chaotic attractor, and use linearlization of system equations and small perturbation for control. However, in the OGY method we need transition time to attain the control, and the noise included in the linealization of equations moves the orbit into unstable region again. In this paper we propose a control method which utilize the estimated system equations obtained by the GP so that the direct nonlinear control is applicable to the unstable orbit at any time. In the GP, the system equations are represented by parse trees and the performance (fitness) of each individual is defined as the inversion of the root mean square error between the observed data and the output of the system equation. By selecting a pair of individuals having higher fitness, the crossover operation is applied to generate new individuals. In the simulation study, the method is applied at first to the artificially generated chaotic dynamics such as the Logistic map and the Henon map. The error of approximation is evaluated based upon the prediction error. The effect of noise included in the time series on the approximation is also discussed. In our control, since the system equations are estimated, we only need to change the input incrementally so that the system moves to the stable region. By assuming the targeted dynamic system f(x(t)) with input u(t)=0 is estimated by using the GP (denoted (x(t))), then we impose the input u(t) so that xf=(t+1)=(x(t))+u(t) where xf is the fixed point. Then, the next state x(t+1) of targeted dynamic system f(x(t)) is replaced by x(t+1)+u(t). The control method is applied to the approximation and control of chaotic dynamics generating various time series and even noisy time series by using one dimensional and higher dimensional system. As a result, if the noise level is relatively large, the method of the paper provides better control compared to conventional OGY method.

In this paper, we show the analysis of price changes in artificial double auction markets consisting of multi-agents who learn from past experiences based on the Genetic Programming (GP) and its applications. For simplicity, we focus on the double auction in an electricity market. Agents in the market are allowed to buy or sell items (electricity) depending on the prediction of situations. Each agent has a pool of individuals (decision functions) represented in tree structures to decide bid price by using the past result of auctions. A fitness of each individual is defined by using successful bids and a capacity utilization rate of production units for a production of items, and agents improve their individuals based on the GP to get higher return in coming auctions. In simulation studies, changes of bid prices and returns of bidders are discussed depending on demand curves of customers and the weight between an average profit obtained by successful bids and the capacity utilization rate of production units. The validation of simulation studies is examined by comparing results with classical models and price changes in real double auction markets. Since bid prices bear relatively large changes, we apply an approximate method for a control by forcing agents stabilize the changes in bid prices. As a result, we see the stabilization scheme of bid prices in double auction markets is not realistic, then it is concluded that the market contains substantial instability.

This paper deals with the identification of system equation of the chaotic dynamics by using smaller number of data based upon the genetic programming (GP). The problem to estimate the system equation from the chaotic data is important to analyze the structure of dynamics in the fields such as the business and economics. Especially, for the prediction of chaotic dynamics, if the number of data is restricted, we can not use conventional numerical method such as the linear-reconstruction of attractors and the prediction by using the neural networks. In this paper we utilize an efficient method to identify the system equation by using the GP. In the GP, the performance (fitness) of each individual is defined as the inversion of the root mean square error of the spectrum obtained by the original and predicted time series to suppress the effect of the initial value of variables. Conventional GA (Genetic Algorithm) is combined to optimize the constants in equations and to select the primitives in the GP representation. By selecting a pair of individuals having higher fitness, the crossover operation is applied to generate new individuals. The crossover operation used here means the replacement of a part of tree in individual A by a part of tree in individual B. To avoid the meaningless genetic operation, the validity of prefix representation of the subtree to be embedded to the other tree is probed by using the stack count. These newly generated individuals replace old individuals with lower fitness. The mutation operation is also used to avoid the convergence to the local minimum. In the simulation study, the identification method is applied at first to the well known chaotic dynamics such as the Logistic map and the Henon map. Then, the method is applied to the identification of the chaotic data of various time series by using one dimensional and higher dimensional system. The result shows better prediction than conventional ones in cases where the number of data is small.

Widespread penetration of data communications in a LAN environment is generating a demand for high speed data transfer over wide area networks. It is anticipated that the connectionless (CL) service based on IEEE802.6 technology, called Switched Multi-megabit Data Service (SMDS), will be employed before this is realized by B-ISDN based technology. An important early application of B-ISDN will be interconnections between LANs, and continued support of the IEEE802.6 based CL service. This paper first reviews relevant technologies, clarifies comparison between IEEE802.6 based and B-ISDN based CL services, and points out that the important feature for users is that both CL services conform to the E.164 ISDN numbering plan for message addressing. Since an addressing scheme is the key to network services, conformity between the two will easily rationalize service migration from the IEEE802.6 based CL service to the B-ISDN based CL service. To permit such a service migration, this paper considers interworking scenarios for two CL services taking account of the penetration of inter-LAN communications. An exploring path is also presented to that users will not need to be aware of an alternation of network configuration, and smooth migration can take place. For facilitating high volume CL communications in the B-ISDN era, a virtual CL network is discussed to utilize ATM functionalities and to realize broadcasting and robust connectionless service capabilities. An overall comparison between a ring and mesh/star topology for the CL network is presented, and a detailed performance study is addressed in the context of Quality of Service which may depend on the particular application. This paper then describes a connectionless switch architecture in which a message switch combined with an ATM cell channel switch is presented. One scheme which receives specific attention here is a non-assembly message switching method to achieve robust switching capabilities. Typical performance evaluation results based on an M/G/1 queueing model are also reported.

This paper deals with the use of neural network rule extraction techniques based on the Genetic Programming (GP) to build intelligent and explanatory evaluation systems. Recent development in algorithms that extract rules from trained neural networks enable us to generate classification rules in spite of their intrinsically black-box nature. However, in the original decompositional method looking at the internal structure of the networks, the comprehensive methods combining the output to the inputs using parameters are complicated. Then, in our paper, we utilized the GP to automatize the rule extraction process in the trained neural networks where the statements changed into a binary classification. Even though the production (classification) rule generation based on the GP alone are applicable straightforward to the underlying problems for decision making, but in the original GP method production rules include many statements described by arithmetic expressions as well as basic logical expressions, and it makes the rule generation process very complicated. Therefore, we utilize the neural network and binary classification to obtain simple and relevant classification rules in real applications by avoiding straightforward applications of the GP procedure to the arithmetic expressions. At first, the pruning process of weight among neurons is applied to obtain simple but substantial binary expressions which are used as statements is classification rules. Then, the GP is applied to generate ultimate rules. As applications, we generate rules to prediction of bankruptcy and creditworthiness for binary classifications, and the apply the method to multi-level classification of corporate bonds (rating) by using the financial indicators.