Directed Graph Structure Research Articles

Towards the Maintenance of Population Diversity: A Hybrid Probabilistic Model Building Genetic Network Programming

Some researchers have investigated that the diversity loss will significantly decrease the performance of Probabilistic Model Building Genetic Algorithm (PMBGA), especially under large search space, leading to the premature convergence and local optimum. However, few work has been done on the diversity maintenance in the Probabilistic Model Building Evolutionary Algorithms (PMBEAs) with more complex chromosome structures, such as tree structure based Probabilistic Model Building Genetic Programming (PMBGP) and graph structure based Probabilistic Model Building Genetic Network Programming (PMBGNP). For the PMBEAs with more complex chromosome structures, the required sample size is usually much larger than that of binary structure based PMBGA. Therefore, these algorithms usually become much more sensitive to the population diversity. In order to obtain enough population diversity, the large population size is needed, which is not the best way. In this paper, the maintenance of the population diversity is studied in PMBGNP, which is a kind of PMBEA, but has its unique characteristics because of its directed graph structure. This paper proposed a hybrid PMBGNP algorithm to maintain the population diversity to avoid the premature convergence and local optimum, and presented a theoretical analysis of the diversity loss in PMBGA, PMBGP and PMBGNP. Two techniques have been proposed for the diversity maintenance when the population size is set at not large values, which are multiple probability vectors and genetic operators. The proposed algorithm is applied and evaluated in a kind of autonomous robot, Khepera robot. The simulation study demonstrates that the proposed hybrid PMBGNP is often able to achieve a better performance than the conventional algorithms.

Multi-Order Rules Extraction by Genetic Network Programming with Rule Accumulation and its Application to Stock Trading Problems

As the effectiveness of the trading rules for stock trading problems has been verified, a method of extracting multi-order rules by Genetic Network Programming (GNP) is proposed using the rule accumulation for improving the efficiency of the trading rules in this paper. GNP is one of the evolutionary computations having a directed graph structure. Because of this special structure, the rule accumulation from GNP individuals is more effective for trading the stock than other methods. In this paper, there are two main points: rule extraction and trading action determination. Rule extraction is carried out in the training period, where the rules including the 1st order rules and multi-order rules, are extracted from the best individual and accumulated into the rule pools generation by generation. In the testing period, the trading action is determined by the matching degree of the stock price information with the rules, and the profits of the trading are evaluated. In the simulations, the stock prices of 16 brands in 2004, 2005 and 2006 are used for the training and those in 2007 for the testing. The simulation results show that the multi-order rules perform better than the 1st order rules. So, it is proved that themulti-order rules extracted by GNP is more effective than the 1st order rules for stock trading.

Positive expansiveness versus network dimension in symbolic dynamical systems

A symbolic dynamical system is a continuous transformation Φ : X ⟶ X of closed subset X ⊆ A V , where A is a finite set and V is countable (examples include subshifts, odometers, cellular automata, and automaton networks). The function Φ induces a directed graph (‘network’) structure on V , whose geometry reveals information about the dynamical system ( X , Φ ) . The dimension dim ( V ) is an exponent describing the growth rate of balls in this network as a function of their radius. We show that, if X has positive entropy and dim ( V ) > 1 , and the system ( A V , X , Φ ) satisfies minimal symmetry and mixing conditions, then ( X , Φ ) cannot be positively expansive; this generalizes a well-known result of Shereshevsky about multidimensional cellular automata. We also construct a counterexample to a version of this result without the symmetry condition. Finally, we show that network dimension is invariant under topological conjugacies which are Hölder-continuous.

Efficient program generation by evolving graph structures with multi-start nodes

Automatic program generation is one of the applicable fields of evolutionary computation, and Genetic Programming (GP) is the typical method for this field. On the other hand, Genetic Network Programming (GNP) has been proposed as an extended algorithm of GP in terms of gene structures. GNP is a graph-based evolutionary algorithm and applied to automatic program generation in this paper. GNP has directed graph structures which have some features inherently, for example, re-usability of nodes and the small number of nodes. These features contribute to creating complicated programs with compact structures and never cause bloat. In this paper, the extended algorithm of GNP is proposed, which can create plural programs simultaneously in one individual by using multi-start nodes. In addition, GNP can evolve the programs in one individual considering the fitness and also its standard deviation in order to evolve the plural programs efficiently. In the simulations, Even-n-Parity problem and Mirror Symmetry problem are used for the performance evaluation, and the results show that the proposed method outperforms the standard GNP with single start node.

An Intrusion-Detection Model Based on Fuzzy Class-Association-Rule Mining Using Genetic Network Programming

As the Internet services spread all over the world, many kinds and a large number of security threats are increasing. Therefore, intrusion detection systems, which can effectively detect intrusion accesses, have attracted attention. This paper describes a novel fuzzy class-association-rule mining method based on genetic network programming (GNP) for detecting network intrusions. GNP is an evolutionary optimization technique, which uses directed graph structures instead of strings in genetic algorithm or trees in genetic programming, which leads to enhancing the representation ability with compact programs derived from the reusability of nodes in a graph structure. By combining fuzzy set theory with GNP, the proposed method can deal with the mixed database that contains both discrete and continuous attributes and also extract many important class-association rules that contribute to enhancing detection ability. Therefore, the proposed method can be flexibly applied to both misuse and anomaly detection in network-intrusion-detection problems. Experimental results with KDD99Cup and DARPA98 databases from MIT Lincoln Laboratory show that the proposed method provides competitively high detection rates compared with other machine-learning techniques and GNP with crisp data mining.

Multicar elevator group supervisory control system using genetic network programming

AbstractElevator group control systems are the transportation systems for handling passengers in the buildings. With the increasing demand for high‐rise buildings, it becomes important to improve the elevator service. The multicar elevators consist of plural cars in a single elevator shaft. It contributes to the improvement in passengers' handling capacity, while allowing the reduction of the space occupied in the building. In contrast with traditional elevator systems, the cars can no longer operate freely, where there are several restrictions on their available movements. This requires a more difficult control including stochastic scheduling with high combinatorial complexity in order to make the system more flexible. At present, lots of buildings with more than 40 floors are being built, which are usually divided into several zones served by local elevator groups. In addition, the cars should be operated at equal time intervals, especially in such a building with multicar elevator systems (MCES) in order to obtain its good performance. Genetic network programming (GNP), one of the evolutionary computations, can realize a rule‐based MCES due to its directed graph structure of the individual, which makes the system more flexible. This paper discusses MCES using GNP in high‐rise buildings. Also, the positions of elevators are considered to avoid the bunching phenomenon. The performance of MCES is studied and compared with single‐deck elevator system (SDES) and double‐deck elevator system (DDES). © 2010 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

The Kemeny Constant for Finite Homogeneous Ergodic Markov Chains

A quantity known as the Kemeny constant, which is used to measure the expected number of links that a surfer on the World Wide Web, located on a random web page, needs to follow before reaching his/her desired location, coincides with the more well known notion of the expected time to mixing, i.e., to reaching stationarity of an ergodic Markov chain. In this paper we present a new formula for the Kemeny constant and we develop several perturbation results for the constant, including conditions under which it is a convex function. Finally, for chains whose transition matrix has a certain directed graph structure we show that the Kemeny constant is dependent only on the common length of the cycles and the total number of vertices and not on the specific transition probabilities of the chain.

Multiple‐Round English Auction Agent Based on Genetic Network Programming

AbstractThe auction mechanism widely used in web‐based sites, which is originally designed for human beings, might not be the most efficient one in the future, and there is a demand for evolutionary computation auction agents adaptable to the dynamic auction environments. In this paper, we have applied genetic network programming (GNP) to auction agents and developed multiple‐round English auction mechanisms based on multi‐agent systems. GNP is an evolutionary method that uses directed graph structures as genes to create compact optimal solutions by evolution. According to the simulation results, it has been found that the proposed method could help agents to evolve their strategies generation by generation to get more goods with less money. Also, GNP shows good performance in helping the agent to find out the most suitable strategy under the current situation. Copyright © 2010 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

不完全データベースからの差異ルールと例外ルールの抽出

Two flexible rule mining methods from incomplete database are proposed using Genetic Network Programing (GNP). GNP is one of the evolutionary optimization techniques, which uses the directed graph structure. One of the methods extracts the rules showing the different characteristics between different classes in a database. The method can obtain the rules like 'if P then Q' is interesting only in the focusing class. The other one mines interesting rules like even if itemset X and Y have weak or no statistical relation to class item C, the join of X and Y has strong relation to class item C. An incomplete database includes missing data in some tuples. Generally, it is not easy for Apriori-like methods to extract difference rules and exception rules from incomplete database. We have estimated the performances of the rule extraction using incomplete data in the environmental and medical field.

Traffic Flow Prediction with Genetic Network Programming (GNP)

In this paper, a method for traffic flow prediction has been proposed to obtain prediction rules from the past traffic data using Genetic Network Programming (GNP). GNP is an evolutionary approach which can evolve itself and find the optimal solutions. It has been clarified that GNP works well especially in dynamic environments since GNP is consisted of directed graph structures, creates quite compact programs and has an implicit memory function. In this paper, GNP is applied to create a traffic flow prediction model. And we proposed the spatial adjacency model for the prediction and two kinds of models forN-step prediction. Additionally, the adaptive penalty functions are adopted for the fitness function in order to alleviate the infeasible solutions containing loops in the training process. Furthermore, the sharing function is also used to avoid the premature convergence.

Genetic Network Programming with Rule Accumulation and its Application to Tile-World Problem

Genetic Network Programming (GNP) is an evolutionary algorithm derived from GA and GP. Directed graph structure, reusability of nodes, and implicit memory function enable GNP to deal with complex problems in dynamic environments efficiently and effectively, as many paper demonstrated. This paper proposed a new method to optimize GNP by extracting and using rules. The basic idea of GNP with Rule Accumulation (GNP with RA) is to extract rules with higher fitness values from the elite individuals and store them in the pool every generation. A rule is defined as a sequence of successive judgment results and a processing node, which represent the good experiences of the past behavior. As a result, the rule pool serves as an experience set of GNP obtained in the evolutionary process. By extracting the rules during the evolutionary period and then matching them with the situations of the environment, we could, for example, guide agents' behavior properly and get better performance of the agents. In this paper, we apply GNP with RA to the problem of determining agents' behaviors in the Tile-world environment in order to evaluate its effectiveness. The simulation results demonstrate that GNP with RA could have better performances than the conventional GNP both in the average fitness value and its stability.

Medical association rule mining using genetic network programming

AbstractAn efficient algorithm for building a classifier is proposed based on an important association rule mining using genetic network programming (GNP). The proposed method measures the significance of the association via the chi‐squared test. Users can define the conditions of important association rules for building a classifier flexibly. The definition can include not only the minimum threshold chi‐squared value, but also the number of attributes in the association rules. Therefore, all the extracted important rules can be used for classification directly. GNP is one of the evolutionary optimization techniques, which uses the directed graph structure as genes. Instead of generating a large number of candidate rules, our method can obtain a sufficient number of important association rules for classification. In addition, our method suits association rule mining from dense databases such as medical datasets, where many frequently occurring items are found in each tuple. In this paper, we describe an algorithm for classification using important association rules extracted by GNP with acquisition mechanisms and present some experimental results of medical datasets. © 2008 Wiley Periodicals, Inc. Electron Comm Jpn, 91(2): 46–54, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.10022

Buying and Selling Stocks of Multi Brands Using Genetic Network Programming with Control Nodes

A new evolutionary method named “Genetic Network Programming with control nodes, GNPcn” has been applied to determine the timing of buying or selling stocks. GNPcn represents its solutions as directed graph structures which has some useful features inherently. For example, GNPcn has an implicit memory function which memorizes the past action sequences of agents and GNPcn can re-use nodes repeatedly in the network flow, so very compact graph structures can be made. GNPcn can determine the strategy of buying and selling stocks of multi issues. The effectiveness of the proposed method is confirmed by simulations.

Class Association Rule Mining from Incomplete Database Using Genetic Network Programming

A method of class association rule mining from incomplete databases is proposed using Genetic Network Programming (GNP). GNP is one of the evolutionary optimization techniques, which uses the directed graph structure. An incomplete database includes missing data in some tuples, however, the proposed method can extract important rules using these tuples, and users can define the conditions of important rules flexibly. Generally, it is not easy for Aprior-like methods to extract important rules from incomplete database, so we have estimated the performances of the rule extraction and classification of the proposed method using incomplete data set. The results showed that the accuracy of classification of the proposed method is favorable even if some tuples include missing data.

Alternate Genetic Network Programming with Association Rules Acquisition Mechanisms Between Attribute Families

A method of association rule mining with chi-squared test using Alternate Genetic Network Programming (aGNP) is proposed. GNP is one of the evolutionary optimization techniques, which uses directed graph structures as genes. aGNP is an extended GNP in terms of including two kinds of node function sets. The proposed system can extract important association rules whose antecedent and consequent are composed of the attributes of each family defined by users. Rule extraction is done without identifying frequent itemsets used in Apriori-like methods. The method can be applied to rule extraction from dense database, and can extract dependent pairs of the sets of attributes in the database. Extracted rules are stored in a pool all together through generations and reflected in genetic operators as acquired information. In this paper, we describe the algorithm capable of finding the important association rules and present some experimental results.

From Machine and Tape to Structure and Function: Formulation of a Reflexively Computing System

The relationship between structure and function is explored via a system of labeled directed graph structures upon which a single elementary read/write rule is applied locally. Boundaries between static (information-carrying) and active (information-processing) objects, imposed by mandate of the rules or physics in earlier models, emerge instead as a result of a structure-function dynamic that is reflexive: objects may operate directly on their own structure. A representation of an arbitrary Turing machine is reproduced in terms of structural constraints by means of a simple mapping from tape squares and machine states to a uniform medium of nodes and links, establishing computation universality. Exploiting flexibility of the formulation, examples of other unconventional "self-computing" structures are demonstrated. A straightforward representation of a kinematic machine system based on the model devised by Laing is also reproduced in detail. Implications of the findings are discussed in terms of their relation to other formal models of computation and construction. It is argued that reflexivity of the structure-function relationship is a critical informational dynamic in biochemical systems, overlooked in previous models but well captured by the proposed formulation.

Elevator Group Supervisory Control System Using Genetic Network Programming with Functional Localization

Genetic Network Programming (GNP) having a directed graph structure has been proposed as a new method of evolutionary computation. Recently, GNP has been applied to elevator group supervisory control system (EGSCS), a real-world problem, to demonstrate its applicability and effectiveness. Its previous study considers the known and fixed traffic flow, however, it is changed dynamically with time in real elevator systems. Therefore, an EGSCS with dynamic adaptive control considering such changes should be studied for practical applications. In this paper, we have applied GNP with functional localization to an EGSCS to construct such an adaptive system. In our proposal, the switching GNP can switch the functionally localized GNPs (assigning GNPs) based on the special traffic. Simulation confirmed the adaptability and effectiveness of our proposal in daily office-building traffic.

A graph-based reflexive artificial chemistry

The conceptual divide between formal systems of computation and abstract models of chemistry is considered. As an attempt to concretely bridge this divide, a formalism is proposed that describes a constructive artificial chemistry on a space of directed graph structures. The idea for the formalism originates in computer science theory, with the traditional abstraction of a physical machine, the finite-state machine (FSM). In the FSM, the machine (state-transition graph) and input string (series of binary digits) are fundamentally distinct objects, separated by nature of the underlying formalism. This distinction is dissolved in the proposed system, resulting in a construction process that is r eflexive: graphs interact with their own topological structure to generate a product. It is argued that this property of reflexivity is a key element missing from earlier model chemistries. Examples demonstrate the continuous emergence complex self-similar topologies, novel reaction pathways, and seemingly open-ended diversity. Implications of these findings are discussed.

Medical Association Rule Mining Using Genetic Network Programming

An efficient algorithm for building a classifier is proposed based on an important association rule mining using Genetic Network Programming (GNP). The proposed method measures the significance of the association via the chi-squared test. Users can define the conditions of important association rules for building a classifier flexibly. The definition can include not only the minimum threshold chi-squared value, but also the number of attributes in the association rules. Therefore, all the extracted important rules can be used for classification directly. GNP is one of the evolutionary optimization techniques, which uses the directed graph structure as genes. Instead of generating a large number of candidate rules, our method can obtain a sufficient number of important association rules for classification. In addition, our method suits association rule mining from dense databases such as medical datasets, where many frequently occurring items are found in each tuple. In this paper, we describe an algorithm for classification using important association rules extracted by GNP with acquisition mechanisms and present some experimental results of medical datasets.

Genetic Network Programming with Automatically Generated Macro Nodes of Variable Size

Recently, Genetic Network Programming (GNP) has been proposed as one of the evolutionary algorithms. It represents its solutions as directed graph structures and the distinguished abilities have been shown. However, when we apply GNP to complex problems like the real world one, GNP must have robustness against the changes of environments and evolve quickly. Therefore, we introduced Automatically Generated Macro Nodes (AGMs) to GNP (GNP with AGMs). Actually GNP with AGMs has shown higher performances than the conventional GNP in terms of the fitness and the speed of evolution. In this paper, a new mechanism, AGMs with variable size, is introduced to GNP. Conventional AGMs have the fixed number of nodes and they evolve using only genetic operations, while a new method allows AGM to add nodes by necessity and delete nodes which do not contribute to the evolution of the AGM. The proposed GNP with AGMs of variable size is expected to evolve effectively and efficiently when it is applied to agent systems and also expected to make better behavior sequences of agents more easily than the conventional GNP algorithm. In the simulations, the proposed and conventional methods are applied to a tileworld problem and they are compared with each other. From the results, GNP with AGMs of variable size shows better fitness than GNP with AGMs of fixed size and the conventional GNP when adapting ten different environments.