Performance evaluation of evolutionary multiobjective optimization algorithms for multiobjective fuzzy genetics-based machine learning

Ant Colony Optimization for the Control of Pollutant Spreading on Social Networks

The rapid development of online social networks not only enables prompt and convenient dissemination of desirable information but also incurs fast and wide propagation of undesirable information. A common way to control the spread of pollutants is to block some nodes, but such a strategy may affect the service quality of a social network and leads to a high control cost if too many nodes are blocked. This paper considers the node selection problem as a biobjective optimization problem to find a subset of nodes to be blocked so that the effect of the control is maximized while the cost of the control is minimized. To solve this problem, we design an ant colony optimization algorithm with an adaptive dimension size selection under the multiobjective evolutionary algorithm framework based on decomposition (MOEA/D-ADACO). The proposed algorithm divides the biobjective problem into a set of single-objective subproblems and each ant takes charge of optimizing one subproblem. Moreover, two types of pheromone and heuristic information are incorporated into MOEA/D-ADACO, that is, pheromone and heuristic information of dimension size selection and that of node selection. While constructing solutions, the ants first determine the dimension size according to the former type of pheromone and heuristic information. Then, the ants select a specific number of nodes to build solutions according to the latter type of pheromone and heuristic information. Experiments conducted on a set of real-world online social networks confirm that the proposed biobjective optimization model and the developed MOEA/D-ADACO are promising for the pollutant spreading control.

On q-Quasi-Newton’s Method for Unconstrained Multiobjective Optimization Problems

A parameter-free optimization technique is applied in Quasi-Newton’s method for solving unconstrained multiobjective optimization problems. The components of the Hessian matrix are constructed using q-derivative, which is positive definite at every iteration. The step-length is computed by an Armijo-like rule which is responsible to escape the point from local minimum to global minimum at every iteration due to q-derivative. Further, the rate of convergence is proved as a superlinear in a local neighborhood of a minimum point based on q-derivative. Finally, the numerical experiments show better performance.

A Genetic Algorithm Approach for Discovering Tuned Fuzzy Classification Rules with Intra- and Inter-Class Exceptions

Fuzzy rule-based systems (FRBSs) are proficient in dealing with cognitive uncertainties like vagueness and ambiguity imperative to real-world decision-making situations. Fuzzy classification rules (FCRs) based on fuzzy logic provide a framework for a flexible human-like reasoning involving linguistic variables. Appropriate membership functions (MFs) and suitable number of linguistic terms – according to actual distribution of data – are useful to strengthen the knowledge base (rule base [RB]+ data base [DB]) of FRBSs. An RB is expected to be accurate and interpretable, and a DB must contain appropriate fuzzy constructs (type of MFs, number of linguistic terms, and positioning of parameters of MFs) for the success of any FRBS. Moreover, it would be fascinating to know how a system behaves in some rare/exceptional circumstances and what action ought to be taken in situations where generalized rules cease to work. In this article, we propose a three-phased approach for discovery of FCRs augmented with intra- and inter-class exceptions. A pre-processing algorithm is suggested to tune DB in terms of the MFs and number of linguistic terms for each attribute of a data set in the first phase. The second phase discovers FCRs employing a genetic algorithm approach. Subsequently, intra- and inter-class exceptions are incorporated in the rules in the third phase. The proposed approach is illustrated on an example data set and further validated on six UCI machine learning repository data sets. The results show that the approach has been able to discover more accurate, interpretable, and interesting rules. The rules with intra-class exceptions tell us about the unique objects of a category, and rules with inter-class exceptions enable us to take a right decision in the exceptional circumstances.

INDUCING FUZZY REGRESSION TREE FORESTS USING ARTIFICIAL IMMUNE SYSTEMS

Fuzzy decision forests aim to improve the predictive power of single fuzzy decision trees by allowing multiple views of the same domain to be modelled. Such forests have been successfully created for classification problems where the outcome field is discrete; however predicting a continuous output value is more challenging in combining the output from multiple fuzzy decision trees. This paper presents a new approach to creating fuzzy regression tree forests based upon the induction of multiple fuzzy regression decision trees from one training sample, where each tree will represent a different view of the data domain. The singular fuzzy regression trees are induced using a proven algorithm known as Elgasir which fuzzifies crisp CHAID decision trees using trapezoidal membership functions for fuzzification and applies Takagi-Sugeno inference to obtain the final predicted values. A modified version of Artificial Immune System Network model (opt-aiNet) is then used for the simultaneous optimization of the membership functions across all trees within the forest. A strength of the proposed method is that data does not require fuzzification before forest induction this reducing pre-processing time and the need for subjective human experts. Five problem sets from the UCI repository and KEEL repository are used to evaluate the approach. The experimental results have shown that fuzzy regression tree forests reduce the error rate compared with single fuzzy regression trees.