Anirban Mukherjee

A review of methods for automatic understanding of natural language mathematical problems

This article addresses the problem of understanding mathematics described in natural language. Research in this area dates back to early 1960s. Several systems have so far been proposed to involve machines to solve mathematical problems of various domains like algebra, geometry, physics, mechanics, etc. This correspondence provides a state of the art technical review of these systems and approaches proposed by different research groups. A unified architecture that has been used in most of these approaches is identified and differences among the systems are highlighted. Significant achievements of each method are pointed out. Major strengths and weaknesses of the approaches are also discussed. Finally, present efforts and future trends in this research area are presented.

Study of Economic Load Dispatch by Various Hybrid Optimization Techniques

The economic load dispatch (ELD) is one of the most complex optimization problems of electrical power system. Classically, it is to identify the optimal combination of generation level of all power generating units in order to minimize the total fuel cost while satisfying the loads and losses in power transmission system. In view of the sharply increasing nature of cost of fossil fuel, energy management has gained lot of significance nowadays. Herein lies the relevance of continued research on improving the solution of ELD problem. A lot of research work have been carried out on this problem using several optimization techniques including classical, linear, quadratic, and nonlinear programming methods. The objective function of the ELD problem being of highly nonlinear and non-convex nature, the classical optimization methods cannot guarantee convergence to the global optimal solution. Some soft computing techniques like Artificial Bee Colony (ABC), Particle Swarm Optimization (PSO), Clonal Selection Algorithm (CSA), Ant Colony Optimization (ACO), Simulated Annealing (SA), Genetic Algorithm (GA), etc. are now being applied to find even better solution to the ELD problem. An interesting trend in this area is application of hybrid approaches like GA-PSO, ABC-PSO, CSA-SA, etc. and the results are found to be highly competitive. In this book chapter, we focus on the hybrid soft computing approaches in solving ELD problem and present a concise and updated technical review of systems and approaches proposed by different research groups. To depict the differences in technique of the hybrid approaches over the basic soft computing methods, the individual methods are introduced first. While the basic working principle and case studies of each hybrid approach are described briefly, the achievements of the approaches are discussed separately. Finally, the challenges in the present problem and some of the most promising approaches are highlighted and the possible future direction of research is hinted.

Hybrid PSO — ACO technique to solve economic load dispatch problem

Economic load dispatch (ELD) is an operational planning of a power generation system whereby the demand load is optimally distributed among the generation units such that the total generation cost is minimized. This paper presents a new hybrid technique, Particle Swarm Optimization (PSO) combined with Ant Colony Optimization (ACO), to solve the ELD problem. The results of simulated test run of the technique for optimum distribution of load in 6-generator systems while minimizing transmission loss have been reported in this paper. The results obtained using PSO-ACO are found to be encouraging when compared with that produced by other hybrid methods under similar test condition.

Hybrid PSO-ACO algorithm to solve economic load dispatch problem with transmission loss for small scale power system

This paper presents a novel solution of convex and non-convex economic load dispatch (ELD) problem of small scale thermal power system using a hybrid soft computing approach. The solution method involves a combination of Particle Swarm Optimization (PSO) and Ant Colony Optimization (ACO) algorithms where the latter is used to tune the solution obtained by the former towards finding global optima. The proposed approach is found useful in finding economic dispatch in a 3-generator 5-bus system by considering generator capacity constraints, transmission loss, ramp rate limits, prohibited operating zones and valve point loading. Six test cases have been studied in a simulated environment. The paper shows that by applying the PSO-ACO hybrid algorithm 300MW power demand can be successfully met at minimum generation cost incurring minimum transmission loss.

TEXT-TO-DIAGRAM CONVERSION: A METHOD FOR FORMAL REPRESENTATION OF NATURAL LANGUAGE GEOMETRY PROBLEMS

Natural language geometry problems are translated into formal representation. This is done as an essential step involved in text to diagram conversion. A parser is designed that analyzes a problem statement in order to describe it as a language independent, unambiguous formal representation. Natural language processing tools and a lexical knowledge base are used to assist the parser that finally generates a graph as the parsing output. The parse graph is the formal representation of the input natural language problem. This graph is later translated into another intermediate representation consisting of a set of graphics-friendly statements. High school level geometry problems are used to develop and test the proposed methods. Experimental results show high accuracy of the approach in translating a natural language problem into a formal description.

Hybrid PSO-ACO technique to solve multi-constraint economic load dispatch problems for 6-generator system

Abstract This paper presents a new hybrid soft computing approach in solving typical economic load dispatch (ELD) problem by combining two widely used meta-heuristic techniques, namely particle swarm optimization (PSO) and ant colony optimization (ACO). Though PSO has been popularly used in ELD problems for its flexibility, robustness, and fast convergence, it often produces not so good solution due to premature convergence to local optima. ACO, on the other hand, popular for its good global exploration feature, strikes a fine balance between local and global search for optimum solution when combined with PSO. This aspect has been exploited for the first time by applying a customized combination of PSO and ACO in finding solution for both convex and non-convex ELD problems with smooth and non-smooth cost functions (i.e. with and without valve-point loading) and multiple constraints like generator capacity, transmission loss, ramp rate limits, and prohibited operating zones. This paper showcases the results of different test cases for the proposed approach implemented in a simulated 6-generator thermal power system; the results validate the effectiveness and superiority of PSO–ACO when compared with few other hybrid approaches and pure PSO and ACO approaches under similar test conditions. Considering the quality of solution including convergence characteristics, power loss, and total generation cost, PSO–ACO emerges as a viable alternative for solving ELD problems in a real power generation scenario.

Intelligent Tutoring of School Level Geometry Using Automatic Text to Diagram Conversion Utility

This paper reports a novel text-to-diagram conversion mechanism that simulates human approach of solving a geometry problem stated in English. Thereby it establishes an implement-able framework towards developing intelligent CBT tool for school-level geometry problems. Realization of the framework involves building of a geometry knowledge base and application of many aspects of natural language understanding.

Towards Reliable Clustering of English Text Documents Using Correlation Coefficient

This paper proposes a new approach for clustering English text documents, based on finding the pair wise correlation of documents in a given set of text documents. The correlation coefficient for each pair of documents is calculated on the basis of ranks given to the words in the documents. The ranking of the words occurring in a document is computed on the basis of weights of the words calculated according to the conventional TF-IDF factor. The proposed method is found to be able to cluster a given set of text documents into a number of classes depending on their contents where the number of classes is not known a priori. It is revealed from experimental results that the proposed method of text categorization using correlation coefficient performs better than some of the other text categorization methods, including methods that use artificial neural network.

Automatic Diagram Drawing Based on Natural Language Text Understanding

This article presents a general framework for automatic conversion of a piece of text into a diagram that is described in the given text. Such kind of text is often found in many branches of Science & Engineering. Secondary school-level geometric problems are considered as a reference in this study. A knowledge base or lexical resource named GeometryNet is used in interpreting geometric meaning of a given text to draw the corresponding diagram.

Intelligent Tutoring by Diagram Recognition

It is a proven psychological fact that every student has his own different way of learning. Therefore, effective teaching should be student specific, not a general one. Our aim is to design a computer-based, adaptive learning system that assesses a child’s understanding of a given problem and guides most effectively to correctly understand the problem and the related concept in turn. As a case study, problems of elementary geometry of primary school level are considered. The system would allow a student to follow a learning path that is based on his ability of understanding and the pace he is comfortable with. It would help improve the confidence and skill of the child in geometry by presenting geometrical figures of increasing difficulty level.