Math word problem uses a real word story to present basic arithmetic operations using textual narration. It is used to develop student’s comprehension skill in conjunction with the ability to generate a solution that...Math word problem uses a real word story to present basic arithmetic operations using textual narration. It is used to develop student’s comprehension skill in conjunction with the ability to generate a solution that agrees with the story given in the problem. To master math word problem solving, students need to be given fresh and enormous amount of problems, which normal textbooks as well as teachers fail to provide most of the time. To fill the gap, a few research works have been proposed on techniques to automatically generate math word problems and equations mainly for English speaking community. Amharic is a Semitic language spoken by more than hundred million Ethiopians and is a language of instruction in elementary schools in Ethiopia. And yet it belongs to one of a less resourced language in the field of linguistics and natural language processing (NLP). Hence, in this paper, a strategy for automatic generation of Amharic Math Word (AMW) problem and equation is proposed, which is a first attempt to introduce the use template based shallow NLP approach to generate math word problem for Amharic language as a step towards enabling comprehension and learning problem solving in mathematics for primary school students. The proposed novel technique accepts a sample AMW problem as user input to form a template. A template provides AMW problem with placeholders, type of problem and equation template. It is used as a pattern to generate semantically equivalent AMW problems with their equations. To validate the reality of the proposed approach, a prototype was developed and used as a testing platform. Experimental results have shown 93.84% overall efficiency on the core task of forming templates from a given corpus containing AMW problems collected from elementary school mathematics textbooks and other school worksheets. Human judges have also found generated AMW problem and equation as solvable as the textbook problems.展开更多
Multi-commodity flow problems（MCFs） can be found in many areas, such as transportation, communication, and logistics. Therefore, such problems have been studied by a multitude of researchers, and a variety of method...Multi-commodity flow problems（MCFs） can be found in many areas, such as transportation, communication, and logistics. Therefore, such problems have been studied by a multitude of researchers, and a variety of methods have been proposed for solving it. However, most researchers only discuss the properties of different models and algorithms without taking into account the impacts of actual implementation. In fact, the true performance of a method may differ greatly across various implementations. In this paper, several popular optimization solvers for implementations of column generation and Lagrangian relaxation are discussed. In order to test scalability and optimality, three groups of networks with different structures are used as case studies. Results show that column generation outperforms Lagrangian relaxation in most instances, but the latter is better suited to networks with a large number of commodities.展开更多
文摘Math word problem uses a real word story to present basic arithmetic operations using textual narration. It is used to develop student’s comprehension skill in conjunction with the ability to generate a solution that agrees with the story given in the problem. To master math word problem solving, students need to be given fresh and enormous amount of problems, which normal textbooks as well as teachers fail to provide most of the time. To fill the gap, a few research works have been proposed on techniques to automatically generate math word problems and equations mainly for English speaking community. Amharic is a Semitic language spoken by more than hundred million Ethiopians and is a language of instruction in elementary schools in Ethiopia. And yet it belongs to one of a less resourced language in the field of linguistics and natural language processing (NLP). Hence, in this paper, a strategy for automatic generation of Amharic Math Word (AMW) problem and equation is proposed, which is a first attempt to introduce the use template based shallow NLP approach to generate math word problem for Amharic language as a step towards enabling comprehension and learning problem solving in mathematics for primary school students. The proposed novel technique accepts a sample AMW problem as user input to form a template. A template provides AMW problem with placeholders, type of problem and equation template. It is used as a pattern to generate semantically equivalent AMW problems with their equations. To validate the reality of the proposed approach, a prototype was developed and used as a testing platform. Experimental results have shown 93.84% overall efficiency on the core task of forming templates from a given corpus containing AMW problems collected from elementary school mathematics textbooks and other school worksheets. Human judges have also found generated AMW problem and equation as solvable as the textbook problems.
基金supported by research funds from the National Natural Science Foundation of China (Nos. 61521091, 61650110516, 61601013)
文摘Multi-commodity flow problems（MCFs） can be found in many areas, such as transportation, communication, and logistics. Therefore, such problems have been studied by a multitude of researchers, and a variety of methods have been proposed for solving it. However, most researchers only discuss the properties of different models and algorithms without taking into account the impacts of actual implementation. In fact, the true performance of a method may differ greatly across various implementations. In this paper, several popular optimization solvers for implementations of column generation and Lagrangian relaxation are discussed. In order to test scalability and optimality, three groups of networks with different structures are used as case studies. Results show that column generation outperforms Lagrangian relaxation in most instances, but the latter is better suited to networks with a large number of commodities.
