Clio-Combinatorics

2016 ◽  
pp. 79-101 ◽  
Author(s):  
Jesus Gonzalez-Feliu ◽  
Antoine Parent
Keyword(s):  
Combinatorial Optimization ◽  
Problem Solving ◽  
Operations Research ◽  
Quantitative Data ◽  
Regional Distribution ◽  
Classical Problem ◽  
Search Method ◽  
Military Conflicts ◽  
Computation Analysis ◽  
Strategic Logic

This chapter proposes to apply combinatorial optimization to past military conflicts with the aim of producing quantitative data that help explaining history. To do this, we can go beyond the classical “problem solving” vision of operations research that focuses on algorithmic development and computation analysis to privilege solution analysis and the needs of matching the obtained solution to the reality we aim to represent, study and analyze. In particular, we propose an iterative logic search method that aims to identify and analyze military strategic logic in terms of logistics. Then, to illustrate it, an application to the French troop assignment plan (Plan XVII of Joffre, 1932) is made to analyze which could be the subjacent logic behind the defense plan of French troops and state on the consequences of the optimization choices in terms of regional distribution of troops. A discussion of the proposed framework and the directions to generalize it will be presented as a conclusion.

Boosting branch-and-bound MaxSAT solvers with clause learning

2021 ◽  
pp. 1-21
Author(s):  
Chu-Min Li ◽  
Zhenxing Xu ◽  
Jordi Coll ◽  
Felip Manyà ◽  
Djamal Habet ◽  
...  
Keyword(s):  
Experimental Investigation ◽  
Combinatorial Optimization ◽  
Problem Solving ◽  
Branch And Bound ◽  
Real World ◽  
Optimization Problems ◽  
Satisfiability Problem ◽  
Maximum Satisfiability ◽  
Combinatorial Optimization Problems ◽  
Clause Learning

The Maximum Satisfiability Problem, or MaxSAT, offers a suitable problem solving formalism for combinatorial optimization problems. Nevertheless, MaxSAT solvers implementing the Branch-and-Bound (BnB) scheme have not succeeded in solving challenging real-world optimization problems. It is widely believed that BnB MaxSAT solvers are only superior on random and some specific crafted instances. At the same time, SAT-based MaxSAT solvers perform particularly well on real-world instances. To overcome this shortcoming of BnB MaxSAT solvers, this paper proposes a new BnB MaxSAT solver called MaxCDCL. The main feature of MaxCDCL is the combination of clause learning of soft conflicts and an efficient bounding procedure. Moreover, the paper reports on an experimental investigation showing that MaxCDCL is competitive when compared with the best performing solvers of the 2020 MaxSAT Evaluation. MaxCDCL performs very well on real-world instances, and solves a number of instances that other solvers cannot solve. Furthermore, MaxCDCL, when combined with the best performing MaxSAT solvers, solves the highest number of instances of a collection from all the MaxSAT evaluations held so far.

scholarly journals ANALISIS KEMAMPUAN REPRESENTASI MATEMATIS SISWA DALAM MENYELESAIKAN SOAL PEMECAHAN MASALAH MATEMATIKA

Ta dib ◽  
2019 ◽  
Vol 22 (1) ◽  
pp. 19
Author(s):  
Ummul Huda ◽  
Edwin Musdi ◽  
Nola Nari
Keyword(s):  
Problem Solving ◽  
Quantitative Data ◽  
Qualitative Data ◽  
Mathematical Problem ◽  
Field Research ◽  
Mathematical Representation ◽  
Mathematical Problem Solving ◽  
Test Results ◽  
Interview Guide ◽  
Descriptive Method

This research is motivated by the low mathematical representation ability of students in solving mathematical problem solving questions based on TIMSS data and facts in the field. The study aims to analyze the mathematical representation ability of MTsN Batusangkar students visually, verbally and symbolically in solving mathematical problem solving problems. This field research uses descriptive method. The instrument used is a description question and interview guide. Quantitative data based on test results were analyzed to determine the predicate of mathematical representation ability, while Miles and Huberman model wwas used to analyze qualitative data from interviews. The results show that students' mathematical visual and symbolic abilities are satisfactory, while verbal mathematical representations are less satisfactory.

scholarly journals ENHANCING CREATIVITY AND PROBLEM SOLVING SKILLS THROUGH CREATIVE PROBLEM SOLVING IN TEACHING MATHEMATICS

2020 ◽  
Vol 13 (2) ◽  
pp. 270-291 ◽  
Author(s):  
Madihah Khalid ◽  
Supiah Saad ◽  
Siti Rafiah Abdul Hamid ◽  
Muhammad Ridhuan Abdullah ◽  
Hasniza Ibrahim ◽  
...  
Keyword(s):  
Problem Solving ◽  
Quantitative Data ◽  
Creative Thinking ◽  
Creative Problem Solving ◽  
Problem Solving Skills ◽  
Science Technology ◽  
Comparison Groups ◽  
Quasi Experimental ◽  
Creative Problem ◽  
And Mathematics

In recent years, calls to nurture and teach creativity from an early age in schools has intensified. Creativity is something regular in the teaching of arts subjects but is not a common feature in teaching science, technology, engineering and mathematics subjects. However, what really matters, is how the subject is being taught. This research aimed to foster creativity through the teaching of mathematics via problem solving that challenges the solving of problems in a creative manner, which is defined as creative problem solving. This quasi-experimental study investigates changes in students learning of mathematics via creative problem solving. Altogether, 172 Form 1 students forming treatment and comparison groups from four schools in Gombak District area, Malaysia were involved. A mixed qualitative and quantitative data were collected to investigate the effect of the 3 cycles of creative problem solving lessons implemented. Instruments used were Torrance Test of Creative Thinking, a mathematics problem solving test and creativity checklist. This paper will only present the quantitative data obtained. Results show statistically significant increases in scores for most categories of creativity and problem solving tests. This research brought together teachers and researchers in trialling creative problem solving to teach mathematics, to achieve the enhancement of students’ creative thinking and problem solving skills. This coincided with the introduction of Kurikulum Standard Sekolah Menengah with new emphasis to strengthen the quality of science, technology, engineering and mathematics education in general, where higher-order thinking reforms are emphasized.

DESIGN OF COMPETITION-BASED NEURAL NETWORKS FOR COMBINATORIAL OPTIMIZATION

1990 ◽  
Vol 01 (03) ◽  
pp. 221-235 ◽  
Author(s):  
Luyuan Fang ◽  
Tao Li
Keyword(s):  
Neural Networks ◽  
Combinatorial Optimization ◽  
Problem Solving ◽  
Network Design ◽  
Optimization Problem ◽  
Systematic Approach ◽  
Performance Study ◽  
The Neural Networks ◽  
Optimization Problem Solving ◽  
Simple Heuristics

A systematic approach to the design of neural networks for combinatorial optimization is presented in this paper. This approach adopts a methodology which is based on competition. The neural networks for optimization problem solving are connected using the competitive geometry. Our approach relies on the use of simple heuristics in network design. It is therefore easy to learn. The performance of such networks is also impressive. Two examples are also included in this paper to demonstrate our approach and to present results of performance study.

scholarly journals Using Excel to reduce a Square Matrix

2012 ◽  
Vol 60 (4) ◽  
pp. 109-114
Author(s):  
Josef Holoubek ◽  
Petr Zach
Keyword(s):  
Problem Solving ◽  
Operations Research ◽  
Input Data ◽  
Travelling Salesman Problem ◽  
Menu Option ◽  
The Matrix ◽  
Commercial Program ◽  
Research Problems ◽  
The Way ◽  
Square Matrix

When solving operations research problems, one can use either specialised computer programs such as Lingo, Lindo, Storm or more universal programs such Excel, Matlab, and R. To obtain the input data, one can use either a program’s own editor or other programs commonly available such as Excel. While the problem-solving methods, being part of various programs, are the subjects of numerous publications (such as Gros, 2003; Jablonský, 2002; Plevný – Žižka, 2007; Stevenson – Ozgur, 2009), the way the input data are obtained, recorded, and processed receives far less attention although this part of problem-solving requires considerable effort and, if the method for data recording is inadequate, may cause subsequent difficulties in their further processing. A problem known as “the travelling salesman problem” (TSP) may serve as an example. Here, the input data form a “square matrix of distances”. This paper is concerned with some Excel tools that can be used to obtain and subsequently modify such a square matrix. Given a square m × m matrix, an ordinary user might want to reduce it to an i × i square matrix (where i < m) without having to copy data from the matrix, skip some of its rows and/or columns or write a program to implement such a reduction.In her degree project, Kourková, 2009 was looking for an efficient method of reducing an Excel matrix. She had found no relevant papers on this subject concluding that the authors of the commercial program had not considered this. Therefore, she offered her own solution unconventionally using the contingency table menu option. Although this had resulted in the desired submatrix, some of its parts were superfluous and even baffling for the user.For this reason, the authors analyse the method of representing an m × m matrix and the way of its reduction. Finally, a better option is offered to achieve the desired objective as well as other methods of obtaining the required submatrix that even users without sufficient programming skills can use.

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