Search results for: geometric problem

Authors: Aleksandr S. Ermolenko

Abstract:

Allometry is an important factor of morphological integration, contributing to the organization of the phenotype and its variability. The allometric change in the shape of the hand is particularly important in primate evolution, as the hand has important taxonomic features. Some of these features are known to parts with the shape, especially the ratio of the lengths of the index and ring fingers (2d: 4d ratio). The hand is a fairly well-studied system in the context of the evolutionary development of complex morphological structures since it consists of various departments (basipodium, metapodium, acropodium) that form a single structure –autopodium. In the present study, we examined the allometric variability of acropodium. We tested the null hypothesis that there would be no difference in allometric variation between the two components. Geometric morphometry based on a procrustation of 16 two-dimensional (2D) landmarks was analyzed using multivariate shape-by-size regressions in samples from 100 people (50 men and 50 women). The results obtained show that men have significantly greater allometric variability for the ring finger (variability in the transverse axis prevails), while women have significantly greater allometric variability for the index finger (variability in the longitudinal axis prevails). The influence of the middle finger on the shape of the hand is typical for both men and women. The influence of the little finger on the shape of the hand, regardless of gender, was not revealed. The results of this study support the hypothesis that allometry contributes to the organization of variation in the human hand.

Keywords: human hand, size and shape, 2d:4d ratio, geometric morphometry

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Authors: Miguel Mariano Rivera Galvan

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The purpose of this research was to create a digital tool by which users can obtain an immediate and accurate solution of the angular characteristics of an irregular quadrilateral. The development of this project arose because of the frequent absence of a polygon’s geometric information in land ownership accreditation documents. The researcher created a mathematical model using a linear approximation iterative method, employing various disciplines and techniques including trigonometry, geometry, algebra, and topography. This mathematical model uses as input data the surface of the quadrilateral, as well as the length of its sides, to obtain its interior angles and make possible its representation in a coordinate system. The results are as accurate and reliable as the user requires, offering the possibility of using this tool as a support to develop future engineering and architecture projects quickly and reliably.

Keywords: digital tool, geometry, mathematical model, quadrilateral, solution

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Authors: Mohammad Farid

Abstract:

In this paper, we introduce and study an explicit iterative method based on hybrid extragradient method to approximate a common solution of generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup in Hilbert space. Further, we prove that the sequence generated by the proposed iterative scheme converge strongly to the common solution of generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup. This common solution is the unique solution of a variational inequality problem and is the optimality condition for a minimization problem. The results presented in this paper are the supplement, extension and generalization of the previously known results in this area.

Keywords: generalized mixed equilibrium problem, fixed-point problem, nonexpansive semigroup, variational inequality problem, iterative algorithms, hybrid extragradient method

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Authors: Deyadeen Ali Alshibani

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In the literature, the multi-armed bandit problem as a statistical decision model of an agent trying to optimize his decisions while improving his information at the same time. There are several different algorithms models and their applications on this problem. In this paper, we evaluate the Regret-regression through comparing with Q-learning method. A simulation on determination of optimal treatment regime is presented in detail.

Keywords: optimal, bandit problem, optimization, dynamic programming

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Authors: Yong-Su Jo, Seung-Min Yang, Seok Hong Min, Tae Kwon Ha

Abstract:

The synthesis of nickel nanoparticles by the reduction of nickel chloride with hydrazine in an aqueous solution. The effect of hydrazine concentration on batch-processed particle characteristics was investigated using Field Emission Scanning Electron Microscopy (FESEM). Both average particle size and geometric standard deviation (GSD) were decreasing with increasing hydrazine concentration. The continuous synthesis of nickel nanoparticles by microemulsion method was also studied using FESEM and X-ray Diffraction (XRD). The average size and geometric standard deviation of continuous-processed particles were 87.4 nm and 1.16, respectively. X-ray diffraction revealed continuous-processed particles were pure nickel crystalline with a face-centered cubic (fcc) structure.

Keywords: nanoparticle, hydrazine reduction, continuous process, microemulsion method

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Authors: P. Caimmi, E. Bele, A. Abolfathi

Abstract:

Lattice materials are cellular structures composed of a periodic network of beams. They offer high weight-specific mechanical properties and lend themselves to numerous weight-sensitive applications. The periodic internal structure responds to external vibrations through characteristic frequency bandgaps, making these materials suitable for the reduction of noise and vibration. However, the deviation from architectural homogeneity, due to, e.g., manufacturing imperfections, has a strong influence on the mechanical properties and vibration response of these materials. In this work, we present results on the influence of geometric imperfections on the vibration response of hexagonal lattices. Three classes of geometrical variables are used: the characteristics of the architecture (relative density, ligament length/cell size ratio), imperfection type (degree of non-periodicity, cracks, hard inclusions) and defect morphology (size, distribution). Test specimens with controlled size and distribution of imperfections are manufactured through selective laser sintering. The Frequency Response Functions (FRFs) in the form of accelerance are measured, and the modal shapes are captured through a high-speed camera. The finite element method is used to provide insights on the extension of these results to semi-infinite lattices. An updating procedure is conducted to increase the reliability of numerical simulation results compared to experimental measurements. This is achieved by updating the boundary conditions and material stiffness. Variations in FRFs of periodic structures due to changes in the relative density of the constituent unit cell are analysed. The effects of geometric imperfections on the dynamic response of periodic structures are investigated. The findings can be used to open up the opportunity for tailoring these lattice materials to achieve optimal amplitude attenuations at specific frequency ranges.

Keywords: lattice architectures, geometric imperfections, vibration attenuation, experimental modal analysis

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Authors: Sujeet Kumar Singh, Shiv Prasad Yadav

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This paper develops an approach for solving intuitionistic fuzzy linear fractional programming (IFLFP) problem where the cost of the objective function, the resources, and the technological coefficients are triangular intuitionistic fuzzy numbers. Here, the IFLFP problem is transformed into an equivalent crisp multi-objective linear fractional programming (MOLFP) problem. By using fuzzy mathematical programming approach the transformed MOLFP problem is reduced into a single objective linear programming (LP) problem. The proposed procedure is illustrated through a numerical example.

Keywords: triangular intuitionistic fuzzy number, linear programming problem, multi objective linear programming problem, fuzzy mathematical programming, membership function

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Authors: A. R. Momeninezhad

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Erosion of Slurry Pumps in Related Industries, is one of the major costs in their production process. Many factories in extractive industries try to find ways to diminish this cost. In this paper, we consider the flow pattern modifications by geometric variations made of numerical simulation of flow inside pump casing, which is one of the most important parts analyzed for erosion. The mentioned pump is a cyclone centrifugal slurry pump, which is operating in Sarcheshmeh Copper Industries in Kerman-Iran, named and tagged as HM600 cyclone pump. Simulation shows many improvements in local wear information and situations for better and more qualified design of casing shape and impeller position, before and after geometric corrections. By theory of liquid-solid two-phase flow, the local wear defeats are analyzed and omitted.

Keywords: flow pattern, slurry pump, simulation, wear

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Authors: F. Viprey, H. Nouira, S. Lavernhe, C. Tournier

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Manufacturing of freeform parts may be achieved on 5-axis machine tools currently considered as a common means of production. In particular, the geometrical quality of the freeform parts depends on the accuracy of the multi-axis structural loop, which is composed of several component assemblies maintaining the relative positioning between the tool and the workpiece. Therefore, to reach high quality of the geometries of the freeform parts the geometric errors of the 5 axis machine should be evaluated and compensated, which leads one to master the deviations between the tool and the workpiece (volumetric accuracy). In this study, a novel hole-bar design was developed and used for the characterization of the geometric errors of a RRTTT 5-axis machine tool. The hole-bar standard design is made of Invar material, selected since it is less sensitive to thermal drift. The proposed design allows once to extract 3 intrinsic parameters: one linear positioning and two straightnesses. These parameters can be obtained by measuring the cylindricity of 12 holes (bores) and 11 cylinders located on a perpendicular plane. By mathematical analysis, twelve 3D points coordinates can be identified and correspond to the intersection of each hole axis with the least square plane passing through two perpendicular neighbour cylinders axes. The hole-bar was calibrated using a precision CMM at LNE traceable the SI meter definition. The reversal technique was applied in order to separate the error forms of the hole bar from the motion errors of the mechanical guiding systems. An inter-comparison was additionally conducted between four NMIs (National Metrology Institutes) within the EMRP IND62: JRP-TIM project. Afterwards, the hole-bar was integrated in RRTTT 5-axis machine tool to identify its volumetric errors. Measurements were carried out in real time and combine raw data acquired by the Renishaw RMP600 touch probe and the linear and rotary encoders. The geometric errors of the 5 axis machine were also evaluated by an accurate laser tracer interferometer system. The results were compared to those obtained with the hole bar.

Keywords: volumetric errors, CMM, 3D hole-bar, inter-comparison

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Authors: Mohammadsadegh Zanganehfar

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Since the introduction of fractal geometry in 1970, numerous efforts have been made by architects and researchers to transfer this area of mathematical knowledge in the discipline of architecture and postmodernist discourse. The discourse of complexity and architecture is one of the most significant ongoing discourses in the discipline of architecture from the '70s until today and has generated significant styles such as deconstructivism and parametrism in architecture. During these years, several projects were designed and presented by designers and architects using fractal geometry, but due to the lack of sufficient knowledge and appropriate comprehension of the features and characteristics of this nonlinear geometry, none of the fractal-based designs have been successful and satisfying. Fractal geometry as a geometric technology has a long presence in the history of architecture. The current research attempts to identify and discover the characteristics, features, potentials, and functionality of fractals despite their aesthetic aspect by examining case studies of pre-modern architecture in Asia and investigating the function of fractals.

Keywords: Asian architecture, fractal geometry, fractal technique, geometric properties

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Authors: Rafael Muñoz, Juan Melchor, Alicia Valera, Laura Peralta, Guillermo Rus

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A torsional piezoelectric ultrasonic transducer design is proposed to measure shear moduli in soft tissue with direct access availability, using shear wave elastography technique. The measurement of shear moduli of tissues is a challenging problem, mainly derived from a) the difficulty of isolating a pure shear wave, given the interference of multiple waves of different types (P, S, even guided) emitted by the transducers and reflected in geometric boundaries, and b) the highly attenuating nature of soft tissular materials. An immediate application, overcoming these drawbacks, is the measurement of changes in cervix stiffness to estimate the gestational age at delivery. The design has been optimized using a finite element model (FEM) and a semi-analytical estimator of the probability of detection (POD) to determine a suitable geometry, materials and generated waves. The technique is based on the time of flight measurement between emitter and receiver, to infer shear wave velocity. Current research is centered in prototype testing and validation. The geometric optimization of the transducer was able to annihilate the compressional wave emission, generating a quite pure shear torsional wave. Currently, mechanical and electromagnetic coupling between emitter and receiver signals are being the research focus. Conclusions: the design overcomes the main described problems. The almost pure shear torsional wave along with the short time of flight avoids the possibility of multiple wave interference. This short propagation distance reduce the effect of attenuation, and allow the emission of very low energies assuring a good biological security for human use.

Keywords: cervix ripening, preterm birth, shear modulus, shear wave elastography, soft tissue, torsional wave

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Authors: Abhishek Srivastava, Jeevesh Nandan, Manish Kumar

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The study was taken to analyse the alternative source of traffic system for effective and more convenient traffic flow by reducing points of conflicts as well as angle of conflict and keeping in view to minimize the problem of unnecessarily long waiting time, delays, congestion, traffic jam and geometric delays due to intersection between circular and straight lanes. It is a twin kidney-spine type structure system with special allowance for Highway users for quicker passes. Thus reduction in number and intensity of accidents, significance reduction in traffic jam, conservation of valuable time.

Keywords: traffic system, collision reduction of vehicles, smooth flow of vehicles, traffic jam

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Authors: Fouad Inel, Lakhdar Khochemane

Abstract:

This article presents a comparative response specification performance between two controllers of three and four cable based robots for various applications. The main objective of this work is: the first is to use the direct and inverse geometric model to study and simulate the end effector position of the robot with three and four cables. A graphical user interface has been implemented in order to visualizing the position of the robot. Secondly, we present the determination of static and dynamic tensions and lengths of cables required to flow different trajectories. At the end, we study the response of our systems in closed loop with a Proportional-IntegratedDerivative (PID) and Proportional-Integrated (PD) controllers then this last are compared the results of the same examples using MATLAB/Simulink; we found that the PID method gives the better performance, such as rapidly speed response, settling time, compared to PD controller.

Keywords: dynamic modeling, geometric modeling, graphical user interface, open loop, parallel cable-based robots, PID/PD controllers

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Authors: Noppadon Phumeechanya, Panita Wannapiroon

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The purpose of this research is to design the ubiquitous scaffold learning environment using problem-based learning activities that enhance problem-solving skills and context awareness, and to evaluate the suitability of the ubiquitous scaffold learning environment using problem-based learning activities. We divide the research procedures into two phases. The first phase is to design the ubiquitous scaffold learning environment using problem-based learning activities, and the second is to evaluate the ubiquitous scaffold learning environment using problem-based learning activities. The sample group in this study consists of five experts selected using the purposive sampling method. We analyse data by arithmetic mean and standard deviation. The research findings are as follows; the ubiquitous scaffold learning environment using problem-based learning activities consists of three major steps, the first is preparation before learning. This prepares learners to acknowledge details and learn through u-LMS. The second is the learning process, where learning activities happen in the ubiquitous learning environment and learners learn online with scaffold systems for each step of problem solving. The third step is measurement and evaluation. The experts agree that the ubiquitous scaffold learning environment using problem-based learning activities is highly appropriate.

Keywords: ubiquitous learning environment scaffolding, learning activities, problem-based learning, problem-solving skills, context awareness

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Authors: Tuğba Horzum, Ahmet Arikan

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This paper was part of a broader study that investigated what blind students (BSs) understood and how they used concept definitions (CDs) and concept images (CIs) for some mathematical concepts. This paper focused on the polygon concept. For this purpose, four open-ended questions were asked to five blind middle school students. During the interviews, BSs were presented with raised-line materials and were given opportunities to construct geometric shapes with magnetic sticks and micro-balls. Qualitative research techniques applied in grounded theory were used for analyzing documents pictures which were taken from magnetic geometric shapes that BSs constructed, raised-line materials and researcher’s observation notes and interviews. At the end of the analysis, it was observed that BSs used mostly their CIs and never took into account the CDs. Besides, BSs encountered with the difficulties associated with the combination of polygon edges’ endpoints consecutively. Additionally, they focused on the interior of the polygon and the angles which have smaller a size. Lastly, BSs were often conflicted about triangle, rectangle, square and circle whether or not a polygon.

Keywords: blind students, concept definition, concept image, polygon

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Authors: Kamariah Abu Bakar, Jennifer Way

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This study investigated how young children (six years old) constructed and used representations in mathematics classroom; particularly in problem solving. The purpose of this study is to explore the ways children used representations in solving addition problems and to determine whether their representations can play a supportive role in understanding the problem situation and solving them correctly. Data collection includes observations, children’s artifact, photographs and conversation with children during task completion. The results revealed that children were able to construct and use various representations in solving problems. However, they have certain preferences in generating representations to support their problem solving.

Keywords: young children, representations, addition, problem solving

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Authors: Liudmyla Koliechkina, Olena Dvirna

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The statement of the multi-objective optimization problem on combinatorial configurations is formulated, and the approach to its solution is proposed. The problem is of interest as a combinatorial optimization one with many criteria, which is a model of many applied tasks. The approach to solving the multi-objective optimization problem on combinatorial configurations consists of two stages; the first is the reduction of the multi-objective problem to the single criterion based on existing multi-objective optimization methods, the second stage solves the directly replaced single criterion combinatorial optimization problem by the horizontal combinatorial method. This approach provides the optimal solution to the multi-objective optimization problem on combinatorial configurations, taking into account additional restrictions for a finite number of steps.

Keywords: discrete set, linear combinatorial optimization, multi-objective optimization, Pareto solutions, partial permutation set, structural graph

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Authors: M. G. M. Khan, V. D. Prasad, D. K. Rao

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In this manuscript, we discuss the problem of determining the optimum stratification of a study (or main) variable based on the auxiliary variable that follows a uniform distribution. If the stratification of survey variable is made using the auxiliary variable it may lead to substantial gains in precision of the estimates. This problem is formulated as a Nonlinear Programming Problem (NLPP), which turn out to multistage decision problem and is solved using dynamic programming technique.

Keywords: auxiliary variable, dynamic programming technique, nonlinear programming problem, optimum stratification, uniform distribution

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Authors: Zahra Ahmed Al-zadjali

Abstract:

The influence of Islam on arts can be found primarily in calligraphy, arabesque designs and architecture. Also, geometric designs were used quite extensively. Muslim craftsmen produced stunning designs based on simple geometric principles and traditional motifs which were used to decorate many surfaces. The idea of interlacing simple rectilinear lines to form the patterns impressed Arabs. Nomads of Persia, Turks and Mongols were equally impressed with the designs so they begin to use them in their homes in carpet weaving. Islamic designs, motifs and colours which were used became common place and served to influence people’s tastes. Modern life style and contemporary products have changed the style of people’s daily lives, however, people still long for the nomadic way of life. This is clearly reflected in people’s homes. In a great many Muslim homes, Islamic decorative motifs can be seen along with traditional ‘Bedouin’ style furnishing, especially in homes of the Arabian Peninsula.

Keywords: art, craft, design, Oman, weaving

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Authors: Fouad. Inel, Lakhdar. Khochemane

Abstract:

This article presents a comparative response specification performance between two controllers of three and four cable based robots for various applications. The main objective of this work is: The first is to use the direct and inverse geometric model to study and simulate the end effector position of the robot with three and four cables. A graphical user interface has been implemented in order to visualizing the position of the robot. Secondly, we present the determination of static and dynamic tensions and lengths of cables required to flow different trajectories. At the end, we study the response of our systems in closed loop with a Proportional-Integrated Derivative (PID) and Proportional-Integrated (PD) controllers then this last are compared the results of the same examples using MATLAB/Simulink; we found that the PID method gives the better performance, such as rapidly speed response, settling time, compared to PD controller.

Keywords: parallel cable-based robots, geometric modeling, dynamic modeling, graphical user interface, open loop, PID/PD controllers

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Authors: Guilherme Baldo Carlos

Abstract:

The flexible job-shop scheduling problem (FJSP) is an NP-hard combinatorial optimization problem, which can be applied to model several applications in a wide array of industries. This problem will have its importance increase due to the shift in the production mode that modern society is going through. The demands are increasing and for products personalized and customized. This work aims to apply a meta-heuristic called a genetic algorithm (GA) to solve this problem. A GA is a meta-heuristic inspired by the natural selection of Charles Darwin; it produces a population of individuals (solutions) and selects, mutates, and mates the individuals through generations in order to find a good solution for the problem. The results found indicate that the GA is suitable for FJSP solving.

Keywords: genetic algorithm, evolutionary algorithm, scheduling, flexible job-shop scheduling

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Authors: Shamraiz Ahmad, Riaz Ahmad, Adnan Maqsood

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This paper describes the application of 2k-design of experiment in order to screen the geometric parameters and experimental refinement of ceiling fan blades. The ratio of the air delivery to the power consumed is commonly known as service value (SV) in ceiling fan designer’s community. Service value was considered as the response for 56 inch ceiling fan and four geometric parameters (bend position at root, bend position at tip, bent angle at root and bent angle at tip) of blade were analyzed. With two levels, the 4-design parameters along with their eleven interactions were studied and design of experiment was employed for experimental arrangement. Blade manufacturing and testing were done in a medium scale enterprise. The objective was achieved and service value of ceiling fan was increased by 10.4 % without increasing the cost of production and manufacturing system. Experiments were designed and results were analyzed using Minitab® 16 software package.

Keywords: parametric screening, 2k-design of experiment, ceiling fan, service value, performance improvement

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Authors: Laissa Mae Francisco, John Rolex Ingreso, Anna Krizel Menguito, Criselda Robrigado, Rej Maegan Tuazon

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This study aims to determine and describe the existing relationship between number sense proficiency and problem-solving performance of grade seven students from Victorino Mapa High School, Manila. A paper pencil exam containing of 50-item number sense test and 5-item problem-solving test which measures their number sense proficiency and problem-solving performance adapted from McIntosh, Reys, and Bana were used as the research instruments. The data obtained from this study were interpreted and analyzed using the Pearson – Product Moment Coefficient of Correlation to determine the relationship between the two variables. It was found out that students who were low in number sense proficiency tend to be the students with poor problem-solving performance and students with medium number sense proficiency are most likely to have an average problem-solving performance. Likewise, students with high number sense proficiency are those who do excellently in problem-solving performance.

Keywords: number sense, performance, problem solving, proficiency

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Authors: Alexis Aldo Mendoza Villarroel, Ademir Clemente Villena Zevallos, Cristian Jose Lopez Del Alamo

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With the advancement of technology it is now possible to scan entire objects and obtain their digital representation by using point clouds or polygon meshes. However, some objects may be broken or have missing parts; thus, several methods focused on this problem have been proposed based on Geometric Deep Learning, such as GCNN, ACNN, PointNet, among others. In this article an approach from a different paradigm is proposed, using metric data structures to index global descriptors in the spectral domain and allow the recovery of a set of similar models in polynomial time; to later use the Iterative Close Point algorithm and recover the parts of the incomplete model using the geometry and topology of the model with less Hausdorff distance.

Keywords: 3D reconstruction method, point cloud completion, shape completion, similarity search

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Authors: Pei Chin Lim

Abstract:

School of Mathematics and Science of Singapore Polytechnic offers a Basic Mathematics module to students who did not pass GCE O-Level Additional Mathematics. These students are weaker in Mathematics. In particular, they struggle with word problems and tend to leave them blank in tests and examinations. In order to improve students’ problem-solving skills, the school redesigned the Basic Mathematics module to incorporate Polya’s problem-solving methodology. During tutorial lessons, students have to work through learning activities designed to raise their metacognitive awareness by following Polya’s problem-solving process. To assess the effectiveness of the redesign, students’ working for a challenging word problem in the mid-semester test were analyzed. Sixty-five percent of students attempted to understand the problem by making sketches. Twenty-eight percent of students went on to devise a plan and implement it. Only five percent of the students still left the question blank. These preliminary results suggest that with regular exposure to an explicit and systematic problem-solving approach, weak students’ problem-solving skills can potentially be improved.

Keywords: mathematics education, metacognition, problem solving, weak students

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Authors: Derkaoui Orkia, Lehireche Ahmed

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The topic of this article is to exploring the potentialities of a powerful optimization technique, namely Semidefinite Programming, for solving NP-hard problems. This approach provides tight relaxations of combinatorial and quadratic problems. In this work, we solve the maximum clique problem using this relaxation. The clique problem is the computational problem of finding cliques in a graph. It is widely acknowledged for its many applications in real-world problems. The numerical results show that it is possible to find a maximum clique in polynomial time, using an algorithm based on semidefinite programming. We implement a primal-dual interior points algorithm to solve this problem based on semidefinite programming. The semidefinite relaxation of this problem can be solved in polynomial time.

Keywords: semidefinite programming, maximum clique problem, primal-dual interior point method, relaxation

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Authors: Mehmet Hakan Karaata

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In this paper, we first coin a new graph theocratic problem with numerous applications. Second, we provide two algorithms for the problem. The first solution is using a brute-force techniques, whereas the second solution is based on an initial identification of the cycles in the given graph. We then provide a correctness proof of the algorithm. The applications of the problem include graph analysis, graph drawing and network structuring.

Keywords: algorithm, cycle, graph algorithm, graph theory, network structuring

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Authors: Hashini E. Mohottala

Abstract:

We report the combine use of Wikispaces (WikiS) and Group Problem Solving (GPS) sessions conducted in the introductory level physics classes. As a part of this new teaching tool, some essay type problems were posted on the WikiS in weekly basis and students were encouraged to participate in problem solving without providing numerical final answers but the steps. Wikispace is used as a platform for students to meet online and create discussions. Each week students were further evaluated on problem solving skills opening up more opportunity for peer interaction through GPS. Each group was given a different problem to solve and the answers were graded. Students developed a set of skills in decision-making, problem solving, communication, negotiation, critical and independent thinking and teamwork through the combination of WikiS and GPS.

Keywords: group problem solving (GPS), wikispace (WikiS), physics education, learning

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Authors: Sourabh Joshi, Tarun Sharma, Anurag Sharma

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Ant Colony Optimization is heuristic Algorithm which has been proven a successful technique applied on number of combinatorial optimization problems. Two variants of Ant Colony Optimization algorithm named Ant System and Max-Min Ant System are implemented in MATLAB to solve travelling Salesman Problem and the results are compared. In, this paper both systems are analyzed by solving the some Travelling Salesman Problem and depict which system solve the problem better in term of cost and time.

Keywords: Ant Colony Optimization, Travelling Salesman Problem, Ant System, Max-Min Ant System

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Authors: Boris Melnikov, Dmitrii Chaikovskii, Elena Melnikova

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The traveling salesman problem (TSP) is a well-known optimization problem that seeks to find the shortest possible route that visits a set of points and returns to the starting point. In this paper, we apply some heuristics of the TSP for the task of restoring the DNA matrix. This restoration problem is often considered in biocybernetics. For it, we must recover the matrix of distances between DNA sequences if not all the elements of the matrix under consideration are known at the input. We consider the possibility of using this method in the testing of distance calculation algorithms between a pair of DNAs to restore the partially filled matrix.

Keywords: optimization problems, DNA matrix, partially filled matrix, traveling salesman problem, heuristic algorithms

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