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Mathematics
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Mathematics with Industrial Problem Solving
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Mathematics with Industrial Problem Solving

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E2: Control Theory and Mechanics".

Deadline for manuscript submissions: closed (31 January 2022) | Viewed by 8103

Special Issue Editor

Prof. Dr. Poul Hjorth

E-Mail Website
Guest Editor
Department of Applied Mathematics and Computer Science, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark
Interests: dynamical systems theory; geometry; mathematical physics and industrial mathematics

Special Issue Information

Dear Colleagues,

The past quarter century has seen a rapid growth in the subject known as industrial mathematics: mathematics applied to issues and questions arising direct from industry and, in fact, from many areas of immediate relevance for society as a whole. The ubiquitous trinity of modelling, simulation, and optimization (MSO) can take on many forms, and draws on the entire spectrum of mathematical subject areas, from graph theory and differential geometry to numerical algorithms and operational analysis. It is a source of endless wonder to see how ideas and results from what may seem to be very abstract realms suddenly take on a surprising relevance when they are connected to real world problems

Prof. Poul Hjorth
Guest Editor

Manuscript Submission Information

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Keywords

  • Industrial mathematics
  • Dynamical systems theory
  • Crowd dynamics
  • Classical mechanics

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Published Papers (3 papers)

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Research

15 pages, 1571 KiB  
Article
Machining Parameters Optimization Based on Objective Function Linearization
by Cristina Gavrus, Nicolae-Valentin Ivan and Gheorghe Oancea
Mathematics 2022, 10(5), 803; https://doi.org/10.3390/math10050803 - 3 Mar 2022
Cited by 3 | Viewed by 2389
Abstract
Manufacturing process optimization is an ever-actual goal. Within this goal, machining parameters optimization is a very important task. Machining parameters strongly influence the manufacturing costs, process productivity and piece quality. Literature presents a series of optimization methods. The results supplied by these methods [...] Read more.
Manufacturing process optimization is an ever-actual goal. Within this goal, machining parameters optimization is a very important task. Machining parameters strongly influence the manufacturing costs, process productivity and piece quality. Literature presents a series of optimization methods. The results supplied by these methods are comparable and it is difficult to establish which method is the best. For machining parameters optimization, this paper proposes a novel, simple and efficient method, without additional costs related to new software packages. This approach is based on linear mathematical programming. The optimization mathematical models are, however, nonlinear. Therefore, mathematical model linearization is required. The major and difficult problem is the linearization of the objective function. This represents the key element of the proposed optimization method. In this respect, the paper proposes an original mathematical procedure for calculating the part of the objective function that refers to the analytical integration of the tool life into the model. This calculus procedure was transposed into an original software tool. For demonstrating the validity of the method, a comparison is presented among the results obtained by certain optimization techniques. It results that the proposed method is simple and as good as those presented by the literature. Full article
(This article belongs to the Special Issue Mathematics with Industrial Problem Solving)
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18 pages, 2848 KiB  
Article
Vehicle Routing Problem with Deadline and Stochastic Service Times: Case of the Ice Cream Industry in Santiago City of Chile
by Sebastián Dávila, Miguel Alfaro, Guillermo Fuertes, Manuel Vargas and Mauricio Camargo
Mathematics 2021, 9(21), 2750; https://doi.org/10.3390/math9212750 - 29 Oct 2021
Cited by 11 | Viewed by 2630
Abstract
The research evaluates the vehicular routing problem for distributing refrigerated products. The mathematical model corresponds to the vehicle routing problem with hard time windows and a stochastic service time (VRPTW-ST) model applied in Santiago de Chile. For model optimization, we used tabu search, [...] Read more.
The research evaluates the vehicular routing problem for distributing refrigerated products. The mathematical model corresponds to the vehicle routing problem with hard time windows and a stochastic service time (VRPTW-ST) model applied in Santiago de Chile. For model optimization, we used tabu search, chaotic search and general algebraic modeling. The model’s objective function is to minimize the total distance traveled and the number of vehicles using stochastic waiting restrictions at the customers’ facilities. The experiments were implemented in ten scenarios by modifying the number of customers. Experiments were established with several customers that can be solved using the general algebraic modeling technique in order to validate the tabu search and the chaotic search methods. The study considered two algorithms modified with Monte Carlo (tabu search and chaotic search). Additionally, two modified algorithms, TSv2 and CSv2, were proposed to reduce execution time. These algorithms were modified by delaying the Monte Carlo procedure until the first set of sub-optimal routes were found. The results validate the metaheuristic chaotic search to solve the VRPTW-ST. The chaotic search method obtained a superior performance than the tabu search method when solving a real problem in a large city. Finally, the experiments demonstrated a direct relationship between the percentage of customers with stochastic waiting time and the model resolution time. Full article
(This article belongs to the Special Issue Mathematics with Industrial Problem Solving)
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16 pages, 2819 KiB  
Article
A Lie Group-Based Iterative Algorithm Framework for Numerically Solving Forward Kinematics of Gough–Stewart Platform
by Binhai Xie, Shuling Dai and Feng Liu
Mathematics 2021, 9(7), 757; https://doi.org/10.3390/math9070757 - 1 Apr 2021
Cited by 6 | Viewed by 2335
Abstract
In this work, we began to take forward kinematics of the Gough–Stewart (G-S) platform as an unconstrained optimization problem on the Lie group-structured manifold SE(3) instead of simply relaxing its intrinsic orthogonal constraint when algorithms are updated on six-dimensional local flat Euclidean space [...] Read more.
In this work, we began to take forward kinematics of the Gough–Stewart (G-S) platform as an unconstrained optimization problem on the Lie group-structured manifold SE(3) instead of simply relaxing its intrinsic orthogonal constraint when algorithms are updated on six-dimensional local flat Euclidean space or adding extra unit norm constraint when orientation parts are parametrized by a unit quaternion. With this thought in mind, we construct two kinds of iterative problem-solving algorithms (Gauss–Newton (G-N) and Levenberg–Marquardt (L-M)) with mathematical tools from the Lie group and Lie algebra. Finally, a case study for a general G-S platform was carried out to compare these two kinds of algorithms on SE(3) with corresponding algorithms that updated on six-dimensional flat Euclidean space or seven-dimensional quaternion-based parametrization Euclidean space. Experiment results demonstrate that those algorithms on SE(3) behave better than others in convergence performance especially when the initial guess selection is near to branch solutions. Full article
(This article belongs to the Special Issue Mathematics with Industrial Problem Solving)
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