• Title/Summary/Keyword: Mathematical Optimization

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Mathematical Planning for Revealing Optimal Synthetic Conditions of Naphthalene Chloromethylation

  • Pak, V.V.;Karimov, R.K.;Shakhidoyatov, Kh.M.;Yun, L.M.;Soh, D.W.
    • Journal of the Speleological Society of Korea
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    • no.71
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    • pp.1-4
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    • 2006
  • Chloromethylnaphthalene is a valuable compound for obtaining of the plant growing stimulator - -napthylacetic acid. Chloromethylation of naphthalene by paraformaldehyde in the presence of glacial acetic acid, phosphoric and hydrochloric acids at temperature 80 - 85C and duration - 6 hours the -chloromethylnaphthalene yield was 55-57%. Using Box-Wilson method for mathematical planning of experiment carried out optimization of its synthesis for purpose increasing -chloromethylnaphthalene yield. Preliminary, one - factor experiments were carried out for selecting independence main parameters influencing on the synthesis. A full factor experiment of 23 with extended matrix of planning was used for optimization. Aiming to increase the -chloromethylnaphthalene yield, the obtained mathematical model was used for program of sharp raising on the reply surface. The received optimal conditions for the -chloromethylnaphthalene synthesis were selected as following: molar ratio of naphthalene parapfsormaldehyde of 1 : 2 temperature - 105C duration of the reaction - 3 hours. The yield of -chloromethylnaphthalene under these optimal conditions was 75%.

Chloromethylation of Naphthalene and Mathematical Planning of Experiment for Revealing Optimal Synthetic Conditions

  • V.V. Pak;R.K. Karimov;Kh.M. Shakhidoyatov;L.M. Yun;Soh, Dea-Wha
    • Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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    • 2004.05a
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    • pp.36-37
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    • 2004
  • $\alpha$-Chloromethylnaphthalene is a valuable compound for obtaining of the plant growing stimulator - $\alpha$-napthylacetic acid. Chloromethylation of naphthalene by paraformaldehyde in the presence of glacial acetic acid, phosphoric and hydrochloric acids at temperature 80-85$^{\circ}C$ and duration - 6 hours the $\alpha$-chloromethyl-naphthalene yield was 55-57%. Using Box-Wilson method for mathematical planning of experiment carried out optimization of its synthesis for purpose increasing $\alpha$-chloromethylnaphthalene yield. Preliminary, one - factor experiments were carried out for selecting independence main parameters influencing on the synthesis. A full factor experiment of 2$^3$with extended matrix of planning was used for optimization. Aiming to increase the $\alpha$-chloromethylnaphthalene yield, the obtained mathematical model was used for program of sharp raising on the reply surface. The received optimal conditions for the $\alpha$-chloromethylnaphthalene synthesis were selected as following: molar ratio of naphthalene - parapfsormaldehyde of 1 : 2; temperature -105$^{\circ}C$; duration of the reaction -3 hours. The yield of $\alpha$-chloromethylnaphthalene under these optimal conditions was 75 %.

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The Research of Optimal Plant Layout Optimization based on Particle Swarm Optimization for Ethylene Oxide Plant (PSO 최적화 기법을 이용한 Ethylene Oxide Plant 배치에 관한 연구)

  • Park, Pyung Jae;Lee, Chang Jun
    • Journal of the Korean Society of Safety
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    • v.30 no.3
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    • pp.32-37
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    • 2015
  • In the fields of plant layout optimization, the main goal is to minimize the construction cost including pipelines as satisfying all constraints such as safety and operating issues. However, what is the lacking of considerations in previous researches is to consider proper safety and maintenance spaces for a complex plant. Based on the mathematical programming, MILP(Mixed Integer Linear Programming) problems including various constraints can be formulated to find the optimal solution which is to achieve the best economic benefits. The objective function of this problem is the sum of piping cost, pumping cost and area cost. In general, many conventional optimization solvers are used to find a MILP problem. However, it is really hard to solve this problem due to complex inequality and equality constraints, since it is impossible to use the derivatives of objective functions and constraints. To resolve this problem, the PSO (Particle Swarm Optimization), which is one of the representative sampling approaches and does not need to use derivatives of equations, is employed to find the optimal solution considering various complex constraints in this study. The EO (Ethylene Oxide) plant is tested to verify the efficacy of the proposed method.

An Efficient Heuristic Algorithm of Surrogate-Based Optimization for Global Optimal Design Problems (전역 최적화 문제의 효율적인 해결을 위한 근사최적화 기법)

  • Lee, Se-Jung
    • Korean Journal of Computational Design and Engineering
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    • v.17 no.5
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    • pp.375-386
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    • 2012
  • Most engineering design problems require analyses or simulations to evaluate objective functions. However, a single simulation can take many hours or even days to finish for many real world problems. As a result, design optimization becomes impossible since they require hundreds or thousands of simulation evaluations. The surrogate-based optimization (SBO) strategy became a remedy for such computationally expensive analyses and simulations. A surrogate-based optimization strategy has been developed in this study in order to improve global optimization performance. The strategy is a heuristic algorithm and it exploits not only multiple surrogates, but also multiple optimizers. Multiple optimizations of multiple surrogate models yield multiple candidate design points of optima. During the sequential sampling process, the algorithm ranks candidate design points, selects the points as many as specified, and builds the improved surrogate model. Various mathematical functions with different numbers of design variables are chosen to compare the proposed method with the other most recent algorithm, MSEGO. The proposed method shows superior performance to the other method.

Trade-off Analysis in Multi-objective Optimization Using Chebyshev Orthogonal Polynomials

  • Baek Seok-Heum;Cho Seok-Swoo;Kim Hyun-Su;Joo Won-Sik
    • Journal of Mechanical Science and Technology
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    • v.20 no.3
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    • pp.366-375
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    • 2006
  • In this paper, it is intended to introduce a method to solve multi-objective optimization problems and to evaluate its performance. In order to verify the performance of this method it is applied for a vertical roller mill for Portland cement. A design process is defined with the compromise decision support problem concept and a design process consists of two steps: the design of experiments and mathematical programming. In this process, a designer decides an object that the objective function is going to pursuit and a non-linear optimization is performed composing objective constraints with practical constraints. In this method, response surfaces are used to model objectives (stress, deflection and weight) and the optimization is performed for each of the objectives while handling the remaining ones as constraints. The response surfaces are constructed using orthogonal polynomials, and orthogonal array as design of experiment, with analysis of variance for variable selection. In addition, it establishes the relative influence of the design variables in the objectives variability. The constrained optimization problems are solved using sequential quadratic programming. From the results, it is found that the method in this paper is a very effective and powerful for the multi-objective optimization of various practical design problems. It provides, moreover, a reference of design to judge the amount of excess or shortage from the final object.

Shape Optimization of the Lower Control Arm using the Characteristic Function and the Fatigue Analysis (특성함수와 피로해석을 이용한 로워컨트롤암의 형상최적설계)

  • Park Youngchul;Lee Donghwa
    • Transactions of the Korean Society of Automotive Engineers
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    • v.13 no.1
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    • pp.119-125
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    • 2005
  • The current automotive is seeking the improvement of performance, the prevention of environmental pollution and the saving of energy resources according to miniaturization and lightweight of the components. And the variance analysis on the basis of structure analysis and DOE is applied to the lower control am. We have proposed a statistical design model to evaluate the effect of structural modification by performing the practical multi-objective optimization considering weight, stress and fatigue lift. The lower control arm is performed the fatigue analysis using the load history of real road test. The design model is determined using the optimization of acquired load history with the fatigue characteristic. The characteristic function is made use of the optimization according to fatigue characteristics to consider constrained function in the optimization of DOE. The structure optimization of a lower control arm according to fatigue characteristics is performed. And the optimized design variable is D=47 m, T=36mm, W=12 mm. In the real engineering problem of considering many objective functions, the multi-objective optimization process using the mathematical programming and the characteristic function is derived an useful design solution.

Knee-driven many-objective sine-cosine algorithm

  • Hongxia, Zhao;Yongjie, Wang;Maolin, Li
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • v.17 no.2
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    • pp.335-352
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    • 2023
  • When solving multi-objective optimization problems, the blindness of the evolution direction of the population gradually emerges with the increase in the number of objectives, and there are also problems of convergence and diversity that are difficult to balance. The many- objective optimization problem makes some classic multi-objective optimization algorithms face challenges due to the huge objective space. The sine cosine algorithm is a new type of natural simulation optimization algorithm, which uses the sine and cosine mathematical model to solve the optimization problem. In this paper, a knee-driven many-objective sine-cosine algorithm (MaSCA-KD) is proposed. First, the Latin hypercube population initialization strategy is used to generate the initial population, in order to ensure that the population is evenly distributed in the decision space. Secondly, special points in the population, such as nadir point and knee points, are adopted to increase selection pressure and guide population evolution. In the process of environmental selection, the diversity of the population is promoted through diversity criteria. Through the above strategies, the balance of population convergence and diversity is achieved. Experimental research on the WFG series of benchmark problems shows that the MaSCA-KD algorithm has a certain degree of competitiveness compared with the existing algorithms. The algorithm has good performance and can be used as an alternative tool for many-objective optimization problems.

Soccer league optimization-based championship algorithm (SLOCA): A fast novel meta-heuristic technique for optimization problems

  • Ghasemi, Mohammad R.;Ghasri, Mehdi;Salarnia, Abdolhamid
    • Advances in Computational Design
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    • v.7 no.4
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    • pp.297-319
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    • 2022
  • Due to their natural and social revelation, also their ease and flexibility, human collective behavior and teamwork sports are inspired to introduce optimization algorithms to solve various engineering and scientific problems. Nowadays, meta-heuristic algorithms are becoming some striking methods for solving complex real-world problems. In that respect in the present study, the authors propose a novel meta-innovative algorithm based on soccer teamwork sport, suitable for optimization problems. The method may be referred to as the Soccer League Optimization-based Championship Algorithm, inspired by the Soccer league. This method consists of two main steps, including: 1. Qualifying competitions and 2. Main competitions. To evaluate the robustness of the proposed method, six different benchmark mathematical functions, and two engineering design problem was performed for optimization to assess its efficiency in achieving optimal solutions to various problems. The results show that the proposed algorithm may well explore better performance than some well-known algorithms in various aspects such as consistency through runs and a fast and steep convergence in all problems towards the global optimal fitness value.

Mathematical Modeling of the Roundness for Plastic Injection Mold Parts with Complicated 3D curvatures (복잡한 3차원 곡면을 가지는 플라스틱 사출 성형품을 위한 진원도의 수학적 모델링)

  • Yoon, Seon Jhin
    • Design & Manufacturing
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    • v.13 no.2
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    • pp.6-11
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    • 2019
  • In this study, we constructed the mathematical model to evaluate the roundness for plastic injection mold parts with complicated 3D curvatures. Mathematically we started off from the equation of circle and successfully derived an analytical solution so as to minimize the area of the residuals. On the other hand, we employed the numerical method the similar optimization process for the comparison. To verify the mathematical models, we manufactured and used a ball valve type plastic parts to apply the derived model. The plastic parts was fabricated under the process conditions of 220-ton injection mold machine with a raw material of polyester. we experimentally measured (x, y) position using 3D contact automated system and applied two mathematical methods to evaluated the accuracy of the mathematical models. We found that the analytical solution gives better accuracy of 0.4036 compared to 0.4872 of the numerical solution. The numerical method however may give adaptiveness and versatility for optional simulations such as a fixed center.

ON EIGENSHARPNESS AND ALMOST EIGENSHARPNESS OF LEXICOGRAPHIC PRODUCTS OF SOME GRAPHS

  • Abbasi, Ahmad;Taleshani, Mona Gholamnia
    • Bulletin of the Korean Mathematical Society
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    • v.59 no.3
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    • pp.685-695
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    • 2022
  • The minimum number of complete bipartite subgraphs needed to partition the edges of a graph G is denoted by b(G). A known lower bound on b(G) states that b(G) ≥ max{p(G), q(G)}, where p(G) and q(G) are the numbers of positive and negative eigenvalues of the adjacency matrix of G, respectively. When equality is attained, G is said to be eigensharp and when b(G) = max{p(G), q(G)} + 1, G is called an almost eigensharp graph. In this paper, we investigate the eigensharpness and almost eigensharpness of lexicographic products of some graphs.