scholarly journals OPTIMIZATION OF TIMETABLE AT THE UNIVERSITY

2021 ◽  
pp. 175-183
Author(s):  
A. I. Kosolap ◽  
T. M. Dubovik
Keyword(s):  
Regularization Method ◽  
Optimization Problems ◽  
New Technology ◽  
Educational Institution ◽  
Optimal Schedule ◽  
Optimal Solution ◽  
Optimization Methods ◽  
Optimization Method ◽  
Optimization Models ◽  
The University

Context. In this paper, we consider a well-known university scheduling problem. Such tasks are solved several times a year in every educational institution. The problem of constructing an optimal schedule remains open despite numerous studies in this area. This is due to the complexity of the corresponding optimization problem, in particular, its significant dimension. This complicates its numerical solution with existing optimization methods. Scheduling models also need improvement. Thus, schedule optimization is a complex computational problem and requires the development of new methods for solving it.  Objective. Improvement of optimization models for timetabling at the university and the use of new effective methods to solve them. Method. We use the exact quadratic regularization method to solve timetabling optimization problems. Exact quadratic regularization allows transforming complex optimization models with Boolean variables into the problem of maximizing the vector norm on a convex set. We use the efficient direct dual interior point method and dichotomy method to solve this problem. This method has shown significantly better results in solving many complex multimodal problems. This is confirmed by many comparative computational experiments. The exact quadratic regularization method is even more effective in solving timetabling problems. This optimization method is used for the first time for this class of problems, so it required the development of adequate algorithmic support. Results. We propose a new, simpler timetabling optimization model that can be easily implemented software in Excel with the OpenSolver, RoskSolver, and others. We give a small example of building a schedule and describe step-by-step instructions for obtaining the optimal solution.  Conclusions. An efficient new technology developed for university timetable, which is simple to implement and does not require the development of special software. The efficiency of the technology is ensured by the use of a new method of exact quadratic regularization. 

Design Optimization Method for MR-Brake Actuators

2011 ◽  
Author(s):  
Ozan G. Erol ◽  
Hakan Gurocak ◽  
Berk Gonenc
Keyword(s):  
Optimal Solution ◽  
Volume Ratio ◽  
Optimization Methods ◽  
Search Space ◽  
Optimization Method ◽  
Friction Torque ◽  
Element Analysis ◽  
Taguchi Design Of Experiments ◽  
Variable Friction ◽  
Electronically Controllable

MR-brakes work by varying viscosity of a magnetorheological (MR) fluid inside the brake. This electronically controllable viscosity leads to variable friction torque generated by the actuator. A properly designed MR-brake can have a high torque-to-volume ratio which is quite desirable for an actuator. However, designing an MR-brake is a complex process as there are many parameters involved in the design which can affect the size and torque output significantly. The contribution of this study is a new design approach that combines the Taguchi design of experiments method with parameterized finite element analysis for optimization. Unlike the typical multivariate optimization methods, this approach can identify the dominant parameters of the design and allows the designer to only explore their interactions during the optimization process. This unique feature reduces the size of the search space and the time it takes to find an optimal solution. It normally takes about a week to design an MR-brake manually. Our interactive method allows the designer to finish the design in about two minutes. In this paper, we first present the details of the MR-brake design problem. This is followed by the details of our new approach. Next, we show how to design an MR-brake using this method. Prototype of a new brake was fabricated. Results of experiments with the prototype brake are very encouraging and are in close agreement with the theoretical performance predictions.

Stellar Mass Black Hole for Engineering Optimization

2017 ◽  
pp. 62-90
Author(s):  
Premalatha Kandhasamy ◽  
Balamurugan R ◽  
Kannimuthu S
Keyword(s):  
Black Hole ◽  
Artificial Bee Colony ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Cuckoo Search ◽  
Optimization Method ◽  
Stellar Mass ◽  
Bee Colony ◽  
Nature Inspired Algorithms ◽  
The Universe

In recent years, nature-inspired algorithms have been popular due to the fact that many real-world optimization problems are increasingly large, complex and dynamic. By reasons of the size and complexity of the problems, it is necessary to develop an optimization method whose efficiency is measured by finding the near optimal solution within a reasonable amount of time. A black hole is an object that has enough masses in a small enough volume that its gravitational force is strong enough to prevent light or anything else from escaping. Stellar mass Black hole Optimization (SBO) is a novel optimization algorithm inspired from the property of the gravity's relentless pull of black holes which are presented in the Universe. In this paper SBO algorithm is tested on benchmark optimization test functions and compared with the Cuckoo Search, Particle Swarm Optimization and Artificial Bee Colony systems. The experiment results show that the SBO outperforms the existing methods.

Non-Probabilistic Based Topology Optimization Under External Load Uncertainty With Eigenvalue-Superposition of Convex Models

2013 ◽  
Author(s):  
Xike Zhao ◽  
Hae Chang Gea ◽  
Wei Song
Keyword(s):  
Topology Optimization ◽  
External Load ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Optimization Method ◽  
Convex Model ◽  
Structure Response ◽  
Gradient Based ◽  
Bounded Convex ◽  
Topology Optimization Method

In this paper the Eigenvalue-Superposition of Convex Models (ESCM) based topology optimization method for solving topology optimization problems under external load uncertainties is presented. The load uncertainties are formulated using the non-probabilistic based unknown-but-bounded convex model. The sensitivities are derived and the problem is solved using gradient based algorithm. The proposed ESCM based method yields the material distribution which would optimize the worst structure response under the uncertain loads. Comparing to the deterministic based topology optimization formulation the ESCM based method provided more reasonable solutions when load uncertainties were involved. The simplicity, efficiency and versatility of the proposed ESCM based topology optimization method can be considered as a supplement to the sophisticated reliability based topology optimization methods.

Optimization Method Based on a Mix Strategy

2013 ◽  
Vol 816-817 ◽  
pp. 1154-1157
Author(s):  
Xu Yin ◽  
Ai Min Ji
Keyword(s):  
Optimization Problems ◽  
Optimal Solution ◽  
Optimization Method ◽  
Local Solution ◽  
Collaborative Optimization ◽  
Design Variables ◽  
Gradient Optimization ◽  
Local Optimal Solution ◽  
Optimal Values ◽  
Low Efficiency

To solve problems that exist in optimal design such as falling into local optimal solution easily and low efficiency in collaborative optimization, a new mix strategy optimization method combined design of experiments (DOE) with gradient optimization (GO) was proposed. In order to reduce the effect on the result of optimization made by the designers decision, DOE for preliminary analysis of the function model was used, and the optimal values obtained in DOE stage was taken as the initial values of design variables in GO stage in the new optimization method. The reducer MDO problem was taken as a example to confirm the global degree, efficiency, and accuracy of the method. The results show the optimization method could not only avoid falling into local solution, but also have an obvious superiority in treating the complex collaborative optimization problems.

A Study of Parallel Efficiency of Modified Direct Algorithm Applied to Thermohydrodynamic Lubrication

2009 ◽  
Vol 25 (2) ◽  
pp. 143-150 ◽  
Author(s):  
N. Wang ◽  
C.-M. Tsai ◽  
K.-C. Cha
Keyword(s):  
Parallel Computing ◽  
Optimization Problems ◽  
Load Capacity ◽  
Optimization Methods ◽  
Optimization Method ◽  
Parallel Optimization ◽  
Direct Algorithm ◽  
Slider Bearing ◽  
Parallel Efficiency ◽  
Fine Grain

AbstractThis study examines the parallel computing as a means to minimize the execution time in the optimization applied to thermohydrodynamic (THD) lubrication. The objective of the optimization is to maximize the load capacity of a slider bearing with two design variables. A global optimization method, DIviding RECTangle (DIRECT) algorithm, is used. The first approach was to apply the parallel computing within the THD model in a shared-memory processing (SMP) environment to examine the parallel efficiency of fine-grain computation. Next, a distributed parallel computing in the search level was conducted by use of the standard DIRECT algorithm. Then, the algorithm is modified to provide a version suitable for effective parallel computing. In the latter coarse-grain computation the speedups obtained by the DIRECT algorithms are compared with some previous studies using other parallel optimization methods. In the fine-grain computation of the SMP machine, the communication and overhead time costs prohibit high speedup in the cases of four or more simultaneous threads. It is found that the standard DIRECT algorithm is an efficient sequential but less parallel-computing-friendly method. When the modified algorithm is used in the slider bearing optimization, a parallel efficiency of 96.3% is obtained in the 16-computing-node cluster. This study presents the modified DIRECT algorithm, an efficient parallel search method, for general engineering optimization problems.

Genetic Algorithms for Optimization of Building Envelopes and the Design and Control of HVAC Systems

2003 ◽  
Vol 125 (3) ◽  
pp. 343-351 ◽  
Author(s):  
L. G. Caldas ◽  
L. K. Norford
Keyword(s):  
Genetic Algorithms ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Optimization Method ◽  
Hvac Systems ◽  
Design Problems ◽  
Building Walls ◽  
Building Form ◽  
And Control ◽  
Future Work

Many design problems related to buildings involve minimizing capital and operating costs while providing acceptable service. Genetic algorithms (GAs) are an optimization method that has been applied to these problems. GAs are easily configured, an advantage that often compensates for a sacrifice in performance relative to optimization methods selected specifically for a given problem, and have been shown to give solutions where other methods cannot. This paper reviews the basics of GAs, emphasizing multi-objective optimization problems. It then presents several applications, including determining the size and placement of windows and the composition of building walls, the generation of building form, and the design and operation of HVAC systems. Future work is identified, notably interfaces between a GA and both simulation and CAD programs.

Optimization Method for Globally Solving a Kind of Multiplicative Problems with Coefficients

2011 ◽  
Vol 467-469 ◽  
pp. 526-530 ◽  
Author(s):  
Hong Wei Jiao ◽  
Jing Ben Yin ◽  
Yun Rui Guo
Keyword(s):  
Original Problem ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Optimization Method ◽  
Linearization Method ◽  
Equivalent Transformation ◽  
Engineering System ◽  
Linear Programming Problems ◽  
Global Optimal ◽  
Multiplicative Problems

Multiplicative problems are a kind of difficult global optimization problems known to be NP-hard. At the same time, these problems have some important applications in engineering, system, finance, economics, and other fields. In this paper, an optimization method is proposed to globally solve a class of multiplicative problems with coefficients. Firstly, by utilizing equivalent transformation and linearization method, a linear relaxation programming problem is established. Secondly, by using branch and bound technique, a determined algorithm is proposed for solving equivalent problem. Finally, the proposed algorithm is convergent to the global optimal solution of original problem by means of the subsequent solutions of a series of linear programming problems.

A New Global Optimization Method for Simultaneous Computation on Expensive Black-Box Functions

2003 ◽  
Author(s):  
Liqun Wang ◽  
Songqing Shan ◽  
G. Gary Wang
Keyword(s):  
Global Optimization ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Search Space ◽  
Optimization Method ◽  
Global Optimum ◽  
Black Box ◽  
Efficient Global Optimization ◽  
Global Optimization Method ◽  
Global Optimization Methods

The presence of black-box functions in engineering design, which are usually computation-intensive, demands efficient global optimization methods. This work proposes a new global optimization method for black-box functions. The global optimization method is based on a novel mode-pursuing sampling (MPS) method which systematically generates more sample points in the neighborhood of the function mode while statistically covers the entire search space. Quadratic regression is performed to detect the region containing the global optimum. The sampling and detection process iterates until the global optimum is obtained. Through intensive testing, this method is found to be effective, efficient, robust, and applicable to both continuous and discontinuous functions. It supports simultaneous computation and applies to both unconstrained and constrained optimization problems. Because it does not call any existing global optimization tool, it can be used as a standalone global optimization method for inexpensive problems as well. Limitation of the method is also identified and discussed.

Non-convex Optimization via Strongly Convex Majorization-minimization

2019 ◽  
Vol 63 (4) ◽  
pp. 726-737
Author(s):  
Azita Mayeli
Keyword(s):  
Convex Optimization ◽  
Cost Function ◽  
Local Minimum ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Optimization Methods ◽  
Small Radius ◽  
Mm Algorithm ◽  
Strongly Convex ◽  
Nonsmooth Nonconvex Optimization

AbstractIn this paper, we introduce a class of nonsmooth nonconvex optimization problems, and we propose to use a local iterative minimization-majorization (MM) algorithm to find an optimal solution for the optimization problem. The cost functions in our optimization problems are an extension of convex functions with MC separable penalty, which were previously introduced by Ivan Selesnick. These functions are not convex; therefore, convex optimization methods cannot be applied here to prove the existence of optimal minimum point for these functions. For our purpose, we use convex analysis tools to first construct a class of convex majorizers, which approximate the value of non-convex cost function locally, then use the MM algorithm to prove the existence of local minimum. The convergence of the algorithm is guaranteed when the iterative points $x^{(k)}$ are obtained in a ball centred at $x^{(k-1)}$ with small radius. We prove that the algorithm converges to a stationary point (local minimum) of cost function when the surregators are strongly convex.

A Kind of New Immune Genetic Algorithm and its Application

2011 ◽  
Vol 48-49 ◽  
pp. 25-28
Author(s):  
Wei Jian Ren ◽  
Yuan Jun Qi ◽  
Wei Lv ◽  
Cheng Da Li
Keyword(s):  
Genetic Algorithm ◽  
Large Scale ◽  
Optimization Problems ◽  
Logistic Map ◽  
Optimal Solution ◽  
Optimization Method ◽  
Local Optimum ◽  
Immune Genetic Algorithm ◽  
Chaos Optimization ◽  
Scale Optimization

According to the phenomenon of falling into local optimum during solving large-scale optimization problems and the shortcomings of poor convergence of Immune Genetic Algorithm, a new kind of probability selection method based on the concentration for the genetic operation is presented. Considering the features of chaos optimization method, such like not requiring the solved problems with continuity or differentiability, which is unlike the conventional method, and also with a solving process within a certain range traverse in order to find the global optimal solution, a kind of Chaos Immune Genetic Algorithm based on Logistic map and Hénon map is proposed. Through the application to TSP problem, the results have showed the superior to other algorithms.

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