Selected Mathematical Optimization Methods for Solving Problems of Engineering Practice (original) (raw)

A Software Framework for Optimization of Process Parameters in Material Production

A framework for optimization of process parameters in material processing and production is described. The framework is designed for effective set up and solution of optimization problems as part of process design, as well as to support development of numerical models by inverse identification of model parameters. The general framework is outlined, which has been supplemented by a neural networks module in order to enable real time decision support. Simulator based on meshless method with radial basis functions (RBF) has been utilized. Optimization Framework The optimization part of the framework is designed as a stand-alone optimization system. Its development was centered around a library of optimization techniques for industrial problems where optimization is carried out on basis of computationally expensive numerical simulations whose results contain substantial level of numerical noise [1,2]. This has been predominantly treated by algorithms based on adaptive approximation of the response functions. Successive approximations of sampled response over suitably sized domains enable exploitation of higher order function information. Restricted step approach is used to ensure global convergence, and adaptive sampling strategies play significant role in reducing the necessary number of evaluations of the response functions. Work was initiated as an attempt to re-implement the C library IOptLib [1-3] in a rigorous object oriented manner in order to more easily master complexity of the developed algorithms and to speed up the development process. The framework is being extended in order to enable straight forward inclusion and seamless use of third party optimizers. This requires careful design of abstraction levels and standardization of input/output and calling conventions, which is achieved by suitable wrappers when third party software is incorporated. Further steps will be made towards more unified treatment of different kinds of problems such as constrained/unconstrained or single objective/multiobjective optimization. Multidisciplinary approach is also considered in a way that different simulators may be used for different problem fields involved in definition of an optimization problem. Neural Networks Approximation Module. In several practical cases the process design parameters must be adapted quickly in order to produce results that comply with customer requests. With classical approach to optimization of process parameters, long computational times needed for each run of the process simulation at trial design parameters can therefore limit applicability of optimization in industrial environment. Solution has been conceived in the form of approximation of system response, which is calculated on basis of sampled response prepared in advance either by runs of numerical model or by measurements previously performed on the process of interest with varying process parameters. The optimization procedure that produces process design parameters consistent with the current requirements is then performed on the surrogate model based on the approximated response.

Optimization Methods in Mathematical Modeling of Technological Processes

Mathematical engineering, 2023

The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

Modern optimization techniques for advanced manufacturing: Heuristic and Metaheuristic Techniques

Springer, 2023

Advanced manufacturing via computer numerical machining is the art of producing mechanical components employed in aerospace, automobile, and industrial applications where a high level of accuracy is needed. This book focuses on the nano-machining of aluminum alloy and its optimization. The application of aluminum alloy in the manufacturing industry has increased tremendously due to its lightweight to high strength ratio and high-level resistance to corrosion. However, aluminum alloy has some challenges during the machining and manufacturing stage in order to solve real-life manufacturing challenges in advanced machining operation for sustainable production processes. Therefore, it is a need for the implementation of a general algebraic modeling system (GAMS) and other metaheuristic techniques for problem solving and to effectively develop mathematical models for high accuracy prediction and optimization under nano-lubrication machining conditions. This book discusses majorly on the major three responses in machining such as surface roughness, cutting force, and material removal rate, which will give an excellent guide to undergraduate and postgraduate students, senior research fellows in academia, operational, and strategic staff in manufacturing industries.

Engineering Optimization and Industrial Applications

Surrogate-Based Modeling and Optimization, 2013

Design optimization is important in engineering and industrial applications. It is usually very challenging to find optimum designs, which require both efficient optimization algorithms and high-quality simulators that are often time-consuming. To some extent, an optimization process is equivalent to a selforganizing system, and the organized states are the optima that are to be searched for. In this chapter, we discuss both optimization and self-organization in a unified framework, and we use three metaheuristic algorithms, the firefly algorithm, the bat algorithm and cuckoo search, as examples to see how this self-organized process works. We then present a set of nine design problems in engineering and industry. We also discuss the challenging issues that need to be addressed in the near future. maximize the profit, output, performance and efficiency. In reality, resources, time and money are always limited; consequently, optimization is far more important in practice .

A Methodology for Optimization in Multistage Industrial Processes: A Pilot Study

Mathematical Problems in Engineering, 2015

The paper introduces a methodology for optimization in multistage industrial processes with multiple quality criteria. Two ways of formulation of optimization problem and four different approaches to solve the problem are considered. Proposed methodologies were tested first on a virtual process described by benchmark functions and next were applied in optimization of multistage lead refining process.

A new approach to optimization of chemical processes

AIChE Journal, 1980

Based on recent work by Powell, a new optimization algorithm is presented. It merges the Newton-Raphson method and quadratic programming. A unique feature is that one does not converge the equality and tight inequality constraints for each step taken by the optimization algorithm. The article shows how to perform the necessary calculations efficiently for very large problems which require the use of mass memory. Experience with the algorithm on small problems indicates it converges exceptionally quickly to the optimal answer, often in as few iterations (5 to 15) as are needed to perform a single simulation with no optimization using more conventional approaches.

A New Tool Providing an Integrated Framework for Process Optimization

Nowadays, process optimization plays an important role in the chemical industries, providing many benefits. The aim of this work is to present a new framework for process optimization of chemical industries based on rigorous process models and with many integrated features, such as: customized thermodynamic data package, dynamic and steady-state simulation, optimization, parameter estimation, data reconciliation, gross error detection and integration with data bank. The integrated framework with all these features increases significantly the benefits of process optimization. This tool, named EMSO (Environment for Modeling, Simulation, and Optimization), is an equation-oriented dynamic and steadystate simulator and optimizer. It has an equipment library with rigorous models that can be viewed and edited by the user, using a high-level modeling language. The process flow diagram can be built either in text or graphical mode and the equipments can be modeled using an object-oriented approach. This software provides a set of sparse algebra and automatic differentiation feature to solve NLA (Non-Linear Algebraic Equations) systems in a fast and efficient way. NLP solvers, such as IPOPT and OPT++, were interfaced with this framework taking advantage of EMSO's efficiency to solve NLA systems, reducing the computational effort required to achieve the solution of optimization problems. Other optimization solvers can be readily interfaced through a plug-in system. Besides steady-state optimization of process flow diagrams with rigorous models it is also possible to perform steady-state and dynamic parameter estimation using the optimization feature. Furthermore, given a set of process measurements, it is also possible to solve data reconciliation problems and perform gross error detection. A language to describe the formulation of the optimization problems was developed and is presented in detail. The implementations mentioned above were evaluated with literature and practical examples, showing the benefits of using the proposed framework.