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Application of evolutionary methods for solving optimization problems in engineering
Abstract
This paper is focused on solving engineering optimization problems, which contain often real and integer variables, a number of local extremes, multiple optimality criteria and disciplines. In latter case the conventional approaches based on traditional gradient technique fail or perform poorly. In the current study, an optimization approach that integrates meta-modeling and hybrid genetic algorithm (HGA) is developed. The methodology proposed is validated on following practical examples: optimal design of composite bathtub (large composite plastics), design of car frontal protection system.
... Two stack geometries manufactured by SLM are tested by monitoring temperature and sound pressure levels in the small scale standing wave TAE: one provided with internal parallel plates and one with oblique pin array. Future studies will involve the optimization of the performance of metal 3D printed stacks, also by means of functionally graded materials [6][7][8][9], and a comparison between this technology and the traditional stack manufacturing processes. Such a comparison, at this stage, is still premature. ...
In this study the authors investigate the possibility of using Selective Laser Melting (SLM) to manufacture the porous element (stack) of a thermoacoustic engine. Two stacks, provided with different internal geometries but with the same hydraulic radii, have been produced: one with parallel plates and one with a new, oblique pin array configuration. The pin array stacks provide smaller amount of viscous losses during the thermal to acoustic power conversion when working fluids with Pr < 1, e.g. air. Furthermore, the oblique configuration is designed to reduce the heat transmission from the hot to the cold surface of the stack, thus to achieve more easily the temperature gradient for the onset of the thermoacoustic phenomenon. In general, the pin array configurations are difficult to manufacture with conventional technologies. However, the SLM provides precise control of the features of the printed object, thus allowing to objectively compare the behavior of the two stacks. To this aim, the temperature gradient between the hot and cold faces of the stacks and the corresponding sound pressure levels measured at 15 cm from the open end of the engine are measured and compared.
... Although nearly exact models can be made for consumption graph data, the production charts of the wind generator and photovoltaic system are weather dependent and region specific as a result. It is not possible to model production graphs using synthetic data or making some kind of approximation in our case [31], [32]. ...
This paper presents new encoding methods for the binary genetic algorithm (BGA) and new converting methods for the real-coded genetic algorithm (RCGA). These methods are developed for the specific case in which some parameters have to be searched in wide ranges since their actual values are not known. The oversampling effect which occurs at large values in the wide range search are reduced by adjustment of resolutions in mantissa and exponent of real numbers mapped by BGA. Owing to an intrinsic similarity in chromosomal operations, the proposed encoding methods are also applied to RCGA with remapping (converting as named above) from real numbers generated in RCGA. A simple probabilistic analysis and benchmark with two ill-scaled test functions are carried out. System identification of a simple electrical circuit is also undertaken to testify effectiveness of the proposed methods to real world problems. All the optimization results show that the proposed encoding/converting methods are more suitable for problems with ill-scaled parameters or wide parameter ranges for searching.
Many engineering optimal design problems involve multiple conflicting objectives and often they are attempted to be solved by converting them into a single composite objective. Moreover, to be able to use standard classical optimization methods, often such problems are divided into suitable subproblems and solved in stages. A leg mechanism design problem which received some attention in the past involves link length and spring characteristics as decision variables and as many as three objectives and 17 inequality constraints. The problem is difficult to optimize because of strict geometric constraints which make only a tiny fraction of the search space feasible. This article applies an evolutionary multi-objective optimization (EMO) methodology to solve the complete leg mechanism optimization problem for all three objectives simultaneously. The way of solving the complete problem demonstrates how such a complex engineering design problem can be solved by evolutionary algorithms and shows that useful insights into the design problem can be obtained by systematically starting with fewer objectives and gradually adding more objectives. Several optimization concepts are introduced to gain confidence in the obtained solutions. Results of this study are compared with that of an earlier study and in all cases the superiority and flexibility of the EMO approach is demonstrated. The ease and efficiency of the EMO methodology demonstrated in this article should encourage similar studies involving other mechanical component design problems.
In this paper, a new hybrid genetic algorithm is proposed, which combines the genetic algorithm with hill-climbing search steps differently from some former algorithms. The new algorithm can be widely applied to a class of global optimization problems for continuous functions with box constraints. Finally, numerical examples show that this algorithm can yield the global optimum with high efficiency.