• Journal of the Architectural Institute of Korea Structure & Construction
• /
• v.33 no.12
• /
• pp.53-62
• /
• 2017

Many gradient-based mathematical methods have been developed and are in use for structural size optimization problems, in which the cross-sectional areas or sizing variables are usually assumed to be continuous. In most practical structural engineering design problems, however, the design variables are discrete. The main objective of this paper is to propose an efficient optimization method for structures with discrete-sized variables based on the harmony search (HS) meta-heuristic algorithm that is derived using penalty function. The recently developed HS algorithm was conceptualized using the musical process of searching for a perfect state of harmony. It uses a stochastic random search instead of a gradient search so that derivative information is unnecessary. In this paper, a discrete search strategy using the HS algorithm with a static penalty function is presented in detail and its applicability using several standard truss examples is discussed. The numerical results reveal that the HS algorithm with the static penalty function proposed in this study is a powerful search and design optimization technique for structures with discrete-sized members.

• Journal of Mechanical Science and Technology
• /
• v.15 no.8
• /
• pp.1143-1155
• /
• 2001

In order to reduce the expensive CPU time for design sensitivity analysis in dynamic response optimization, this study introduces the design sensitivities approximated within estimated confidence radius in dynamic response optimization with ALM method. The confidence radius is estimated by the linear approximation with Hessian of quasi-Newton formula and qualifies the approximate gradient to be validly used during optimization process. In this study, if the design changes between consecutive iterations are within the estimated confidence radius, then the approximate gradients are accepted. Otherwise, the exact gradients are used such as analytical or finite differenced gradients. This hybrid design sensitivity analysis method is embedded in an in-house ALM based dynamic response optimizer, which solves three typical dynamic response optimization problems and one practical design problem for a tracked vehicle suspension system. The optimization results are compared with those of the conventional method that uses only exact gradients throughout optimization process. These comparisons show that the hybrid method is more efficient than the conventional method. Especially, in the tracked vehicle suspension system design, the proposed method yields 14 percent reduction of the total CPU time and the number of analyses than the conventional method, while giving similar optimum values.

• Journal of Korean Society of Industrial and Systems Engineering
• /
• v.42 no.3
• /
• pp.1-7
• /
• 2019

It is one of the known methods to obtain the optimal solution using the Ant Colony Optimization Algorithm for the Traveling Salesman Problem (TSP), which is a combination optimization problem. In this paper, we solve the TSP problem by proposing an improved new ant colony optimization algorithm that combines genetic algorithm mutations in existing ant colony optimization algorithms to solve TSP problems in many cities. The new ant colony optimization algorithm provides the opportunity to move easily fall on the issue of developing local optimum values of the existing ant colony optimization algorithm to global optimum value through a new path through mutation. The new path will update the pheromone through an ant colony optimization algorithm. The renewed new pheromone serves to derive the global optimal value from what could have fallen to the local optimal value. Experimental results show that the existing algorithms and the new algorithms are superior to those of existing algorithms in the search for optimum values of newly improved algorithms.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2004.10a
• /
• pp.355-362
• /
• 2004

An efficient boundary-based technique is developed for addressing shape design sensitivity analysis in various problems. An analytical sensitivity formula in the form of a boundary integral is derived based on the continuum formulation for a general functional defined in problems. The formula, which is expressed in terms of the boundary solutions and shape variation vectors, can be conveniently used for gradient computation in a variety of shape design problems. While the sensitivity can be calculated independent of the analysis means, such as the finite element method (FEM) or the boundary element method (BEM), the FEM is used for the analysis in this study because of its popularity and easy-to-use features. The advantage of using a boundary-based method is that the shape variation vectors are needed only on the boundary, not over the whole domain. The boundary shape variation vectors are conveniently computed by using finite perturbations of the shape geometry instead of complex analytical differentiation of the geometry functions. The supercavitating flow problem and fillet problem are chosen to illustrate the efficiency of the proposed methodology. Implementation issues for the sensitivity analysis and optimization procedure are also addressed in these problems.

• Journal of the Korea Academia-Industrial cooperation Society
• /
• v.19 no.3
• /
• pp.630-637
• /
• 2018

Harmony search (HS) is a recently developed metaheuristic optimization algorithm. HS is inspired by the process of musical improvisation and repeatedly searches for the optimal solution using three operations: random selection, memory recall (or harmony memory consideration), and pitch adjustment. HS has been applied by many researchers in various fields. The increasing complexity of real-world optimization problems has created enormous challenges for the current technique, and improved techniques of optimization algorithms and HS are required. We propose an improved clustering harmony search (ICHS) that uses a clustering technique to group solutions in harmony memory based on their objective function values. The proposed ICHS performs modified harmony memory consideration in which decision variables of solutions in a high-ranked cluster have higher probability of being selected than those in a low-ranked cluster. The ICHS is demonstrated in various optimization problems, including mathematical benchmark functions and water distribution system pipe design problems. The results show that the proposed ICHS outperforms other improved versions of HS.

• Computers and Concrete
• /
• v.14 no.4
• /
• pp.445-462
• /
• 2014

To solve structural optimization problems, it is necessary to integrate a structural analysis package and an optimization package. There have been many packages that can be employed to analyze reinforced concrete plane frames. However, because most structural analysis packages suffer from closeness of systems, it is very difficult to integrate them with optimization packages. To overcome the difficulty, we proposed a possible alternative, DAMDO, which integrates Design, Analysis, Modeling, Definition, and Optimization phases into an integration environment as follows. (1) Design: first generate many possible structural design alternatives. Each design alternative consists of many design variables X. (2) Analysis: employ the structural analysis software to analyze all structural design alternatives to obtain their internal forces and displacements. They are the response variables Y. (3) Modeling: employ artificial neural networks to build the models Y=f(X) to obtain the relationship functions between the design variables X and the response variables Y. (4) Definition: employ the design variables X and the response variables Y to define the objective function and constraint functions. (5) Optimization: employ the optimization software to solve the optimization problem consisting of the objective function and the constraint functions to produce the optimum design variables. The RC frame optimization problem was examined to evaluate the DAMDO approach, and the empirical results showed that it can be solved by the approach.

• Proceedings of the Korean Society of Precision Engineering Conference
• /
• 2004.10a
• /
• pp.1256-1261
• /
• 2004

Nonlinear Response Optimization using Equivalent Static Loads (NROESL) method/algorithm is proposed to perform optimization of non-linear response structures. It is more expensive to carry out nonlinear response optimization than linear response optimization. The conventional method spends most of the total design time on nonlinear analysis. Thus, the NROESL algorithm makes the equivalent static load cases for each response and repeatedly performs linear response optimization and uses them as multiple loading conditions. The equivalent static loads are defined as the loads in the linear analysis, which generates the same response field as those in non-linear analysis. The algorithm is validated for the convergence and the optimality. The function satisfies the descent condition at each cycle and the NROESL algorithm converges. It is mathematically validated that the solution of the algorithm satisfies the Karush-Kuhn-Tucker necessary condition of the original nonlinear response optimization problem. The NROESL algorithm is applied to two structural problems. Conventional optimization with sensitivity analysis using the finite difference method is also applied to the same examples. The results of the optimizations are compared. The proposed method is very efficient and derives good solutions.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.29 no.9 s.240
• /
• pp.1243-1252
• /
• 2005

A current trend of design methodologies is to make engineers objectify or automate the decision-making process. Numerical optimization is an example of such technologies. However, in numerical optimization, the uncertainties are uncontrollable to efficiently objectify or automate the process. To better manage these uncertainties, the Taguchi method, reliability-based optimization and robust optimization are being used. To obtain the target performance with the maximum robustness is the main functional requirement of a mechanical system. In this research, a design procedure for global robust optimization is developed based on the kriging and global optimization approaches. The DACE modeling, known as the one of Kriging interpolation, is introduced to obtain the surrogate approximation model of the function. Robustness is determined by the DACE model to reduce real function calculations. The simulated annealing algorithm of global optimization methods is adopted to determine the global robust design of a surrogated model. As the postprocess, the first order second-moment approximation method is applied to refine the robust optimum. The mathematical problems and the MEMS design problem are investigated to show the validity of the proposed method.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.27 no.8
• /
• pp.1353-1362
• /
• 2003

This paper considers a simultaneous optimization problem of structure and control systems. The problem is generally formulated as a non-convex optimization problem for the design parameters of mechanical structure and controller. Therefore, it is not easy to obtain the global solutions for practical problems. In this paper, we parameterize all design parameters of the mechanical structure such that the parameters work in the control system as decentralized static output feedback gains. Using this parameterization, we have formulated a simultaneous optimization problem in which the design specification is defined by the Η$_2$and Η$\_$$\infty$/ norms of the closed loop transfer function. So as to lead to a convex problem we approximate the nonlinear terms of design parameters to the linear terms. Then, we propose a convex optimization method that is based on linear matrix inequality (LMI). Using this method, we can surely obtain suboptimal solution for the design specification. A numerical example is given to illustrate the effectiveness of the proposed method.

• Transactions of the Korean Society of Automotive Engineers
• /
• v.23 no.6
• /
• pp.583-590
• /
• 2015

Automobile crash optimization is nonlinear dynamic response structural optimization that uses highly nonlinear crash analysis in the time domain. The equivalent static loads (ESLs) method has been proposed to solve such problems. The ESLs are the static load sets generating the same displacement field as that of nonlinear dynamic analysis. Linear static response structural optimization is employed with the ESLs as multiple loading conditions. Nonlinear dynamic analysis and linear static structural optimization are repeated until the convergence criteria are satisfied. Nonlinear dynamic crash analysis for frontal analysis may not have boundary conditions, but boundary conditions are required in linear static response optimization. This study proposes a method to use the inertia relief method to overcome the mismatch. An optimization problem is formulated for the design of an automobile frontal structure and solved by the proposed method.