• Korean Journal of Computational Design and Engineering
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• v.15 no.1
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• pp.24-32
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• 2010

This paper introduces a B-spline based branch & bound algorithm for global optimization. The branch & bound is a well-known algorithm paradigm for global optimization, of which key components are the subdivision scheme and the bound calculation scheme. For this, we consider the B-spline hypervolume to approximate an objective function defined in a design space. This model enables us to subdivide the design space, and to compute the upper & lower bound of each subspace where the bound calculation is based on the LHS sampling points. We also describe a search tree to represent the searching process for optimal solution, and explain iteration steps and some conditions necessary to carry out the algorithm. Finally, the performance of the proposed algorithm is examined on some test problems which would cover most difficulties faced in global optimization area. It shows that the proposed algorithm is complete algorithm not using heuristics, provides an approximate global solution within prescribed tolerances, and has the good possibility for large scale NP-hard optimization.

• ETRI Journal
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• v.45 no.1
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• pp.119-130
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• 2023

We propose a quantized gradient search algorithm that can achieve global optimization by monotonically reducing the quantization step with respect to time when quantization is composed of integer or fixed-point fractional values applied to an optimization algorithm. According to the white noise hypothesis states, a quantization step is sufficiently small and the quantization is well defined, the round-off error caused by quantization can be regarded as a random variable with identically independent distribution. Thus, we rewrite the searching equation based on a gradient descent as a stochastic differential equation and obtain the monotonically decreasing rate of the quantization step, enabling the global optimization by stochastic analysis for deriving an objective function. Consequently, when the search equation is quantized by a monotonically decreasing quantization step, which suitably reduces the round-off error, we can derive the searching algorithm evolving from an optimization algorithm. Numerical simulations indicate that due to the property of quantization-based global optimization, the proposed algorithm shows better optimization performance on a search space to each iteration than the conventional algorithm with a higher success rate and fewer iterations.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.4
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• pp.671-684
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• 2001

Several design problems of composite structures are studied via a global optimizer based on attraction regions. MSC/NASTRAN is adopted for static and eigenvalue analysis. The method of modified feasible direction in DOT is used for local optimization. Through the review of global optimization algorithms, the triangular patch algorithm is selected because the algorithm is known to be efficient, robust and powerful for general nonlinear optimization problems. For general applicability, various mechanical properties are considered as design objectives; strain energy, eigenvalue, weight, displacement, and buckling load. In all cases considered, the triangular patch algorithm results in a lot of optimum points and useful design patterns, that are not easy by local algorithms or conventional global algorithms can be determined.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.11
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• pp.1809-1814
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• 2003

Differential evolution (DE) algorithm is presented and applied to global optimization in this research. DE suggested initially fur the solution to Chebychev polynomial fitting problem is similar to genetic algorithm(GA) including crossover, mutation and selection process. However, differential evolution algorithm is simpler than GA because it uses a vector concept in populating process. And DE turns out to be converged faster than CA, since it employs the difference information as pseudo-sensitivity In this paper, a trial vector and its control parameters of DE are examined and unconstrained optimization problems of highly nonlinear multimodal functions are demonstrated. To illustrate the efficiency of DE, convergence rates and robustness of global optimization algorithms are compared with those of simple GA.

• Smart Structures and Systems
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• v.18 no.3
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• pp.425-448
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• 2016

In this paper, a new Pigeon Colony Algorithm (PCA) based on the features of a pigeon colony flying is proposed for solving global numerical optimization problems. The algorithm mainly consists of the take-off process, flying process and homing process, in which the take-off process is employed to homogenize the initial values and look for the direction of the optimal solution; the flying process is designed to search for the local and global optimum and improve the global worst solution; and the homing process aims to avoid having the algorithm fall into a local optimum. The impact of parameters on the PCA solution quality is investigated in detail. There are low-dimensional functions, high-dimensional functions and systems of nonlinear equations that are used to test the global optimization ability of the PCA. Finally, comparative experiments between the PCA, standard genetic algorithm and particle swarm optimization were performed. The results showed that PCA has the best global convergence, smallest cycle indexes, and strongest stability when solving high-dimensional, multi-peak and complicated problems.

• Kyungpook Mathematical Journal
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• v.64 no.1
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• pp.95-111
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• 2024

The filled function method is useful in solving unconstrained global optimization problems. However, depending on the type of function, and parameters used, there are limitations that cause difficultiies in implemenations. Exponential and logarithmic functions lead to the overflow effect, requiring iterative adjustment of the parameters. This paper proposes a polynomial-filled function that has a general form, is non-exponential, nonlogarithmic, non-parameteric, and continuously differentiable. With this newly proposed filled function, the aforementioned shortcomings of the filled function method can be overcome. To confirm the superiority of the proposed filled function algorithm, we apply it to a set of unconstrained global optimization problems. The data derived by numerical implementation shows that the proposed filled function can be used as an alternative algorithm when solving unconstrained global optimization problems.

• Journal of Computing Science and Engineering
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• v.8 no.4
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• pp.199-206
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• 2014

The ant colony optimization (ACO) algorithm is a new heuristic algorithm that offers good robustness and searching ability. With in-depth exploration, the ACO algorithm exhibits slow convergence speed, and yields local optimization solutions. Based on analysis of the ACO algorithm and the genetic algorithm, we propose a novel hybrid genetic ant colony optimization (NHGAO) algorithm that integrates multi-population strategy, collaborative strategy, genetic strategy, and ant colony strategy, to avoid the premature phenomenon, dynamically balance the global search ability and local search ability, and accelerate the convergence speed. We select the traveling salesman problem to demonstrate the validity and feasibility of the NHGAO algorithm for solving complex optimization problems. The simulation experiment results show that the proposed NHGAO algorithm can obtain the global optimal solution, achieve self-adaptive control parameters, and avoid the phenomena of stagnation and prematurity.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.6
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• pp.1008-1015
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• 2002

This paper proposes a combinatorial method to compute the global and local solutions of optimization problem. The present hybrid algorithm is the synthesis of a genetic algorithm and a local concentrate search algorithm (simplex method). The hybrid algorithm is not only faster than the standard genetic algorithm, but also gives a more accurate solution. In addition, this algorithm can find both the global and local optimum solutions. An optimization result is presented to demonstrate that the proposed approach successfully focuses on the advantages of global and local searches. Three numerical examples are also presented in this paper to compare with conventional methods.

• Proceedings of the KSME Conference
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• 2001.06c
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• pp.537-542
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• 2001

In recent engineering, the designer has become more and more dependent on computer simulation. But defining exact model using computer simulation is too expensive and time consuming in the complicate systems. Thus, designers often use approximation models, which express the relation between design variables and response variables. These models are called metamodel. In this paper, we introduce one of the metamodel, named Kriging. This model employs an interpolation scheme and is developed in the fields of spatial statistics and geostatistics. This class of interpolating model has flexibility to model response data with multiple local extreme. By reason of this multi modality, we can't use any gradient-based optimization algorithm to find global extreme value of this model. Thus we have to introduce global optimization algorithm. To do this, we introduce DE(Differential Evolution). DE algorithm is developed by Ken Price and Rainer Storn, and it has recently proven to be an efficient method for optimizing real-valued multi-modal objective functions. This algorithm is similar to GA(Genetic Algorithm) in populating points, crossing over, and mutating. But it introduces vector concept in populating process. So it is very simple and easy to use. Finally, we show how we determine Kriging metamodel and find global extreme value through two mathematical examples.

• Journal of information and communication convergence engineering
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• v.13 no.2
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• pp.123-131
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• 2015

Training neural networks is a complex task with great importance in the field of supervised learning. In the training process, a set of input-output patterns is repeated to an artificial neural network (ANN). From those patterns weights of all the interconnections between neurons are adjusted until the specified input yields the desired output. In this paper, a new hybrid algorithm is proposed for global optimization of connection weights in an ANN. Dynamic swarms are shown to converge rapidly during the initial stages of a global search, but around the global optimum, the search process becomes very slow. In contrast, the gradient descent method can achieve faster convergence speed around the global optimum, and at the same time, the convergence accuracy can be relatively high. Therefore, the proposed hybrid algorithm combines the dynamic particle swarm optimization (DPSO) algorithm with the backpropagation (BP) algorithm, also referred to as the DPSO-BP algorithm, to train the weights of an ANN. In this paper, we intend to show the superiority (time performance and quality of solution) of the proposed hybrid algorithm (DPSO-BP) over other more standard algorithms in neural network training. The algorithms are compared using two different datasets, and the results are simulated.