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Browsing by Author "Wan, Wen"

Now showing 1 - 7 of 7
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    An Improved Genetic Algorithm Using a Directional Search
    Wan, Wen; Birch, Jeffrey B. (Virginia Tech, 2009)
    The genetic algorithm (GA), a very powerful tool used in optimization, has been applied in various fields including statistics. However, the general GA is usually computationally intensive, often having to perform a large number of evaluations of an objective function. This paper presents four different versions of computationally efficient genetic algorithms by incorporating several different local directional searches into the GA process. These local searches are based on using the method of steepest descent (SD), the Newton-Raphson method (NR), a derivative-free directional search method (denoted by “DFDS”), and a method that combines SD with DFDS. Some benchmark functions, such as a low-dimensional function versus a high-dimensional function, and a relatively bumpy function versus a very bumpy function, are employed to illustrate the improvement of these proposed methods through a Monte Carlo simulation study using a split-plot design. A real problem related to the multi-response optimization problem is also used to illustrate the improvement of these proposed methods over the traditional GA and over the method implemented in the Design-Expert statistical software package. Our results show that the GA can be improved both in accuracy and in computational efficiency in most cases by incorporating a local directional search into the GA process.
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    An Improved Hybrid Genetic Algorithm with a New Local Search Procedure
    Wan, Wen; Birch, Jeffrey B. (Hindawi, 2013-10-07)
    One important challenge of a hybrid genetic algorithm (HGA) (also called memetic algorithm) is the tradeoff between global and local searching (LS) as it is the case that the cost of an LS can be rather high. This paper proposes a novel, simplified, and efficient HGA with a new individual learning procedure that performs a LS only when the best offspring (solution) in the offspring population is also the best in the current parent population. Additionally, a new LS method is developed based on a three-directional search (TD), which is derivative-free and self-adaptive. The new HGA with two different LS methods (the TD and Neld-Mead simplex) is compared with a traditional HGA. Four benchmark functions are employed to illustrate the improvement of the proposed method with the new learning procedure. The results show that the new HGA greatly reduces the number of function evaluations and converges much faster to the global optimum than a traditional HGA. The TD local search method is a good choice in helping to locate a global “mountain” (or “valley”) but may not perform the Nelder-Mead method in the final fine tuning toward the optimal solution.
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    An Improved Hybrid Genetic Algorithm with a New Local Search Procedure
    Wan, Wen; Birch, Jeffrey B. (Virginia Tech, 2012)
    A hybrid genetic algorithm (HGA) combines a genetic algorithm (GA) with an individual learning procedure. One such learning procedure is a local search technique (LS) used by the GA for refining global solutions. A HGA is also called a memetic algorithm (MA), one of the most successful and popular heuristic search methods. An important challenge of MAs is the trade-off between global and local searching as it is the case that the cost of a LS can be rather high. This paper proposes a novel, simplified, and efficient HGA with a new individual learning procedure that performs a LS only when the best offspring (solution) in the offspring population is also the best in the current parent population. Additionally, a new LS method is developed based on a three-directional search (TD), which is derivative-free and self-adaptive. The new HGA with two different LS methods (the TD and Neld-Mead simplex) is compared with a traditional HGA. Two benchmark functions are employed to illustrate the improvement of the proposed method with the new learning procedure. The results show that the new HGA greatly reduces the number of function evaluations and converges much faster to the global optimum than a traditional HGA. The TD local search method is a good choice in helping to locate a global “mountain” (or “valley”) but may not perform as well as the Nelder-Mead method in the final fine tuning toward the optimal solution.
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    Interaction Analysis of Three Combination Drugs via a Modified Genetic Algorithm
    Wan, Wen; Pei, Xin-Yan; Grant, Steven; Birch, Jeffrey B.; Felthousen, Jessica; Dai, Yun; Fang, Hong-Bin; Tan, Ming; Sun, Shumei (Virginia Tech, 2014)
    Few articles have been written on analyzing and visualizing three-way interactions between drugs. Although it may be quite straightforward to extend a statistical method from two-drugs to three-drugs, it is hard to visually illustrate which dose regions are synergistic, additive, or antagonistic, due to a four-dimensional (4-D) problem of plot- ting three-drug dose regions plus a response. This problem can be converted and solved by showing some dose regions of our interest in a 3-D, three-drug dose regions. We propose to apply a modified genetic algorithm (MGA) to construct the dose regions of interest after fitting the response surface to the interaction index (II) by a semiparametric method, the model robust regression method (MRR). A case study with three anti-cancer drugs in an in vitro experiment is employed to illustrate how to find the dose regions of interest. For example, suppose researchers are interested in visualizing where the synergistic areas with II ≤ 0:4 are in 3-D. After fitting a MRR model to the calculated II, the MGA procedure is used to collect those feasible points that satisfy the estimated values of II ≤ 0:4. All these feasible points are used to construct the approximate dose regions of interest in a 3-D.
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    Semi-Parametric Techniques for Multi-Response Optimization
    Wan, Wen (Virginia Tech, 2007-10-29)
    The multi-response optimization (MRO) problem in response surface methodology (RSM) is quite common in industry and in many other areas of science. During the optimization stage in MRO, the desirability function method, one of the most flexible and popular MRO approaches and which has been utilized in this research, is a highly nonlinear function. Therefore, we have proposed use of a genetic algorithm (GA), a global optimization tool, to help solve the MRO problem. Although a GA is a very powerful optimization tool, it has a computational efficiency problem. To deal with this problem, we have developed an improved GA by incorporating a local directional search into a GA process. In real life, practitioners usually prefer to identify all of the near-optimal solutions, or all feasible regions, for the desirability function, not just a single or several optimal solutions, because some feasible regions may be more desirable than others based on practical considerations. We have presented a procedure using our improved GA to approximately construct all feasible regions for the desirability function. This method is not limited by the number of factors in the design space. Before the optimization stage in MRO, appropriate fitted models for each response are required. The parametric approach, a traditional RSM regression technique, which is inflexible and heavily relies on the assumption of well-estimated models for the response of interests, can lead to highly biased estimates and result in miscalculating optimal solutions when the user's model is incorrectly specified. Nonparametric methods have been suggested as an alternative, yet they often result in highly variable estimates, especially for sparse data with a small sample size which are the typical properties of traditional RSM experiments. Therefore, in this research, we have proposed use of model robust regression 2 (MRR2), a semi-parametric method, which combines parametric and nonparametric methods. This combination does combine the advantages from each of the parametric and nonparametric methods and, at the same time, reduces some of the disadvantages inherent in each.
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    A Semiparametric Technique for the Multi-Response Optimization Problem
    Wan, Wen; Birch, Jeffrey B. (Virginia Tech, 2009)
    Multi-response optimization (MRO) in response surface methodology (RSM) is quite common in applications. Before the optimization phase, appropriate fitted models for each response are required. A common problem is model misspecification and occurs when any of the models built for the responses are misspecified resulting in an erroneous optimal solution. The model robust regression technique, a semiparametric method, has been shown to be more robust to misspecification than either parametric or nonparamet- ric methods. In this study, we propose the use of model robust regression to improve the quality of model estimation and adapt its fits of each response to the desirability function approach, one of the most popular MRO techniques. A case study and simulation studies are presented to illustrate the procedure and to compare the semiparametric method with the parametric and nonparametric methods. The results show that model robust regression performs much better than the other two methods in terms of model comparison criteria in most situations during the modeling stage. In addition, the simulated optimization results for model robust regression are more reliable during the optimization stage.
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    Using a Modified Genetic Algorithm to Find Feasible Regions of a Desirability Function
    Wan, Wen; Birch, Jeffrey B. (Virginia Tech, 2011)
    The multi-response optimization (MRO) problem in response surface methodology is quite common in applications. Most of the MRO techniques such as the desirability function method by Derringer and Suich are utilized to find one or several optimal solutions. However, in fact, practitioners usually prefer to identify all of the near-optimal solutions, or all feasible regions, because some feasible regions may be more desirable than others based on practical considerations. In this paper, with benefits from the stochastic property of a genetic algorithm (GA), we present an innovative procedure using a modified GA (MGA), a computational efficient GA with a local directional search incorporated into the GA process, to approximately generate all feasible regions for the desirability function without the limitation of the number of factors in the design space. The procedure is illustrated through a case study. The MGA is also compared to other commonly used methods for determining the set of feasible regions. Using Monte Carlo simulations with two benchmark functions and a case study, it is shown that the MGA can more efficiently determine the set of feasible regions than the GA, grid methods, and the Nelder-Mead simplex algorithm.