Filled Function Algorithm Research Articles

A new filled function method for solving constrained global optimization problems

ABSTRACT Filled function methods have been considered as effective algorithms for solving global optimization problems. However, their effectiveness is greatly affected by the selection of parameters, the noncontinuous or non-differentiable properties of the constructed filled function. In addition, many of the constructed filled functions are only for unconstrained optimization problems, and they are unable to solve constrained optimization problems. In this paper, a new filled function is constructed for solving constrained global optimization problems. The new filled function has only one parameter which needs to be adjusted, and, when the objective functions and constrained functions are all continuously differentiable functions, the constructed filled function is also a continuously differentiable function. Then, the classical local optimization methods can be used to find a better minimum of the proposed filled function and a few parameter adjustments are needed. At last, a new filled function algorithm for constrained global optimization is developed based on the proposed filled function. The new algorithm is applied to several test examples. The results of the numerical experiments show that the new filled function algorithm is effective and efficient.

A class of one-parameter filled functions with the same local minima as the objective function for global optimization problems

As an effective global optimization method, the filled function algorithm obtains the optimal solution of optimization problems by alternately minimizing the objective function and filled function. One development direction of the filled function method is to construct the filled function with good properties, which directly affects the efficiency of the algorithm and has attracted the attention of scholars. This paper presents a class of one-parameter filled function that is easy to adjust. It is proved theoretically that the filled function is continuously differentiable and has the same local minimizers as the objective function, and these minimizers are all better than the current local minimizer of the objective function. Meanwhile, some natures of the constructed filled function are conducted as followed by a new algorithm is presented. The new filled function algorithm optimizes the iterative framework of the conventional filled function method, improving the efficiency and decreasing the computational cost. The numerical experiments of the new algorithm on several optimization issues are reported with satisfactory computational results, verifying the feasibility and efficiency of the algorithm.

A novel single-parameter continuously differentiable filled function for global optimization

ABSTRACT The filled function approach is an effective global optimization method. The properties of the filled function directly affect the efficiency of the algorithm and have been discussed by many scholars, resulting in various new forms of filled functions. However, most of existing filled functions are not continuously differentiable and have parameters that are difficult to adjust. To remedy this problem, a new continuously differentiable filled function with an easily adjustable parameter is constructed. According to the theoretical analysis of the filled function, a new easy-to-implement filled function algorithm is designed utilizing the efficient local search algorithm based on gradient information. Numerical experiments show that the proposed filled function algorithm is a feasible and effective global optimization algorithm with less computational cost.

Numerical algorithm for hypersonic vehicle optimal flight control

We consider a hypersonic vehicle optimal flight control problem. The problem is modeled as an optimal control problem of switched systems (OCPSS), which can become a parameter optimization problem (POP). Following that, to achieve the globally optimal solution of the POP, an improved continuous filled function (CFF) algorithm including one adjusting parameter is proposed based on a penalty function, in which the CFF is differentiable, excludes logarithmic terms or exponential terms, and does not require to minimize the cost function. Numerical results show that the proposed algorithm is effective.

A New Parameterless Filled Function Method for Global Optimization

The filled function method is an effective way to solve global optimization problems. However, its effectiveness is greatly affected by the selection of parameters, and the non-continuous or non-differentiable properties of the constructed filled function. To overcome the above-mentioned drawbacks, in this paper, a new parameterless filled function is proposed that is continuous and differentiable. Theoretical proofs have been made to show the properties of the proposed filled function. Based on the new filled function, a filled function algorithm is proposed to solve unconstrained global optimization problems. Experiments are carried out on widely used test problems and an application of supply chain problems with equality and inequality constraints. The numerical results show that the proposed filled function is effective.

Finding global minima with an inflection point-based filled function algorithm

Finding global minima with an inflection point-based filled function algorithm

A novel convergent filled function algorithm for multi-dimensional global optimization

As we all know, the filled function method as an effective algorithm to solve global optimization problems can overcome the defect that the non-linear algorithm is trapped in the local minimizer and cannot jump to attach the global minimizer, which has attracted the attention of researchers. However, when solving multi-dimensional global optimization problems, the filled function often lacks good properties such as mandatory, convexity and continuity, which makes the conventional filled function algorithm to always encounter the difficulty that its convergence cannot be guaranteed. In view of this, a novel convergent filled function algorithm for multi-dimensional global optimization is proposed. In this algorithm, by the way of the coordinates rotate, the multi-dimensional global optimization problem is transformed into several one-dimensional sub-problems, and then the new filled function with good properties is constructed to solve the one-dimensional sub-problem, which leads to attachment of the convergence in algorithm. Finally, compared with the existing algorithms on test optimization problems in NETLIB library, the effectiveness of the algorithm is verified by numerical experiments.

Filled function method to optimize supply chain transportation costs

<p style='text-indent:20px;'>The transportation-based supply chain model can be formulated as the constrained nonlinear programming problems. When solving such problems, the classic optimization algorithms are often limited to local minimums, causing the difficulty to find the global optimal solution. Aiming at this problem, a filled function method with a single parameter is given to cross the local minimum. Based on the characteristics of the filled function, a new filled function algorithm that can obtain the global optimal solution is designed. Numerical experiments verify the feasibility and effectiveness of the algorithm. Finally, the filled function algorithm is applied to the solution of supply chain problems, and the numerical results show that the algorithm can also address decision-making problems of supply chain transportation effectively.</p>

Robust Optimization of PMLSM Based on a New Filled Function Algorithm With a Sigma Level Stability Convergence Criterion

Traditional design optimization methods for permanent magnet linear synchronous motor (PMLSM) always pursuit the optimal result without considering the influence of uncertainties (manufacturing errors, use wear, etc.), which will result in big fluctuations for the stability of motor thrust performance. This article proposes a new filled function algorithm (NFFA) to improve the stability of PMLSM. It searches for the structure parameters that not only lay in the smooth area of thrust ripple distribution but also satisfy the thrust ripple constraints under the effect of uncertainties. First, an analytical model of thrust ripple is established for the next-step optimization. Second, a sigma level stability criterion is proposed, which will be used to judge the robustness of optimal thrust ripple under uncertainties, and a new global robust algorithm NFFA is studied to realize the stability of thrust ripple by managing the sigma level stability criterion as the convergence criterion of traditional filled function optimization algorithm (TFFA). Third, the NFFA is used to optimize the thrust ripple of PMLSM based on the analytical model. The optimization results are proven to be stable and superior compared with other methods, such as TFFA, Taguchi robust optimization method, and design for six sigma method. Finally, the experiments confirm the feasibility and validity of the proposed method.

A novel method for global minimization combined filled function method and dimensionality reduction technique

This paper introduces a new filled function method based on the dimensionality reduction technique for the global minimization problem. By utilizing the so called α - dense curves, we first transform the original function of n-variables into a single variable function, and then minimize the transformed function with the filled function method. The constructed filled function contains just one parameter which can be adjusted readily during the iterative process. The theoretical properties of the filled function are discussed, and the filled function algorithm is given. At last, a few numerical experiments are included.

A Filled Function for Non-smooth Box-constrained Global Optimization and Its Application

This paper constructs a filled function for non-smooth box-constrained global minimization, investigates its properties and designs a corresponding algorithm. The constructed new filled function contains only one parameter and it has more merits than those with several parameters. Moreover, the iterative operations of the proposed filled function algorithm can be easily implemented. we also perform numerical experiments to show the efficiency of the proposed approach.

Optimal switching control for drug therapy process in cancer chemotherapy

In this paper, the drug therapy problem in cancer chemotherapy is formulated as an optimal control problem of switched systems. In this problem, the modes switch under state-dependent. This is different from the existing optimal control problem of switched systems, in which the modes switch under time-dependent. Thus, the existing optimal control approaches of switched systems with time-dependent switching can not directly used to solve this Problem, and a new numerical computation method is required to develop for solving such problem. Firstly, based on introducing a binary function, relaxing the binary functions and including a penalty term on the relaxation, we obtain an equivalent optimal control problem of constrained nonlinear system. By using the time-scaling transformation, the smoothing technique, and the idea of l1 penalty function method, the equivalent optimal control problem is transformed into a nonlinear parameter optimization problem. Then, a gradient-based continuous filled function algorithm is developed for solving the nonlinear parameter optimization problem. Finally, a numerical example is used to illustrate our method is low time-consuming, has faster convergence speed, and yields a better objective function value than the existing algorithms.

Particle Swarm Optimization for Continuous Function Optimization Problems

In this paper, particle swarm optimization is proposed for finding the global minimum of continuous functions and experimented on benchmark test problems. Particle swarm optimization applied on 21 benchmark test functions, and its solutions are compared to those former proposed approaches: ant colony optimization, a heuristic random optimization, the discrete filled function algorithm, an adaptive random search, dynamic random search technique and random selection walk technique. The implementation of the PSO on several test problems are reported with satisfactory numerical results when compared to previously proposed heuristic techniques. PSO is proved to be successful approach to solve continuous optimization problems.

Constrained Global Minimization with Filled Function Method

This paper presents a filled function algorithm for constrained global minimization problems. The devised filled function contains only one parameter which could be adjusted easily during the iterations. The properties of the proposed filled function are discussed, and a filled function algorithm is given. At the end of the paper, a few numerical examples are included to show the effectiveness of the filled function algorithm.

LMIRA: Large Margin Instance Reduction Algorithm

Abstract In instance-based learning, a training set is given to a classifier for classifying new instances. In practice, not all information in the training set is useful for classifiers. Therefore, it is convenient to discard irrelevant instances from the training set. This process is known as instance reduction, which is an important task for classifiers since through this process the time for classification or training could be reduced. In this paper, we propose a Large Margin Instance Reduction Algorithm, namely LMIRA. LMIRA removes non-border instances and keeps border ones. In the proposed method, the instance reduction process is formulated as a constrained binary optimization problem and then it is solved by employing a filled function algorithm. Instance-based learning algorithms are often confronted with the difficulty of choosing those instances which must be stored to be used during an actual test. Storing too many instances can result in large memory requirements and slow execution. In LMIRA, core of instance reduction process is based on keeping the hyperplane that separates a two-class data and provides large margin separation. LMIRA selects the most representative instances, satisfying both following objectives: high accuracy and reduction rates. The performance has been evaluated on real world data sets from UCI repository by the ten-fold cross-validation method. The results of experiments are compared with state-of-the-art methods, which show the superiority of proposed method in terms of classification accuracy and reduction percentage.

Large symmetric margin instance selection algorithm

In instance-based classifiers, there is a need for storing a large number of samples as a training set. In this paper, we propose a large symmetric margin instance selection algorithm, namely LAMIS. LAMIS removes non-border (interior) instances and keeps border ones. This paper presents an instance selection process through formulating it as a constrained binary optimization problem and solves it by employment filled function algorithm. Instance-based learning algorithms are often confronted with the problem of deciding which instances must be stored for use during an actual test. Storing too many instances can result in large memory requirements and slow execution. In LAMIS, the core of instance selection process is based on keeping the hyperplane that separates a two-class data, to provide large margin separation. LAMIS selects the most representative instances, satisfying both objectives: high accuracy and reduction rates. The performance has been evaluated on real world data sets from UCI repository by the ten-fold cross-validation method. The results of experiments have been compared with state-of-the-art methods, where the overall results, show the superiority of the proposed method in terms of classification accuracy and reduction percentage.

A filled function method for nonlinear systems of equalities and inequalities

In this paper a filled function method is suggested for solving nonlinear systems of equalities and inequalities. Firstly, the original problem is reformulated into an equivalent constrained global optimization problem. Subsequently, a new filled function with one parameter is constructed based on the special characteristics of the reformulated optimization problem. Some properties of the filled function are studied and discussed. Finally, an algorithm based on the proposed filled function for solving nonlinear systems of equalities and inequalities is presented. The objective function value can be reduced by half in each iteration of our filled function algorithm. The implementation of the algorithm on several test problems is reported with numerical results. Mathematical subject classification: 65K05, 90C30.

Identifying a Global Optimizer with Filled Function for Nonlinear Integer Programming

This paper presents a filled function method for finding a global optimizer of integer programming problem. The method contains two phases: the local minimization phase and the filling phase. The goal of the former phase is to identify a local minimizer of the objective function, while the filling phase aims to search for a better initial point for the first phase with the aid of the filled function. A two‐parameter filled function is proposed, and its properties are investigated. A corresponding filled function algorithm is established. Numerical experiments on several test problems are performed, and preliminary computational results are reported.

A new filled function algorithm for constrained global optimization problems

A new filled function with one parameter is proposed for solving constrained global optimization problems without the coercive condition, in which the filled function contains neither exponential term nor fractional term and is easy to be calculated. A corresponding filled function algorithm is established based on analysis of the properties of the filled function. At last, we perform numerical experiments on some typical test problems using the algorithm and the detailed numerical results show that the algorithm is effective.

A discrete filled function algorithm embedded with continuous approximation for solving max-cut problems

In this paper, a discrete filled function algorithm embedded with continuous approximation is proposed to solve max-cut problems. A new discrete filled function is defined for max-cut problems, and properties of the function are studied. In the process of finding an approximation to the global solution of a max-cut problem, a continuation optimization algorithm is employed to find local solutions of a continuous relaxation of the max-cut problem, and then global searches are performed by minimizing the proposed filled function. Unlike general filled function methods, characteristics of max-cut problems are used. The parameters in the proposed filled function need not to be adjusted and are exactly the same for all max-cut problems that greatly increases the efficiency of the filled function method. Numerical results and comparisons on some well known max-cut test problems show that the proposed algorithm is efficient to get approximate global solutions of max-cut problems.