In order to overcome the difficulties caused by singular optima, in the present paper, a new method for the solutions of structural topology optimization problems is proposed. The distinctive feature of this method is...In order to overcome the difficulties caused by singular optima, in the present paper, a new method for the solutions of structural topology optimization problems is proposed. The distinctive feature of this method is that instead of solving the original optimization problem directly, we turn to seeking the solutions of a sequence of approximated problems which are formulated by relaxing the constraints of the original problem to some extent. The approximated problem can be solved efficiently by employing the algorithms developed for sizing optimization problems because its solution is not singular. It can also be proved that when the relaxation parameter is tending to zero, the solution of the approximated problem will converge to the solution of the original problem uniformly. Numerical examples illustrate the effectiveness and validity of the present approach. Results are also compared with those obtained by traditional methods.展开更多
In this paper, we are presenting a new vector order, a solution to the open problem of the generalization of mathematical morphology to multicomponent images and multidimensional data. This approach uses the paradigm ...In this paper, we are presenting a new vector order, a solution to the open problem of the generalization of mathematical morphology to multicomponent images and multidimensional data. This approach uses the paradigm of P–order. Its primary principle consists, first in partitioning the multi-component image in the attribute space by a classification method in different numbers of classes, and then the vector attributes are ordered within each class (intra-order-class). And finally the classes themselves are ordered in turn from their barycenter (inter-class order). Thus, two attribute vectors (or colors) whatever, belonging to the vector image can be compared. Provided with this relation of order, vectors attributes of a multivariate image define a complete lattice ingredient necessary for the definition of the various morphological operators. In fact, this method creates a strong close similarity between vectors in order to move towards an order of the same principle as defined in the set of real numbers. The more the number of classes increases, the more the colors of the same class are similar and therefore the absolute adaptive referent tends to be optimal. On the other hand, the more the class number decreases or equals two, the more our approach tends towards the hybrid order developed previously. The proposed order has been implemented on different morphological operators through different multicomponent images. The fundamental robustness of our approach and that relating to noise have been tested. The results on the gradient, Laplacian and Median filter operators show the performance of our new order.展开更多
In this paper, we use the cycle basis from graph theory to reduce the size of the decision variable space of optimal network flow problems by eliminating the aggregated flow conservation constraint. We use a minimum c...In this paper, we use the cycle basis from graph theory to reduce the size of the decision variable space of optimal network flow problems by eliminating the aggregated flow conservation constraint. We use a minimum cost flow problem and an optimal power flow problem with generation and storage at the nodes to demonstrate our decision variable reduction method.The main advantage of the proposed technique is that it retains the natural sparse/decomposable structure of network flow problems. As such, the reformulated problems are still amenable to distributed solutions. We demonstrate this by proposing a distributed alternating direction method of multipliers(ADMM)solution for a minimum cost flow problem. We also show that the communication cost of the distributed ADMM algorithm for our proposed cycle-based formulation of the minimum cost flow problem is lower than that of a distributed ADMM algorithm for the original arc-based formulation.展开更多
Active control of a flexible cantilever plate with multiple time delays is investigated using the discrete optimal control method. A controller with multiple time delays is presented. In this controller, time delay ef...Active control of a flexible cantilever plate with multiple time delays is investigated using the discrete optimal control method. A controller with multiple time delays is presented. In this controller, time delay effect is incorporated in the mathematical model of the dynamic system throughout the control design and no approximations and assumptions are made in the controller derivation, so the system stability is easily guaranteed. Furthermore, this controller is available for both small time delays and large time delays. The feasibility and efficiency of the proposed controller are verified through numerical simulations in the end of this paper.展开更多
Particle swarm optimization(PSO)is a stochastic computation tech-nique that has become an increasingly important branch of swarm intelligence optimization.However,like other evolutionary algorithms,PSO also suffers fr...Particle swarm optimization(PSO)is a stochastic computation tech-nique that has become an increasingly important branch of swarm intelligence optimization.However,like other evolutionary algorithms,PSO also suffers from premature convergence and entrapment into local optima in dealing with complex multimodal problems.Thus this paper puts forward an adaptive multi-updating strategy based particle swarm optimization(abbreviated as AMS-PSO).To start with,the chaotic sequence is employed to generate high-quality initial particles to accelerate the convergence rate of the AMS-PSO.Subsequently,according to the current iteration,different update schemes are used to regulate the particle search process at different evolution stages.To be specific,two different sets of velocity update strategies are utilized to enhance the exploration ability in the early evolution stage while the other two sets of velocity update schemes are applied to improve the exploitation capability in the later evolution stage.Followed by the unequal weightage of acceleration coefficients is used to guide the search for the global worst particle to enhance the swarm diversity.In addition,an auxiliary update strategy is exclusively leveraged to the global best particle for the purpose of ensuring the convergence of the PSO method.Finally,extensive experiments on two sets of well-known benchmark functions bear out that AMS-PSO outperforms several state-of-the-art PSOs in terms of solution accuracy and convergence rate.展开更多
This paper proposes the concepts of generalized αk-major efficient solutions and generalized αk- major optimal solutions for multi-objective programming, and studies their some important properties.
基金The project supported by the National Natural Science Foundation of China under project No.19572023
文摘In order to overcome the difficulties caused by singular optima, in the present paper, a new method for the solutions of structural topology optimization problems is proposed. The distinctive feature of this method is that instead of solving the original optimization problem directly, we turn to seeking the solutions of a sequence of approximated problems which are formulated by relaxing the constraints of the original problem to some extent. The approximated problem can be solved efficiently by employing the algorithms developed for sizing optimization problems because its solution is not singular. It can also be proved that when the relaxation parameter is tending to zero, the solution of the approximated problem will converge to the solution of the original problem uniformly. Numerical examples illustrate the effectiveness and validity of the present approach. Results are also compared with those obtained by traditional methods.
文摘In this paper, we are presenting a new vector order, a solution to the open problem of the generalization of mathematical morphology to multicomponent images and multidimensional data. This approach uses the paradigm of P–order. Its primary principle consists, first in partitioning the multi-component image in the attribute space by a classification method in different numbers of classes, and then the vector attributes are ordered within each class (intra-order-class). And finally the classes themselves are ordered in turn from their barycenter (inter-class order). Thus, two attribute vectors (or colors) whatever, belonging to the vector image can be compared. Provided with this relation of order, vectors attributes of a multivariate image define a complete lattice ingredient necessary for the definition of the various morphological operators. In fact, this method creates a strong close similarity between vectors in order to move towards an order of the same principle as defined in the set of real numbers. The more the number of classes increases, the more the colors of the same class are similar and therefore the absolute adaptive referent tends to be optimal. On the other hand, the more the class number decreases or equals two, the more our approach tends towards the hybrid order developed previously. The proposed order has been implemented on different morphological operators through different multicomponent images. The fundamental robustness of our approach and that relating to noise have been tested. The results on the gradient, Laplacian and Median filter operators show the performance of our new order.
基金supported by National Science Foundation award ECCS-1653838
文摘In this paper, we use the cycle basis from graph theory to reduce the size of the decision variable space of optimal network flow problems by eliminating the aggregated flow conservation constraint. We use a minimum cost flow problem and an optimal power flow problem with generation and storage at the nodes to demonstrate our decision variable reduction method.The main advantage of the proposed technique is that it retains the natural sparse/decomposable structure of network flow problems. As such, the reformulated problems are still amenable to distributed solutions. We demonstrate this by proposing a distributed alternating direction method of multipliers(ADMM)solution for a minimum cost flow problem. We also show that the communication cost of the distributed ADMM algorithm for our proposed cycle-based formulation of the minimum cost flow problem is lower than that of a distributed ADMM algorithm for the original arc-based formulation.
基金the National Natural Science Foundation of China (Nos. 10772112 and 10472065)the KeyProject of Ministry of Education of China (No. 107043)the Specialized Research Fund for the Doctoral Program ofHigher Education of China (No. 20070248032).
文摘Active control of a flexible cantilever plate with multiple time delays is investigated using the discrete optimal control method. A controller with multiple time delays is presented. In this controller, time delay effect is incorporated in the mathematical model of the dynamic system throughout the control design and no approximations and assumptions are made in the controller derivation, so the system stability is easily guaranteed. Furthermore, this controller is available for both small time delays and large time delays. The feasibility and efficiency of the proposed controller are verified through numerical simulations in the end of this paper.
基金sponsored by the Natural Science Foundation of Xinjiang Uygur Autonomous Region(No.2022D01A16)the Program of the Applied Technology Research and Development of Kashi Prefecture(No.KS2021026).
文摘Particle swarm optimization(PSO)is a stochastic computation tech-nique that has become an increasingly important branch of swarm intelligence optimization.However,like other evolutionary algorithms,PSO also suffers from premature convergence and entrapment into local optima in dealing with complex multimodal problems.Thus this paper puts forward an adaptive multi-updating strategy based particle swarm optimization(abbreviated as AMS-PSO).To start with,the chaotic sequence is employed to generate high-quality initial particles to accelerate the convergence rate of the AMS-PSO.Subsequently,according to the current iteration,different update schemes are used to regulate the particle search process at different evolution stages.To be specific,two different sets of velocity update strategies are utilized to enhance the exploration ability in the early evolution stage while the other two sets of velocity update schemes are applied to improve the exploitation capability in the later evolution stage.Followed by the unequal weightage of acceleration coefficients is used to guide the search for the global worst particle to enhance the swarm diversity.In addition,an auxiliary update strategy is exclusively leveraged to the global best particle for the purpose of ensuring the convergence of the PSO method.Finally,extensive experiments on two sets of well-known benchmark functions bear out that AMS-PSO outperforms several state-of-the-art PSOs in terms of solution accuracy and convergence rate.
文摘This paper proposes the concepts of generalized αk-major efficient solutions and generalized αk- major optimal solutions for multi-objective programming, and studies their some important properties.
