A new approach based on support vector machine for solving stochastic optimization

Making decision usually occurs in the state of being uncertain. These kinds of problems often expresses in a formula as optimization problems. It is desire for decision makers to find a solution for optimization problems. Typically, solving optimization problems in uncertain environment is difficult. This paper proposes a new hybrid intelligent algorithm to solve a kind of stochastic optimization i.e. dependent chance programming (DCP) model. In order to speed up the solution process, we used support vector machine regression (SVM regression) to approximate chance functions which is the probability of a sequence of uncertain event occurs based on the training data generated by the stochastic simulation. The proposed algorithm consists of three steps: (1) generate data to estimate the objective function, (2) utilize SVM regression to reveal a trend hidden in the data (3) apply genetic algorithm (GA) based on SVM regression to obtain an estimation for the chance function. Numerical example is presented to show the ability of algorithm in terms of time-consuming and precision.

Benchmark generation algorithm for stochastic mixed model assembly shop simulation and optimization

The Operations Research (OR) community have defined many deterministic manufacturing control problems mainly focused on scheduling. Well-defined benchmark problems provide a mechanism for communication of the effectiveness of different optimization algorithms. Manufacturing problems within industry are stochastic and complex. Common features of these problems include: variable demand, machine part specific breakdown patterns, part machine specific process durations, continuous production, Finished Goods Inventory (FGI) buffers, bottleneck machines and limited production capacity. Discrete Event Simulation (DES) is a commonly used tool for studying manufacturing systems of realistic complexity. There are few reports of detail-rich benchmark problems for use within the simulation optimization community that are as complex as those faced by production managers. This work details an algorithm that can be used to create single and multistage production control problems. The reported software implementation of the algorithm generates text files in eXtensible Markup Language (XML) format that are easily edited and understood as well as being cross-platform compatible. The distribution and acceptance of benchmark problems generated with the algorithm would enable researchers working on simulation and optimization of manufacturing problems to effectively communicate results to benefit the field in general.

Continuous finite-time state feedback stabilizers for some nonlinear stochastic systems

This paper is concerned with the problem of finite-time stabilization for some nonlinear stochastic systems. Based on the stochastic Lyapunov theorem on finite-time stability that has been established by the authors in the paper, it is proven that Euler-type stochastic nonlinear systems can be finite-time stabilized via a family of continuous feedback controllers. Using the technique of adding a power integrator, a continuous, global state feedback controller is constructed to stabilize in finite time a large class of two-dimensional lower-triangular stochastic nonlinear systems. Also, for a class of three-dimensional lower-triangular stochastic nonlinear systems, a recursive design scheme of finite-time stabilization is given by developing the technique of adding a power integrator and constructing a continuous feedback controller. Finally, a simulation example is given to illustrate the theoretical results. © 2014 John Wiley & Sons, Ltd.

Global finite-time stabilisation for a class of stochastic nonlinear systems by output feedback

In this paper, the problem of global finite-time stabilisation by output feedback is considered for a class of stochastic nonlinear systems. First, based on homogeneous systems theory and the adding a power integrator technique, a homogeneous reduced order observer and control law are constructed in a recursive manner for the nominal system. Then, the homogeneous domination approach is used to deal with the nonlinearities in drift and diffusion terms; it is shown that the proposed output-feedback control law can guarantee that the closed-loop system is global finite-time stable in probability. Finally, simulation examples are carried out to demonstrate the effectiveness of the proposed control scheme.

Sparse adaptive multi-hyperplane machine

The Adaptive Multiple-hyperplane Machine (AMM) was recently proposed to deal with large-scale datasets. However, it has no principle to tune the complexity and sparsity levels of the solution. Addressing the sparsity is important to improve learning generalization, prediction accuracy and computational speedup. In this paper, we employ the max-margin principle and sparse approach to propose a new Sparse AMM (SAMM). We solve the new optimization objective function with stochastic gradient descent (SGD). Besides inheriting the good features of SGD-based learning method and the original AMM, our proposed Sparse AMM provides machinery and flexibility to tune the complexity and sparsity of the solution, making it possible to avoid overfitting and underfitting. We validate our approach on several large benchmark datasets. We show that with the ability to control sparsity, the proposed Sparse AMM yields superior classification accuracy to the original AMM while simultaneously achieving computational speedup.