Hybrid stochastic algorithm

Salis and Kaznessis proposed a hybrid stochastic algorithm that is based on a dynamical partitioning of the set of reactions into fast and slow subsets. The fast subset is treated as a continuous Markov process governed by a multidimensional Fokker-Planck equation, while the slow subset is considered to be a jump or discrete Markov process governed by a CME. The approximation of fast/continuous reactions as a continuous Markov process significantly reduces the computational intensity and introduces a marginal error when compared to the exact jump Markov simulation. This idea becomes very useful in systems where reactions with multiple reaction scales are constantly present. 

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The mathematical model of two-stage stochastic mixed-integer linear optimization problems was discussed as well as state-of-the-art solution algorithms. A new hybrid evolutionary algorithm for solving this class of optimization problems was presented. The new algorithm exploits the specific problem structure by stage decomposition. 

In the third part, we design a hybrid intelligent algorithm to solve the model by combining stochastic simulation and genetic algorithm. 

Next we will design a hybrid intelligent algorithm based on stochastic simulation to solve this model. 

Process of Hybrid Genetic Algorithm Based on Stochastic Simulation... 

The termination condition is determined by the max number of generation max gen. If timplement Step 3-Step 6 during the process of hybrid genetic algorithm based on stochastic simulation (in Sect. 5.3.3). 

In order to further test the validity of the algorithm and the stochastic chance-constrained programming model, we start the simulation process by taking different values of parameters of the hybrid intelligent algorithm. 

In the hybrid intelligent algorithm, confidence level = 0.9, population size N = 90, crossover probability = 0.7, mutation probability p = 0.5, iteration times = 30,000, in the rank-based evaluation function a = 0.05, and the stochastic simulation times are 6000. Figure 5.8 shows the convergence process of the objective function. Table 5.9 illustrates the objective function value of core enterprise in each supply chain cell and the total profit of the supply chain within the computational layer. 

Then we simulate the uncertain function U X (Ui(X), UziX)) to get the input and output data by fuzzy stochastic simulation Third, we approach the uncertain function U(X) using three-layer feedforward neural networks Finally, we embed the well trained neural network into the generic algorithms to get the hybrid intelligent algorithm. The details are to be discussed as follows. 

In Hybrid Intelligent Algorithm, population size N = 70, crossover probability Pc = 0.5, mutation probability pm = 0.6, iteration times Gmax = 10,000, number of times for fuzzy stochastic simulation is 6000, with 3000 training samples. Figure 6.10 illustrates the convergence process of the objective function. 

Hy3S, or Hybrid Stochastic Simulation for Supercomputers, is an open sourced software package written for the development, dissemination, and productive use of hybrid stochastic simulation methods. The goal of the software is to allow users to utihze the hybrid stochastic simulation algorithms described in the previous section and to simulate large, realistic stochastic systems. 

The hybrid algorithm is in general suitable for any two-stage stochastic mixed-integer linear program with integer requirements in the first-stage and in the... 

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