Optimization Algorithms Based On Fuzzy Sets And Markov Chain

In real life, there are a lot of uncertainties in optimization problems and two of them are fuzzy and stochastic factors. How to design effective optimization algorithms to solve these problems with uncertainties become the focus of the study, especially, with the development of computer science, how to design a discrete model to make it more suitable for computation is becoming a new concern gradually. In this paper, with backgrounds of time-cost tradeoff problems in project management, portfolio optimization problems in financial engineering and signal optimization problems in urban traffic network management, several optimization algorithms are proposed based on fuzzy sets and Markov chain model and application examples are analyzed for each part.The main contents of the paper go as follows:1. With background of time-cost tradeoff problems in project management, a new model is proposed based on the trapezoidal fuzzy set. Meanwhile, penalty factors for overruns of project time and cost are introduced in the model to enhance the optimization performance. To improve the efficiency of computation, multi-objective genetic algorithm is used because of its feature of parallel calculation. On the other hand, the crossover and mutation operation of the original algorithm are also improved to make the computation more efficient.2. With background of portfolio optimization problems in financial engineering, a new model is proposed based on the Markov chain. Due to the concept of state feedback and rolling optimization, the original complex on-line optimization problem is transformed into an off-line one which is easier to solve and the optimal performance is ensured at the same time. Finally, the stochastic optimization algorithms based on policy iteration is used and one application example is given to prove the efficiency of the approach.3. With background of signal optimization problems in urban traffic management, a new model is proposed based on the Markov chain. And KS test is introduced to confirm the Markov feature of the original problem. Because of the usage of CORSIM and policy iteration-based stochastic optimization algorithm, the original complex on-line optimization problem is transferred into an easier off-line one that expanding the applicability of the model and the optimization algorithm. Finally, one application example is given to prove the efficiency of the approach.