Genetic Algorithm for Scheduling Problem of Chemical Batch Process with Due Date Constraints

The intense competition in the current marketplace ha s forced firms to reexamine their methods of doing business, using superior manu facturing practices in the form of just-in-time (JIT), production with JIT pra ctices pursue completion on time and zero inventory, which is often instruct ed according to the custom’s demand or the sale contract. Earliness and tardine ss are undesirable because both of them will bring the extra cost, cost will als o be increased by some factors such as operation condition, intermediate storage , clean method, etc, to minimize the total cost is often the main scheduling objective, but sometime it is most important for factories to eliminate the tar diness cost in order to maintain the commercial credit and to avoid penalty, the refore, minimum of tardiness cost becomes the first objective. It is more import ant to select a reasonable objective by the actual condition during scheduli ng. In this paper scheduling problem of chemical batch process with due date is studied, two different intermediate storage policies and two different productio n modes are also discussed, production scheduling with different intermediate st orage policy and different production mode is proposed and the result is compare d. In order to complete all products within the due date, not only earliness and tardiness but also holding problem is considered, the objective is to selec t a proper intermediate storage policy and production mode and to minimize the c ost resulted by the earliness and tardiness, even the cost result by the interme diate storage. Scheduling with multiple stage and multiple machine is known as a NP-hard problem, mathematical program (MP) method, such as branch-and-bound (BAB), mixed integer linear program (MILP), etc, is often used to solve the sche duling problem. But as is well known, MP method is not good for combination opti mization, especially for large scale and complex optimal problem, whereas geneti c algorithm (GA) can overcome the MP method’s shortcoming and is fit for solvin g such scheduling problem. In this paper a modified genetic algorithm with speci al crossover operator and mutation operator is presented to solve this schedulin g problem. The results show such problem can be solved effectively with the pres ented method.

An intelligent method to design laser resonator with particle swarm optimization algorithm

In order to design a complex laser resonator with multi-parameters, the method of particle swarm optimization(PSO) algorithm is employed. The parameters influencing the resonator stability and mode size distribution are taken into consideration, and the stability criteria index and the mode size distribution are used as target values. The absolute values of the differences between practical and the target values are set as the fitness function for the PSO. By minimizing the fitness function, a laser resonator with the optimized cavity parameters can be found. The analyses for the design example demonstrate the feasibility and validity of the PSO method in the computer aided design of multi-parameters laser resonator. Applying PSO algorithm in the intelligent design of solid state laser resonators can realize the transition from manual trial-and-error to computer intelligent design of the laser resonators.

Optimal stopping time on discounted semi-Markov processes

This paper attempts to study the optimal stopping time for semi- Markov processes (SMPs) under the discount optimization criteria with unbounded cost rates. In our work, we introduce an explicit construction of the equivalent semi-Markov decision processes (SMDPs). The equivalence is embodied in the expected discounted cost functions of SMPs and SMDPs, that is, every stopping time of SMPs can induce a policy of SMDPs such that the value functions are equal, and vice versa. The existence of the optimal stopping time of SMPs is proved by this equivalence relation. Next, we give the optimality equation of the value function and develop an effective iterative algorithm for computing it. Moreover, we show that the optimal and ε-optimal stopping time can be characterized by the hitting time of the special sets. Finally, to illustrate the validity of our results, an example of a maintenance system is presented in the end.