This paper deals with solution methods for discrete and multi-valued optimization problems. The objective function of the problem incorporates noise effects generated in case that fitness evaluation is accomplished by computer based experiments such as Monte Carlo simulation or discrete event simulation. Meta heuristics including Genetic Algorithm (GA) and Discrete Particle Swarm Optimization (DPSO) can be used to solve these simulation based multi-valued optimization problems. In applying these population based meta heuristics to simulation based optimization problem, samples size to estimate the expected fitness value of a solution and population (particle) size in a generation (step) should be carefully determined to obtain reliable solutions. Under realistic environment with restriction on available computation time, there exists trade-off between these values. In this paper, the effects of sample and population sizes are analyzed under well-known multi-modal and multi-dimensional test functions with randomly generated noise effects. From the experimental results, it is shown that the performance of DPSO is superior to that of GA. While appropriate determination of population sizes is more important than sample size in GA, appropriate determination of sample size is more important than particle size in DPSO. Especially in DPSO, the solution quality under increasing sample sizes with steps is inferior to constant or decreasing sample sizes with steps. Furthermore, the performance of DPSO is improved when OCBA (Optimal Computing Budget Allocation) is incorporated in selecting the best particle in each step. In applying OCBA in DPSO, smaller value of incremental sample size is preferred to obtain better solutions

The purpose of this paper was to apply and express to a particle production system based on mathematical models to raise a cloud of spray. It was used that a crash was used to conflict expanding wave generation model and applying the block cover. Also, we applied to the KD-tree in order to reduce trial search. The block cover was created with the creation on the phase of height values. The waves and wind made by character's emotions, which input use as the value. Reached a certain level in both cases, waves and waves are generated a cloud of spray by the collision. The repetition of generated waver was applied with the Windows function. Handling conflict is affected in a cloud of spray. Generated KD-Tree renewal grid is beyond the range in block cover and is not a uniform height. It is built that the processing of collision is not performed by the level on height of a wave. This process was designed by the best statistical analysis after reviewing sufficient factual nature. This paper is applied with a cloud of splay for emotional online games like game that tried to apply the spray can apply for the environment. If you use a physically-based model requires a lot of calculation time, the physically-based models ask a lot of complicated calculation time for solver this program and high-performance systems. However, a block-cover can be role of a very effective way for enough performance. Through the analysis result can be obtained a sufficient result in easy implementation of the cloud of spray

For precise property control of sintered products, it is important to understand accurately the packing density of the powder. We developed a packing simulation program that could make a packed bed of spherical particles having particle size distribution. In addition, the influence of the particle shape of the actual powder on the packing density was quantitatively analyzed. The predicted packing densities corresponded well to the actual data.