## 1 Introduction  
The probabilistic constrained simulation optimization problems (PCSOP) are concerned with allocating limited resources to achieve a stochastic objective function subject to a probabilistic inequality constraint. The performance of the PCSOP is evaluated by simulations, which may be a complex evaluation in a real-world physical system or a simple computer based mathematical model [1]. Such problems occur in almost all fields of automatic production, such as the network type flow line production system, buffer resource allocation, periodic review inventory system, as well as many industrial managements, including facility-sizing of factory and strategic location of semi-finished products in a pull-type production system. The goal of PCSOP is to search for the optimal design variables to reach desired performance subject to a probabilistic inequality constraint. The PCSOP belong to the class of NP-hard problems [2] for which most likely no polynomial time optimization method exists. In practice, the large search space makes the considered problem more difficult to determine an optimal design variable using classical optimization techniques in a short computational time. There are many methods proved to be interesting in solving the NP-hard problems, such as the evolutionary algorithms (EA) [3], gradient search methods [4], heuristic methods [5], and swarm intelligence (SI) [6]. EA [3] are stochastic optimization approaches based on the biological evolution metaphor, which utilize the \"survival of the fittest\" to produce successively superior approximations to a design variable. Three main types of EA have been developed: evolution strategies (ES), evolutionary programming (EP), and genetic algorithms (GA). However, EA are usually computationally intensive and do not offer an absolute guarantee of the global optimality. The gradient search methods [4], such as conjugated gradient and steepest descent method, tends to converge very slowly and can easily get trapped in local minimum. The heuristic methods [5], such as Tabu search (TS) and simulated annealing (SA), have the capability of finding global optimal solution. However, the quality of optimal solution is highly dependent on fine-tuning of parameters. SI [6] is an emerging field of biologically-inspired artificial intelligence based on the behavioral models of social insects such as colonies of ants, bees, schools of fish and flocks of birds. Some of the recent established SI methods include elephant herding optimization (EHO), bacteria foraging optimization (BFO), social spider optimization (SSO), crow search algorithm (CSA), bat algorithm (BA) and tree-seed algorithm (TSA) [7]. Most SI methods require only objective values and accomplish a proper balance between exploration and exploitation. However, there are still a number of significant barriers and technical hurdles to overcome [8]. The following three issues make the PCSOP difficult to solve: (i) the search space is large; (ii) evaluating performance is time-consuming; and (iii) single probabilistic inequality constraint must be satisfied. The purpose of this paper is to resolve the PCSOP efficiently and effectively. To overcome the three issues simultaneously, an ordinal optimization (OO) theory [9] attempts to quickly determine a good enough solution. OO is used to supplement available optimization methods, but is not itself an optimization approach. OO theory considers order rather than value to reduce the computational complexity of optimization process, and guarantees a high probability that the obtained solution is good enough. In the OO theory, the first step is to create a selected subset by rapidly evaluating all solutions using a rough evaluation. A rough evaluation estimates performance with high tolerance of modeling noise. OO theory indicates that the order of solutions is nearly kept even though they are assessed by a rough evaluation [9]. Next, an outstanding subset is constructed from the selected subset.