## 1 Introduction
proposed a DIRECT-type global optimization algorithm to accelerate the search process for expensive black-box global optimization problems [19]. Furthermore, structural optimization problems are also CESOP. Structural optimization problems are characterized by various objective functions and constraints, which are generally non-linear functions of the design variables. Optimization of complex structures using traditional optimization approaches is known to be computationally expensive, because a very large number of finite element analysis must be conducted for each possible structural design during the optimization [20]. [PERSON] et al. presented successful applications of metaheuristics in structural optimization [21]. [PERSON] et al. reviewed the multi-objective metaheuristics for structural optimization of the topology, shape, and sizing of civil engineering structures [22]. [PERSON] et al. reviewed feature-mapping methods for implementing and solving structural optimization problems [23]. However, the huge solution space makes the CESOP hard to solve by existing optimization approaches to find quasi-optimal solutions within a reasonable period of time. To solve items (i) to (iii) simultaneously, an ordinal optimization (OO) theory [24] has been developed as an efficient framework for simulation optimization. The core concept of OO is that the relative order in the performance of designs is robust to estimated noise. The goal of the OO theory is to accelerate the simulation optimization procedure by gradually narrowing down the solution space. The OO theory consists of three stages. First of all, a representative subset is constructed using a rough model to evaluate all designs. A rough model can quickly estimate the performance of a design. OO theory indicates that order of performances of all designs is preserved even using a rough model [24]. Secondly, a selected subset containing N designs is chosen from the representative subset. Even if a rough model is utilized to rank N designs, some excellent designs will be kept within the selected subset with a high probability. Finally, critical designs in the selected subset are evaluated by an exact model. An exact model can accurately evaluate the performance of a design. The one with the optimum performance in the selected subset is the good enough design. We have successfully applied OO framework for simulation optimization problems, such as one-period multi-skill call center [25], pull-type production system [26], and facility-sizing optimization in factory [27]. For reducing the computing time of CESOP, a heuristic algorithm integrating ordinal optimization with ant lion optimization, abbreviated as OALO, is proposed to find a quasi-optimal design within an acceptable computing time. The OALO algorithm comprises three parts: approximation model, global exploration and local exploitation. Firstly, the multivariate adaptive regression splines (MARS) [28; 29] is adopted as an approximation model to evaluate the fitness of a design. Next, we proceed with a reformed ant lion optimization (RALO) to look for \(N\) exceptional designs from the solution space. Finally, a ranking and selection (R&S) procedure is utilized to decide a quasi-optimal design from the \(N\) exceptional designs. The above three parts substantially decrease the computation time which is required for solving CESOP. Subsequently, the OALO method is employed to minimize the operating cost of routing percentages in a communication system. The goal of queuing design optimization in a communication system is to look for the optimal routing percentages such that the expected total cost is minimal. The queuing design optimization in a communication system can be formulated as a CESOP. There are two contributions of this paper. The first one is to propose an OALO algorithm for CESOP to find a quasi-optimal design in an acceptable time. The second one is to apply the OALO algorithm to the queuing design optimization in a communication system. The paper is organized as follows.