روش واژه نگاری بهینه سازی شبیه سازی "نلدر مید" برای حل مسائل چند معیاره

Simulation optimization is an approach that is used to solve problems involving stochastic components. This paper presents a Lexicographic Nelder–Mead (LNM) based simulation optimization (LNM-SO) method to solve multi-criteria simulation optimization problems. The method is designed to be relatively easy-to-implement and be applicable to a wide range of problem domains. To effectively evaluate the overall performance of this method, a Time-Quality Estimator (TQE) was developed to evaluate the performance of LNM-SO in terms of both quality of solution and computational speed. Computational results of five different test problems showed that the method was highly effective.

Real-world problems frequently involve variables that exhibit some form of random behavior. Traditional optimization techniques often cannot adequately solve these problems. One approach to solve problems that involve stochastic coefficients in optimization components is by incorporating a simulation model within the optimization tool. The simulation model is used to address this stochastic nature of the system and to find feasible and representative values for the coefficients of the model, while optimization is used to find an optimal or near-optimal solution. This process is referred to as simulation optimization. For problems where multiple and usually conflicting objectives are to be optimized, the process is referred to as multi-criteria simulation optimization. Simulation optimization essentially combines simulation with an optimization technique or heuristic to determine the combination of input parameters that produces a near-optimal solution for one or more output measures. The optimization problem can involve stochastic responses in the objective function coefficients, the constraint coefficients, or both. Typical examples of stochastic responses include arrival rates, customer demand rates and quantities, time between failures, lead times, and throughput rates. This research proposes a Lexicographic Nelder–Mead (LNM) method (Kuriger & Ravindran, 2005) based simulation optimization method to solve multi-criteria simulation optimization problems. This method was developed by adapting and extending the LNM method to incorporate simulation and goal programming. The proposed methodology has been applied to solve five different test problems, representing five different problem domains and the results were compared to the solutions obtained from two competing simulation optimization methods. The main objectives of this research were to: • Develop a simulation optimization method based on the LNM optimization technique to solve multi-criteria problems involving stochastic components. • Validate the effectiveness and applicability of the proposed LNM simulation optimization (LNM-SO) methodology by ensuring a high quality solution can be obtained as fast as possible for a wide range of problems. • Identify a performance measure that can be used to simultaneously evaluate the quality of solution and the computational speed. • Establish a series of test problems to evaluate the effectiveness of LNM-SO. The following sections describe the techniques, methodology, and results of the computational analysis of the LNM-SO method. Section 2 provides a review of the related literature and a description of the underlying problem. Section 3 develops the mathematical models used in the problem and presents the methodology that was used to implement the research. Section 4 provides an overview of the LNM-SO method developed in this research. Section 5 details the proposed performance evaluation criteria, the comparison methods, and the test problems. Section 6 presents the results of the computational analysis. Finally, Section 7 presents the general conclusions that can be drawn from this research and offers recommendations for further research

In this paper, a Lexicographic Nelder–Mead (LNM) based simulation optimization (LNM-SO) method was created to solve multi-criteria simulation optimization problems. The method is relatively easy-to-implement and is applicable to a wide range of problem domains. The efficacy of the method was demonstrated by evaluating its performance over five test problems, representing five different domains, against two other simulation optimization methods. The overall performance of each method was evaluated using TQE, which considers both the quality of solution and the computational speed. Three levels of decision-makers were considered: time-quality neutral, time sensitive, and quality sensitive. The experimental results for the problems examined showed that if the decision-maker was only interested in the quality of solution, then GA-SO would likely be the best method. If however, the decision-maker was interested in some combination of speed and quality, then LNM-SO clearly proved to be the superior method. In fact, LNM-SO had the best overall performance (TQE score) for 14 out of the 15 possible cases. One limitation of this work is that all of the test problems examined were of limited size and complexity. This was primarily due to computational and time restrictions. In order to determine the true effectiveness of LNM-SO, future research should examine larger and more complicated test problems. Additionally, a method of determining the speed and quality weights used to calculate TQE needs to be developed. Additional work could also involve examining the effects of re-ranking a problem’s goals and changing the target values. These additional areas of research could provide a more complete and potentially a more accurate picture of the effectiveness and the nature of the LNM-SO method.