Automated Response Surface Methodology for Stochastic Optimization Models with Unknown Variance

Response Surface Methodology (RSM) is a tool that was introduced in the early 50´s by Box and Wilson (1951). It is a collection of mathematical and statistical techniques useful for the approximation and optimization of stochastic models. Applications of RSM can be found in e.g. chemical, engineering and clinical sciences. In this paper we are interested in finding the best settings for an automated RSM procedure when there is very little information about the stochastic objective function. We will present a framework of the RSM procedures for finding optimal solutions in the presence of noise. We emphasize the use of both stopping rules and restart procedures. Good stopping rules recognize when no further improvement is being made. Restarts are used to escape from non-optimal regions of the domain. We compare different versions of the RSM algorithms on a number of test functions, including a simulation model for cancer screening. The results show that co! nsiderable improvement is possible over the proposed settings in the existing literature

Automated Response Surface Methodology for Stochastic Optimization Models with Unknown Variance

Response Surface Methodology (RSM) is a tool that was introduced in the early 50´s by Box and Wilson (1951). It is a collection of mathematical and statistical techniques useful for the approximation and optimization of stochastic models. Applications of RSM can be found in e.g. chemical, engineering and clinical sciences. In this paper we are interested in finding the best settings for an automated RSM procedure when there is very little information about the stochastic objective function. We will present a framework of the RSM procedures for finding optimal solutions in the presence of noise. We emphasize the use of both stopping rules and restart procedures. Good stopping rules recognize when no further improvement is being made. Restarts are used to escape from non-optimal regions of the domain. We compare different versions of the RSM algorithms on a number of test functions, including a simulation model for cancer screening. The results show that co! nsiderable improvement is possible over the proposed settings in the existing literature.response surface methodology;simulation optimization

Determination of vehicle requirements of AGV system based on discrete event simulation and response surface methodology

The determination of AGV vehicle requirements in a manufacturing system has a great impact on the system performance. This paper first defines the AGV vehicle requirement determination as a general optimization problem, and secondly develops a new AGV vehicle requirement determination method capable of effective solving the problem. This method features with the combination of discrete event simulation (DES), sensitivity analysis, fractional factorial design (FFD) and response surface methodology (RSM). Tests and comparisons with other simulation based methods have shown that the proposed method combining the simulation method with analytical method, can make full use of their respective advantages and overcome the defects of existing methods. It is more practical

Determination of Cap Model Parameters using Numerical Optimization Method for Powder Compaction

Many advantages are inherent to the successful powder metallurgy (P/M) process especially in high volume manufacturing. The strength/density distribution of the compacted product is crucial to overall success. The finite element analysis (FEA) method has become an effective way to numerically simulate strength/density distribution in a P/M compact. The modified Drucker-Prager cap (DPC) model has been shown to be a suitable constitutive relationship for metal powder compaction simulation. The calibration of the modified DPC model involves a procedure known as a triaxial compression test. Equipment for completing a triaxial compression test on metal powders is neither readily available nor standardized in the P/M industry. A robust calibration procedure that requires only simple experimental tests would increase the usability of the simulation procedure. This research created a universal cost/time-effective calibration method to accurately determine all parameters of a modified DPC model by using a combination of numerical simulation methods, numerical optimization methods and common material testing techniques. The use of the triaxial compression test is eliminated and the new method relies only upon conventional compaction equipment, standard geometry and readily available metallographic techniques. The DPC parameters were determined by applying the proposed method on ferrous powders. The predicted DPC parameters were verified on a compressed product with complex geometry

Automated Response Surface Methodology for Stochastic Optimization Models with Unknown Variance

textabstractResponse Surface Methodology (RSM) is a tool that was introduced in the early 50´s by Box and Wilson (1951). It is a collection of mathematical and statistical techniques useful for the approximation and optimization of stochastic models. Applications of RSM can be found in e.g. chemical, engineering and clinical sciences. In this paper we are interested in finding the best settings for an automated RSM procedure when there is very little information about the stochastic objective function. We will present a framework of the RSM procedures for finding optimal solutions in the presence of noise. We emphasize the use of both stopping rules and restart procedures. Good stopping rules recognize when no further improvement is being made. Restarts are used to escape from non-optimal regions of the domain. We compare different versions of the RSM algorithms on a number of test functions, including a simulation model for cancer screening. The results show that co! nsiderable improvement is possible over the proposed settings in the existing literature

Automated response surface methodology for stochastic optimization models with unknown variance

Response Surface Methodology (RSM) is an optimization tool that was introduced in the early 50's by Box and Wilson (1951). In this paper we are interested in finding the best settings for an automated RSM procedure when there is very little information about the objective function. We will present a framework of the RSM procedures that is founded in recognizing local optima in the presence of noise. We emphasize both stopping rules and restart procedures. The results show that considerable improvement is possible over the proposed settings in the existing literature

Continuous optimization via simulation using Golden Region search

Simulation Optimization (SO) is the use of mathematical optimization techniques in which the objective function (and/or constraints) could only be numerically evaluated through simulation. Many of the proposed SO methods in the literature are rooted in or originally developed for deterministic optimization problems with available objective function. We argue that since evaluating the objective function in SO requires a simulation run which is more computationally costly than evaluating an available closed form function, SO methods should be more conservative and careful in proposing new candidate solutions for objective function evaluation. Based on this principle, a new SO approach called Golden Region (GR) search is developed for continuous problems. GR divides the feasible region into a number of (sub) regions and selects one region in each iteration for further search based on the quality and distribution of simulated points in the feasible region and the result of scanning the response surface through a metamodel. The experiments show the GR method is efficient compared to three well-established approaches in the literature. We also prove the convergence in probability to global optimum for a large class of random search methods in general and GR in particular

Automated Response Surface Methodology for Stochastic Optimization Models with Unknown Variance

Response Surface Methodology (RSM) is a tool that was introduced in the early 50's by Box and Wilson (1951). It is a collection of mathematical and statistical techniques useful for the approximation and optimization of stochastic models. Applications of RSM can be found in e.g. chemical, engineering and clinical sciences. In this paper we are interested in finding the best settings for an automated RSM procedure when there is very little information about the stochastic objective function. We will present a framework of the RSM procedures for finding optimal solutions in the presence of noise. We emphasize the use of both stopping rules and restart procedures. Good stopping rules recognize when no further improvement is being made. Restarts are used to escape from non-optimal regions of the domain. We compare different versions of the RSM algorithms on a number of test functions, including a simulation model for cancer screening. The results show that co! nsiderable improvement is possible over the proposed settings in the existing literature.Response Surface Methodology; Simulation Optimization